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Interest in gene drive technology has continued to grow as promising new drive systems have been developed in the lab and discussions are moving towards implementing field trials. The prospect of field trials requires models that incorporate a significant degree of ecological detail, including parameters that change over time in response to environmental data such as temperature and rainfall, leading to seasonal patterns in mosquito population density. Epidemiological outcomes are also of growing importance, as: i) the suitability of a gene drive construct for release will depend on its expected impact on disease transmission, and ii) initial field trials are expected to have a measured entomological outcome and a modeled epidemiological outcome. We present MGDrivE 2 (Mosquito Gene Drive Explorer 2): a significant development from the MGDrivE 1 simulation framework that investigates the population dynamics of a variety of gene drive architectures and their spread through spatially-explicit mosquito populations. Key strengths and fundamental improvements of the MGDrivE 2 framework are: i) the ability of parameters to vary with time and induce seasonal population dynamics, ii) an epidemiological module accommodating reciprocal pathogen transmission between humans and mosquitoes, and iii) an implementation framework based on stochastic Petri nets that enables efficient model formulation and flexible implementation. Example MGDrivE 2 simulations are presented to demonstrate the application of the framework to a CRISPR-based split gene drive system intended to drive a disease-refractory gene into a population in a confinable and reversible manner, incorporating time-varying temperature and rainfall data. The simulations also evaluate impact on human disease incidence and prevalence. Further documentation and use examples are provided in vignettes at the project's CRAN repository. MGDrivE 2 is freely available as an open-source R package on CRAN (https://CRAN.R-project.org/package=MGDrivE2). We intend the package to provide a flexible tool capable of modeling gene drive constructs as they move closer to field application and to infer their expected impact on disease transmission.
Example MGDrivE 2 simulations for a split gene drive system designed to drive a malaria-refractory gene in a confinable and reversible manner into an An. gambiae s.l. mosquito population with seasonal population dynamics and transmission intensity calibrated to a setting resembling the island of Grand Comore, Union of the Comoros. The split drive system resembles one recently engineered in Ae. aegypti [2]-the only split drive system in a mosquito vector to date. In the modeled system, two components-the Cas9 and guide RNA (gRNA)-are present at separate, unlinked loci, and a disease-refractory gene is linked to the gRNA. Four alleles are considered at the gRNA locus: an intact gRNA/refractory allele (denoted by "H"), a wild-type allele (denoted by "W"), a functional, cost-free resistant allele (denoted by "R"), and a non-functional or otherwise costly resistant allele (denoted by "B"). At the Cas9 locus, two alleles are considered: an intact Cas9 allele (denoted by "C"), and a wild-type allele (denoted by "W"). Model parameters describing the construct, mosquito bionomics and malaria transmission are summarized in S1 Table. (A) Climatological time-series data-temperature in red and rainfall in blue-that were used to calculate time-varying adult mosquito mortality rate and larval carrying capacity, respectively. The resulting adult female population size is shown in green. (B) Allele frequencies for adult female mosquitoes over the simulation period. Grey vertical bars beginning at year three denote eight consecutive weekly releases of 50,000 male mosquitoes homozygous for both the gRNA and Cas9 alleles (H and C, respectively). (C) Spread of the malaria-refractory trait through the female mosquito population, and consequences for mosquito and human infection status. Following releases of the drive system at year three, the proportion of refractory female mosquitoes (solid red line) increases and the proportion of infectious mosquitoes (dotted light blue line) declines. As humans recover from infection and less develop new infections, the P. falciparum parasite rate (solid green line) declines until it reaches near undetectable levels by year five. (D) Human malaria incidence is halted by the beginning of year four.
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RESEARCH ARTICLE
MGDrivE 2: A simulation framework for gene
drive systems incorporating seasonality and
epidemiological dynamics
Sean L. WuID
1
*, Jared B. BennettID
2
, He
´ctor M. Sa
´nchez C.ID
1
, Andrew J. DolgertID
3
,
Toma
´s M. Leo
´nID
1
, John M. MarshallID
1,4
*
1Divisions of Epidemiology and Biostatistics, School of Public Health, University of California, Berkeley,
California, United States of America, 2Biophysics Graduate Group, Division of Biological Sciences, College
of Letters and Science, University of California, Berkeley, California, United States of America, 3Institute for
Health Metrics and Evaluation, Seattle, Washington, United States of America, 4Innovative Genomics
Institute, Berkeley, California, United States of America
*slwu89@berkeley.edu (SLW); john.marshall@berkeley.edu (JMM)
Abstract
Interest in gene drive technology has continued to grow as promising new drive systems
have been developed in the lab and discussions are moving towards implementing field tri-
als. The prospect of field trials requires models that incorporate a significant degree of eco-
logical detail, including parameters that change over time in response to environmental data
such as temperature and rainfall, leading to seasonal patterns in mosquito population den-
sity. Epidemiological outcomes are also of growing importance, as: i) the suitability of a
gene drive construct for release will depend on its expected impact on disease transmission,
and ii) initial field trials are expected to have a measured entomological outcome and a mod-
eled epidemiological outcome. We present MGDrivE 2 (Mosquito Gene Drive Explorer 2): a
significant development from the MGDrivE 1 simulation framework that investigates the
population dynamics of a variety of gene drive architectures and their spread through spa-
tially-explicit mosquito populations. Key strengths and fundamental improvements of the
MGDrivE 2 framework are: i) the ability of parameters to vary with time and induce seasonal
population dynamics, ii) an epidemiological module accommodating reciprocal pathogen
transmission between humans and mosquitoes, and iii) an implementation framework
based on stochastic Petri nets that enables efficient model formulation and flexible imple-
mentation. Example MGDrivE 2 simulations are presented to demonstrate the application of
the framework to a CRISPR-based split gene drive system intended to drive a disease-
refractory gene into a population in a confinable and reversible manner, incorporating time-
varying temperature and rainfall data. The simulations also evaluate impact on human dis-
ease incidence and prevalence. Further documentation and use examples are provided in
vignettes at the project’s CRAN repository. MGDrivE 2 is freely available as an open-source
R package on CRAN (https://CRAN.R-project.org/package=MGDrivE2). We intend the
package to provide a flexible tool capable of modeling gene drive constructs as they move
closer to field application and to infer their expected impact on disease transmission.
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009030 May 21, 2021 1 / 17
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OPEN ACCESS
Citation: Wu SL, Bennett JB, Sa
´nchez C. HM,
Dolgert AJ, Leo
´n TM, Marshall JM (2021) MGDrivE
2: A simulation framework for gene drive systems
incorporating seasonality and epidemiological
dynamics. PLoS Comput Biol 17(5): e1009030.
https://doi.org/10.1371/journal.pcbi.1009030
Editor: Manja Marz, bioinformatics, GERMANY
Received: November 2, 2020
Accepted: May 2, 2021
Published: May 21, 2021
Copyright: ©2021 Wu et al. This is an open access
article distributed under the terms of the Creative
Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in
any medium, provided the original author and
source are credited.
Data Availability Statement: MGDrivE 2 is
available at https://CRAN.R-project.org/package=
MGDrivE2. The source code is under the GPL3
License and is free for other groups to modify and
extend as needed. Documentation for all MGDrivE
2 functions, including vignettes, are available at the
project’s website at https://marshalllab.github.io/
MGDrivE/docs_v2/index.html.
Funding: SLW, JBB, HMSC, TML and JMM were
supported by a DARPA Safe Genes Program Grant
(HR0011-17-2-0047) awarded to JMM. HMSC,
TML and JMM were supported by funds from the
Author summary
Malaria, dengue and other mosquito-borne diseases continue to pose a major global
health burden through much of the world. Currently available tools, such as insecticides
and antimalarial drugs, are not expected to be sufficient to eliminate these diseases from
highly-endemic areas, hence there is interest in novel strategies including genetics-based
approaches. In recent years, the advent of CRISPR-based gene-editing has greatly
expanded the range of genetic control tools available, and MGDrivE 1 (Mosquito Gene
Drive Explorer 1) was proposed to simulate the dynamics of these systems through spa-
tially-structured mosquito populations. As the technology has advanced and potential
field trials are being discussed, models are now needed that incorporate additional details,
such as life history parameters that respond to daily and seasonal environmental fluctua-
tions, and transmission of pathogens between mosquito and vertebrate hosts. Here, we
present MGDrivE 2, a gene drive simulation framework that significantly improves upon
MGDrivE 1 by addressing these modeling needs. MGDrivE 2 has also been reformulated
as a stochastic Petri net, enabling model specification to be decoupled from simulation,
making it easier to adapt the model for application to other insect and mammalian
species.
This is a PLOS Computational Biology Software paper.
1. Introduction
Interest in gene drive technology has continued to grow in recent years as a range of promising
new constructs have been developed in the lab and discussions have moved towards imple-
menting field trials in some cases. Recently developed systems include a CRISPR-based hom-
ing system intended for population suppression targeting the doublesex gene in Anopheles
gambiae, the main African malaria vector [1], a split gene drive system intended for confine-
able and transient population replacement in Aedes aegypti, the main vector of dengue, chi-
kungunya and Zika viruses [2], and CRISPR-based homing systems intended for population
replacement in An.gambiae [3] and Anopheles stephensi, the main malaria vector in urban
India [4].
As the technology advances and potential field trials are discussed [5], models are needed
that incorporate additional ecological detail, including parameters that change over time in
response to environmental variables such as temperature and rainfall, as well as models linking
entomological and epidemiological outcomes [6]. Many insects, including mosquitoes, display
a high degree of seasonality in their population dynamics, as development time from one life
stage to another, and mortality rates associated with each life stage, vary with temperature and
other environmental variables [7]. For An.gambiae and several other mosquito disease vectors,
population size varies largely in response to recent rainfall, which creates pools of standing
water and hence enhanced carrying capacity of the environment for mosquito larvae [8]. Sea-
sonal changes in temperature and rainfall thus lead to seasonal changes in mosquito popula-
tion density and consequent disease transmission, which must be accounted for in disease
control strategies.
Models of disease transmission are also becoming increasingly relevant to models of gene
drive dynamics, as: i) the readiness of a gene drive system for field trials will be determined in
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MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
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UC Irvine Malaria Initiative. JMM was supported by
an award from the Innovative Genomics Institute.
The funders had no role in the study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.
part by its expected (i.e. modeled) epidemiological impact, and ii) initial field trials are
expected to have a measured entomological outcome alongside a modeled epidemiological
outcome [5]. Given the potential for a non-localized gene drive system to spread broadly, it
has been acknowledged that such constructs at the trial stage should be expected to cause a sig-
nificant reduction in disease transmission, as even a confined trial could lead to wide-scale
spread for an effective system [5]. Therefore, readiness for field trials should be determined by
alignment with a target product profile (TPP) and/or list of preferred product characteristics
(PPCs) that include expected impact on disease transmission [6]. Models that incorporate
both gene drive and epidemiological dynamics can account for local malaria or arboviral trans-
mission dynamics and specify gene drive construct parameters that achieve the desired level of
epidemiological control.
Previously, we developed the MGDrivE 1 modeling framework to model the population
dynamics of a variety of genetics-based and biological control systems and their spread
through spatially-explicit populations of mosquitoes, or insects having a similar life history
[9]. Here, we present MGDrivE 2, which significantly improves upon the capabilities of
MGDrivE 1 by addressing the above-mentioned considerations, namely: i) the ability of
parameter values to change over time, and hence to model seasonal population dynamics,
and ii) the incorporation of an epidemiology module that can accommodate pathogen
transmission between humans and mosquitoes. Minor additional improvements have been
made to the inheritance, life history and landscape modules of the framework to reflect
advances in these fields; for instance, a more resolved understanding of maternal deposition
of Cas protein for CRISPR-based gene drive systems has been incorporated [10]. Models in
MGDrivE 2 are represented as a stochastic Petri net (SPN), which has both computational
and architectural benefits: model specification is separate from simulation, models can be
efficiently stored and updated in memory, and a wealth of fast simulation algorithms from
other fields can be used [11].
In this paper, we describe the key developments implemented in MGDrivE 2. We then
demonstrate the application of the framework to the disease control impact of a CRISPR-
based split gene drive system intended to drive a disease-refractory gene into a population in a
confinable and reversible manner, and conclude with a discussion of future needs and applica-
tions for simulation packages in the field of gene drive modeling.
2. Design and implementation
MGDrivE 2 is a significant extension of and development from MGDrivE 1, a model for the
spread of gene drive systems through spatially-explicit mosquito populations. The MGDrivE 2
model incorporates: i) an “inheritance module” that describes the distribution of offspring
genotypes for given maternal and paternal genotypes, ii) a “life history module” that describes
the development of mosquitoes from egg to larva to pupa to adult, iii) a “landscape module”
that describes the distribution and movement of mosquitoes through a metapopulation, and
iv) an “epidemiology module” that describes pathogen transmission between mosquitoes and
humans (Fig 1). The framework is formulated as a SPN that can be mapped to a continuous-
time Markov process in which model parameters may vary over time. It can also be imple-
mented as a deterministic model via mean-field approximation of the stochastic model [12].
The core framework is developed in R (https://www.r-project.org/). The SPN framework
enables separation of model components, allowing users to modify code on a component-by-
component basis as needed for model specification or computational speed. We now describe
the model extensions and developments from MGDrivE 1 to 2 in more detail. Full details of
the MGDrivE 2 model framework are provided in the S1 Text.
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MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
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2.1. Time-dependent parameters and seasonality
The incorporation of time-dependent parameters represents a significant improvement of the
MGDrivE 2 modeling framework. In MGDrivE 1, the mosquito life history module follows the
lumped age-class model of Hancock and Godfray as adapted by Deredec et al. [13], which
Fig 1. Modules in the MGDrivE 2 framework. (A) Genetic inheritance is embodied by a three-dimensional tensor referred to as an “inheritance cube.” Maternal and
paternal genotypes are depicted on the xand y-axes and offspring genotypes on the z-axis. (B) Mosquito life history is modeled according to an egg-larva-pupa-adult
(female and male) life cycle in which density dependence occurs at the larval stage, and life cycle parameters may vary as a function of environmental variables over
time. Genotypes are tracked across all life stages, and females obtain a composite genotype upon mating—their own and that of the male they mate with. Egg genotypes
are determined by the inheritance cube. (C) The landscape represents a metapopulation in which mosquitoes are distributed across population nodes and move
between them according to a dispersal kernel. Population sizes and movement rates may vary as a function of environmental variables. (D) The epidemiology module
describes reciprocal transmission of a vector-borne pathogen between mosquitoes and humans. This requires modeling human as well as mosquito populations, and
the number of individuals having each infectious state. Epidemiological parameters may vary as a function of environmental variables.
https://doi.org/10.1371/journal.pcbi.1009030.g001
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describes development from egg to larva to pupa to adult using delay-difference equations.
The delay framework allows development times to be modeled as fixed rather than exponen-
tially-distributed; however, it is not compatible with time-varying parameters as these could
vary during the delay. In MGDrivE 2, the discrete-time, fixed-delay framework of MGDrivE 1
is replaced by a continuous-time implementation in which each life stage is divided into a
series of substages. For a single substage, the development time is exponentially-distributed;
but as the number of substages increases, the distribution of development times becomes con-
centrated around the mean. Specifically, if a life stage with a mean development time of 1/dis
divided into a series of nsubstages, the new development times are Erlang-distributed with
mean, 1/d, and variance, 1/(dn
2
), or equivalently, with shape parameter, n, and rate parameter,
d/n. The development time, d(t), may also vary over time, t; however the number of substages,
n, and hence the mean-variance relationship for development times, must remain constant
within a simulation.
Most importantly, the new model implementation allows any model parameter to vary with
time, enabling the framework to account for seasonal variation in development times and
mortality rates due to environmental dependencies. Temperature is known to strongly influ-
ence development times for juvenile mosquito stages, and mortality rates for all mosquito life
stages [7,14], and rainfall is known to influence the carrying capacity of the environment for
larvae, and therefore density-dependent larval mortality rates [8,15]. The new model formula-
tion allows these parameters to vary in continuous time in response to environmental data,
and hence for seasonal variations in temperature and rainfall to drive seasonal variations in
mosquito population density.
Parameters defining other modules of the model—inheritance, landscape and epidemiol-
ogy—are also able to vary over time within the new model formulation. For instance, gene
drive systems under the control of temperature-dependent promoters [16,17] may have time-
varying homing efficiencies, mosquito movement rates may vary seasonally in response to
temperature and other environmental factors [18], and epidemiological parameters such as the
extrinsic incubation period (EIP) and pathogen transmission probabilities from human-to-
mosquito and mosquito-to-human are all known to display seasonal variation through tem-
perature dependence [7,14].
2.2. Epidemiology module
The epidemiology module describes reciprocal transmission of a vector-borne pathogen
between mosquitoes and humans. This requires modeling of both vector and human popula-
tions, as well as an attribute describing the number of individuals in the vector and human
populations having each infectious state (Fig 2). To model malaria, the Ross-Macdonald
model is included, which has susceptible (S
V
), exposed/latently infected (E
V
), and infectious
(I
V
) states for mosquitoes, and susceptible (S
H
), and infected/infectious (I
H
) states for humans
[19,20]. Malaria infection in humans is described by an SIS model, in which humans become
infected at a per-capita rate equal to the “force of infection” in humans, λ
H
, and recover at a
rate, r. Malaria infection in mosquitoes is described by an SEI model, in which adult mosqui-
toes emerge from pupae in the susceptible state, become exposed and latently infected at a per-
capita rate equal to the force of infection in mosquitoes, λ
V
, and progress to infectiousness at a
rate equal to γ
V
. The force of infection in humans, λ
H
, is proportional to the fraction of mos-
quitoes that are infectious, I
V
/N
V
, where N
V
is the adult mosquito population size, and the
force of infection in mosquitoes, λ
V
, is proportional to the fraction of humans that are infec-
tious, I
H
/N
H
, where N
H
is the human population size. Since an exponentially-distributed EIP
leads to some mosquitoes having unrealistically brief incubation periods, we divide the E
V
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MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
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state into a series of nsub-states, as described in section 2.1, leading to the EIP being Erlang-
distributed with shape parameter, n, and rate parameter, γ
V
/n[21]. Finally, transmission
parameters may be tied to specific mosquito genotypes—for instance, an antimalarial effector
gene may be associated with a human-to-mosquito or mosquito-to-human transmission prob-
ability of zero.
To model arboviruses such as chikungunya, Zika and single serotypes of dengue virus, we
include an SEIR model for human transmission, in which the human states are: susceptible
Fig 2. Epidemiology module. MGDrivE 2 includes two basic models for reciprocal pathogen transmission between
mosquitoes and humans—one for malaria (A), and one for arboviruses (B). In both cases, female mosquitoes emerge
from pupae at a rate equal to d
P
/2 as susceptible adults (S
V
), become exposed/latently infected (E
V,1
) at a rate equal to
the force of infection in mosquitoes, λ
V
, and progress to infectiousness (I
V
) through the extrinsic incubation period
(EIP = 1/γ
V
), which is divided into nbins to give an Erlang-distributed dwell time. The mortality rate, μ
F
, is the same
for female mosquitoes in each of these states. For malaria (A), susceptible humans (S
H
) become infected/infectious (I
H
)
at a rate equal to the force of infection in humans, λ
H
, and recover at rate r, becoming susceptible again. For
arboviruses (B), susceptible humans (S
H
) become exposed/latently infected (E
H
) at a rate equal to λ
H
, progress to
infectiousness (I
H
) at rate equal to γ
H
, and recover (R
H
) at rate, r. Infection dynamics couple the mosquito and human
systems via the force of infection terms; λ
V
is a function of I
H
, and λ
H
is a function of I
V
, shown via red edges.
https://doi.org/10.1371/journal.pcbi.1009030.g002
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(S
H
), exposed/latently infected (E
H
), infectious (I
H
), and removed/recovered (R
H
) [22,23]. The
E
H
and R
H
states are included because arboviruses are generally thought to be immunizing,
and have latent periods that tend to be on a similar timescale to the duration of infectiousness.
Humans become latently infected at a per-capita rate equal to λ
H
, progress to infectiousness at
rate, γ
H
, and recover at rate, r. For mosquito transmission, the SEI model with an Erlang-dis-
tributed EIP is used again. Further details of the mathematical formulation of both the malaria
and arbovirus models are provided in the S1 Text. The extensibility of the SPN framework
means that more complex epidemiological models can be developed and implemented by
users.
Modeling vector-borne disease transmission within a metapopulation framework generally
requires each population node in the network to have both a defined mosquito and human
population size. Since the mosquito vectors we are interested in are anthropophilic, they tend
to coexist with humans, so human population sizes and state distributions can be attributed to
the same nodes at which mosquito populations are defined; however, MGDrivE 2 also includes
the possibility of human-only and mosquito-only nodes. Mosquito-only nodes could represent
sites with only non-human vertebrates from which mosquitoes bloodfeed, while human-only
nodes could represent locations unsuitable for mosquitoes. As mosquitoes are able to move
between nodes in the metapopulation, so can humans. This is an important factor to include,
as human movement has been shown to drive the spatial transmission of mosquito-borne dis-
eases such as dengue virus [24].
2.3. Other extensions to inheritance, life history and landscape modules
Additional functionality has been included in the inheritance and life history modules of the
MGDrivE framework since publication of version 1.0. The inheritance module is unchanged,
and inheritance “cubes,” describing the distribution of offspring genotypes given maternal and
paternal genotypes for a given genetic element, are usable in both versions. Several new inheri-
tance cubes have been made available, including: a) homing-based remediation systems,
including ERACR (Element for Reversing the Autocatalytic Chain Reaction) and e-CHACR
(Erasing Construct Hitchhiking on the Autocatalytic Chain Reaction) [25,26], and b) newly
proposed drive systems capable of regional population replacement, including CleaveR (Cleave
and Rescue) [27] and TARE (Toxin-Antidote Recessive Embryo) drive [28].
In the life history module, we have provided two alternative parameterizations of a qua-
dratic density-dependent larval mortality rate function corresponding to logistic and Lotka-
Volterra ecological models. For mosquito vectors such as Ae.aegypti and An.gambiae, den-
sity-dependence is thought to act at the larval stage due to increased resource competition at
higher larval densities [8,15]. The adult population size, N, is used to determine the value of K,
the larval density at which the larval mortality rate is twice the density-independent mortality
rate at a given patch, which produces the appropriate equilibrium population size. For the
logistic model, the per-capita larval mortality rate is given by μ
L
(1 + L(t)/K), where μ
L
is the
density-independent larval mortality rate, and L(t) is the total larval population size for the
patch at time t. For the Lotka-Volterra model, the per-capita larval mortality rate is given by μ
L
+αL(t), where αis the density-dependent term. While related by the expression, α= μ
L
/K,
these two models provide an example of how different functional forms can be used for rates
in MGDrivE 2, and may serve as a template for incorporating more elaborate density-depen-
dent functions.
In the landscape module, movement through the network of population nodes is again
determined by a dispersal kernel; however, due to the continuous-time nature of MGDrivE 2,
movement between patches is described by a rate rather than a probability. MGDrivE 2
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provides functions to map transition probability matrices from MGDrivE 1, such as the zero-
inflated exponential or lognormal dispersal kernels, to continuous-time transition rate matri-
ces for MGDrivE 2. These mapping functions may also be applied to transition probability
matrices derived from empirical or simulated data. The mathematical mapping between the
rate matrix of MGDrivE 2 and the transition probability matrix of MGDrivE 1 is provided in
the S1 Text.
2.4. Stochastic Petri net formulation
The most fundamental change from MGDrivE 1 to 2 is restructuring the model as a SPN [29].
Adopting a SPN framework has several benefits. First, SPNs allow the mathematical specifica-
tion of a model to be decoupled from its algorithmic implementation, allowing users to lever-
age extensive sampling algorithms from the physical and chemical simulation communities
for efficient computation [11,30]. Second, SPNs have a well-established and consistent formal-
ism, allowing them to be readily understood and modified by anyone familiar with this [31].
And third, SPNs are isomorphic to continuous-time Markov chains (CTMCs), meaning that
model parameters can be time-varying, including Erlang-distributed aquatic stage durations
and the pathogen’s EIP.
A Petri net is a bipartite graph consisting of a set of places, P, and a set of transitions, T.
Directed edges or “arcs” lead from places to transitions (input arcs) and from transitions to
places (output arcs). The set of arcs that connect places to transitions and transitions to places
can be denoted by two matrices whose entries are non-negative integers describing the weight
of each arc. The places define the allowable state space of the model; however, in order to
describe any particular state of the model, the Petri net must be given a marking, M, which is
defined by associating each place with a non-negative integer number of tokens. In the lan-
guage of CTMCs, Mis referred to as a “state.” When a transition occurs, it induces a state
change by “consuming” tokens in Mgiven by the set of input arcs, and “producing” tokens in
Maccording to the set of output arcs [32]. Each transition has a “clock process,” parameterized
by a “hazard function” which defines that event’s current rate of occurrence. In MGDrivE 2,
tokens represent an integer number of mosquitoes or humans, and the distribution of tokens
(mosquitoes or humans) across states at time tdefines a marking, M(t). A graphical represen-
tation of a Petri net for the mosquito life history module of MGDrivE 2 is depicted in Fig 3A,
with a full description of the mathematical formalism provided in the S1 Text.
The code that generates the Petri net is independent of the code that simulates trajectories
from it. Once the Petri net is stored as a set of sparse matrices, it is passed to a simulation appli-
cation program interface (API) which allows trajectories to be simulated as ordinary differen-
tial equations (ODEs), stochastic differential equations (SDEs), or CTMCs (Fig 3B). Each of
these are referred to as “step” functions, but are not limited to discrete time steps; these func-
tions are responsible for updating the model between time points where the user requests out-
put to be recorded. The ODE step function provides a deterministic approximation and
interfaces with the numerical routines provided in the “deSolve” R package [33]. Three sto-
chastic numerical routines are provided that treat the model as a continuous-time Markov
process and provide different levels of approximation. The most straightforward method to
sample trajectories is Gillespie’s direct method, which samples each event individually [34].
While statistically exact, this is prohibitively slow for medium-to-large population sizes. Two
approximate stochastic methods are provided that have been widely used in the chemical phys-
ics literature: i) a second order continuous SDE approximation known as the chemical Lange-
vin equation [35], and ii) a fixed-step tau-leaping method [36]. Both methods achieve
substantial gains in computational speed at the expense of statistical accuracy. While the SDE
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approximation is often faster, tau-leaping retains the discrete character of the process it
approximates and is usually the preferred technique. A full description of each of the numeri-
cal routines is provided in the S1 Text. In addition, we demonstrate how a user can write a cus-
tom simulation algorithm and incorporate it within the MGDrivE 2 codebase in the
“Advanced Topics” vignette available at https://marshalllab.github.io/MGDrivE/docs_v2/
articles/advanced_topics.html.
3. Results
To demonstrate how the MGDrivE 2 framework can be used to initialize and run a simulation
of the spread of a gene drive system through a metapopulation with time-varying model
parameters, including its implications for vector-borne pathogen transmission, we have pro-
vided vignettes with the package, available via installation from CRAN at https://CRAN.R-
project.org/package=MGDrivE2 and additional examples and information on GitHub at
https://marshalllab.github.io/MGDrivE/docs_v2/index.html. The vignettes provide extensive
examples of how to use the software, including advanced features such as implementing cus-
tom time-varying rates and numerical simulation algorithms. They consist of a set of five
“core” manuals that describe how to simulate population genetics and dynamics for a mos-
quito-only population and metapopulation, then how to incorporate SEI-SIS Ross-Macdonald
malaria transmission dynamics in a population with humans included, and finally how to
incorporate SEI-SEIR arbovirus transmission dynamics. Following these are three “advanced”
manuals that introduce: i) how to process and analyze output from simulations that write to
CSV files, ii) how users can write custom time-varying hazard functions, and iii) how a user
might implement their own numerical simulation routine, using an explicit Euler method for
ODEs as an example.
Fig 3. Stochastic Petri net (SPN) implementation of MGDrivE 2. (A) Petri net representation of the life history module. The set of purple circles corresponds to places,
P, and red rectangles to transitions, T. This Petri net shows a model in which development times for the egg stage are Erlang-distributed with shape parameter n= 2, and
for the larval stage are Erlang-distributed with shape parameter n= 3. Population dynamics are derived directly from this graph. E.g. The transition corresponding to
oviposition has one edge beginning at F, meaning at least one female mosquito must be present for oviposition to occur. When oviposition occurs, a token is added to E
1
(new eggs are laid) and a token is returned to F. (B) Conceptual representation of the SPN software architecture showing the separation between the model
representation (blue circles) and set of sampling algorithms (red rectangles). These two components of the codebase meet at the simulation API, enabling users to match
models and simulation algorithms interchangeably. Output may be returned as an array in R for exploratory work, or written to CSV files for large simulations.
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Here, we describe the application of the package to model the release of a split gene drive
system designed to drive a malaria-refractory gene into an An.gambiae mosquito population
with seasonal population dynamics and transmission intensity calibrated to a setting resem-
bling the island of Grand Comore, Union of the Comoros. The split gene drive system resem-
bles one engineered in Ae.aegypti [2], which was chosen as the only published split drive
system in a mosquito vector to date. Split drive designs are well-suited to initial field trials of
gene drive systems as they display transient drive activity before being eliminated by virtue of
a fitness cost. The spatial spread of these systems is limited by the distance the host organism
disperses while the drive system persists. In the split drive system explored here, two compo-
nents—the Cas9 and guide RNA (gRNA)—are present at separate, unlinked loci, and a dis-
ease-refractory gene is linked to the gRNA. We assume that only one copy of the disease-
refractory allele is required for it to block pathogen transmission. Four alleles are considered at
the gRNA locus: an intact gRNA/refractory allele (denoted by “H”), a wild-type allele (denoted
by “W”), a functional, cost-free resistant allele (denoted by “R”), and a non-functional or oth-
erwise costly resistant allele (denoted by “B”). At the Cas9 locus, two alleles are considered: an
intact Cas9 allele (denoted by “C”), and a wild-type allele (denoted by “W”). Full details of the
inheritance dynamics are provided in Li et al. [2] and model parameters are summarized in S1
Table.
The life history module is parameterized with typical bionomic parameter values for An.
gambiae (S1 Table), including mean-variance relationships describing the development times
of juvenile life stages [37]. The carrying capacity of the environment for larvae is a function of
recent rainfall, and the adult mortality rate is a function of temperature. Remotely sensed rain-
fall data for Grand Comore was obtained from the ERA5 dataset (https://www.ecmwf.int/en/
forecasts/datasets/reanalysis-datasets/era5), and a mathematical relationship adapted from
White et al. [8] was used to translate this to larval carrying capacity, assuming that half of the
island’s carrying capacity was provided by permanent breeding sites (e.g. large cisterns) and
half was provided by recent rainfall. Temperature data for Grand Comore was also obtained
from the ERA5 dataset, and adult mortality was derived using methods described by Mordecai
et al. [7]. Both climatological time series covered the six-year period beginning January 1,
2010. For the purpose of this demonstration, Grand Comore was treated as a single randomly
mixing population, although simulations involving a more detailed landscape module are
included in the vignettes.
The epidemiology module is parameterized with typical parameter values for Plasmodium
falciparum transmission (S1 Table), human population size and life expectancy parameters
from the National Institute of Statistics and Demographic Studies, Comoros [38], and is cali-
brated to local malaria prevalence estimates from the Malaria Atlas Project [39]. This calibra-
tion was achieved by multiplying the carrying capacity time series by a constant such that the
average adult female mosquito population over a year sustained malaria transmission in the
human population at the estimated local prevalence. Finally, we caution that these simulations
are merely intended to demonstrate the software’s capabilities and that, while the simulations
are parameterized with data from Grand Comore, they are not intended to provide an accurate
forecast of local gene drive mosquito dynamics, or to imply approval of the intervention by the
local population and regulatory agencies.
3.1. Simulation workflow
The code for this simulation is available at https://github.com/MarshallLab/MGDrivE/tree/
master/Examples/SoftwarePaper2. We begin by loading the MGDrivE 2 package in R, as well
as the package for the original MGDrivE simulation, which provides the inheritance cubes
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required for simulation of genetically-stratified mosquito populations. Next, we define model
parameters, including the bionomic parameters of An.gambiae s.l., and demographic and epi-
demiological parameters specific to Grande Comore. To parameterize time-varying adult mos-
quito mortality (hourly) and larval carrying capacity (daily), we load CSV files containing
those data as time series for the ten-year simulation period. We then use the base “stepFun()”
function in R to create an interpolating function of those time-series data that will return a
value for any time within the simulation period, which is required for calculation of hazard
functions. More sophisticated interpolating functions, such as splines, may also be used. We
also specify the inheritance cube at this point, as the number of modeled genotypes and distri-
bution of offspring genotypes for given parental genotypes will be used to build the Petri net.
Next, we use functions from MGDrivE 2 to create the “places” and “transitions” of the Petri
net, which are stored as lists in R and then converted into a sparse matrix representation used
in the simulation code. Epidemiological dynamics and states are coded automatically by call-
ing the functions that create the Petri net. In this case, “spn_P_epiSIS_node()” and “spn_T_e-
piSIS_node()” will generate the places and transitions for a single node model with SEI-SIS
mosquito and human malaria transmission dynamics. Each transition has a tag that specifies
the hazard function it requires. Following that, we write custom time-varying hazard functions
for adult mosquito mortality and larval mortality (a function of carrying capacity). We provide
a guided walkthrough of how a new user might write their own time-varying hazard function
in the vignette “Simulation of Time-inhomogeneous Stochastic Processes.” Once the vector of
hazard functions has been stored (as a list), we create the data frame that stores the times,
genotypes, sex, and size of each release event.
With the construction of all model components necessary for the simulation, we call the
simulation API which handles the details of simulating trajectories from the model. In this
case, we chose the tau-leaping algorithm to sample stochastic trajectories, and to record output
on a daily basis. MGDrivE 2 allows users to choose how model output is reported back—for
exploratory or smaller simulations, users may return output directly to R as an array; however
for larger simulations, it is often preferable to write directly to CSV files due to memory con-
siderations, and MGDrivE 2 has sophisticated functions to both specify CSV output and pro-
cess completed simulations.
3.2. Entomological population dynamics
In Fig 4, we display a potential visualization scheme produced in Python for the simulations
described above. The code to produce this visualization is available at https://github.com/
Chipdelmal/MoNeT/tree/master/DataAnalysis/v2 (note that MGDrivE 2 code does not
depend on Python). Fig 4A displays the climatological time-series data—temperature in
magenta and rainfall in blue—which were used to calculate time-varying adult mosquito mor-
tality rate and larval carrying capacity, respectively. The total adult female population size aver-
aged over 100 stochastic runs is shown in green. This is relatively consistent throughout the
year due to moderate seasonal changes in temperature in the tropical climate of the Comoros
and the presence of permanent breeding sites such as cisterns throughout the island; however
population spikes are observed after significant rainfall. Fig 4B displays allele frequencies for
adult female mosquitoes over the simulation period. After eight consecutive weekly releases of
50,000 male mosquitoes homozygous for both the Cas9 (C) and gRNA/refractory (H) alleles
three years into the simulation, we see the C and H alleles accumulate to high post-release fre-
quencies, and the H allele continue to spread to a higher frequency over the subsequent ~6
months while the H and C alleles regularly co-occur enabling drive to occur at the gRNA
locus. The wild-type allele (W) at the gRNA locus is almost completely lost over this period,
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and both in-frame and out-of-frame resistant alleles (R and B, respectively) accumulate to a
small yet significant extent. The C allele slowly declines in frequency following the releases due
to a fitness cost; and beginning ~1 year after the releases, the H allele gradually declines in fre-
quency as its fitness cost begins to outweigh its inheritance bias. The declines in C and H allele
frequencies continue beyond the simulated timeframe, although not before the H allele has a
chance to interfere with disease transmission.
3.3. Epidemiological dynamics
The split drive system we consider includes a malaria-refractory gene that results in complete
inability of mosquitoes to become infected with the malaria parasite, whether present in either
one or two allele copies. In Fig 4C, we depict the spread of the malaria-refractory trait through
the female mosquito population, and the consequences this has for mosquito and human
infection status. Prior to the release, we see that infection prevalence in humans (P.falciparum
parasite rate, PfPR) is mildly seasonal, with the proportion of infected humans (solid green
line) waxing and waning in response to the fluctuating mosquito population size (green line in
Fig 4A). The proportion of infectious female mosquitoes (dotted light blue line) oscillates in
synchrony with the proportion of infected humans; but at a much lower proportion due to the
short mosquito lifespan and the fact that most mosquitoes die before the parasite completes its
Fig 4. Example MGDrivE 2 simulations for a split gene drive system designed to drive a malaria-refractory gene in a confinable and reversible manner into an
An.gambiae s.l. mosquito population with seasonal population dynamics and transmission intensity calibrated to a setting resembling the island of Grand
Comore, Union of the Comoros. The split drive system resembles one recently engineered in Ae.aegypti [2]–the only split drive system in a mosquito vector to date. In
the modeled system, two components–the Cas9 and guide RNA (gRNA)–are present at separate, unlinked loci, and a disease-refractory gene is linked to the gRNA.
Four alleles are considered at the gRNA locus: an intact gRNA/refractory allele (denoted by “H”), a wild-type allele (denoted by “W”), a functional, cost-free resistant
allele (denoted by “R”), and a non-functional or otherwise costly resistant allele (denoted by “B”). At the Cas9 locus, two alleles are considered: an intact Cas9 allele
(denoted by “C”), and a wild-type allele (denoted by “W”). Model parameters describing the construct, mosquito bionomics and malaria transmission are summarized
in S1 Table.(A) Climatological time-series data—temperature in red and rainfall in blue—that were used to calculate time-varying adult mosquito mortality rate and
larval carrying capacity, respectively. The resulting adult female population size is shown in green. (B) Allele frequencies for adult female mosquitoes over the
simulation period. Grey vertical bars beginning at year three denote eight consecutive weekly releases of 50,000 male mosquitoes homozygous for both the gRNA and
Cas9 alleles (H and C, respectively). (C) Spread of the malaria-refractory trait through the female mosquito population, and consequences for mosquito and human
infection status. Following releases of the drive system at year three, the proportion of refractory female mosquitoes (solid red line) increases and the proportion of
infectious mosquitoes (dotted light blue line) declines. As humans recover from infection and less develop new infections, the P.falciparum parasite rate (solid green
line) declines until it reaches near undetectable levels by year five. (D) Human malaria incidence is halted by the beginning of year four.
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EIP. Following releases of the split drive system and refractory gene at year three, the propor-
tion of refractory female mosquitoes (red line) increases and, consequently, the proportion of
infectious mosquitoes declines. As humans recover from infection and less develop new infec-
tions, the PfPR declines until it reaches near undetectable levels by year five. Lastly, Fig 4D
depicts human malaria incidence, measured as the number of new infections per 1,000
humans per day. Stochastic variation in this model output is more pronounced due to the
small number of incident cases relative to the total population. Incidence is halted by the
beginning of year four, but PfPR takes almost a year longer to approach zero as infected
humans clear parasites.
4. Availability and future directions
MGDrivE 2 is available at https://CRAN.R-project.org/package=MGDrivE2. The source code
is under the GPL3 License and is free for other groups to modify and extend as needed. Mathe-
matical details of the model formulation are available in the S1 Text, and documentation for
all MGDrivE 2 functions, including vignettes, are available at the project’s website at https://
marshalllab.github.io/MGDrivE/docs_v2/index.html. To run the software, we recommend
using R version 2.10 or higher.
We are continuing development of the MGDrivE 2 software package and welcome sugges-
tions and requests from the research community regarding future directions. The field of gene
drive research is moving quickly, and we intend the MGDrivE 2 framework to serve as a flexi-
ble tool to address exploratory, logistical and operational questions regarding genetics-based
control systems for mosquito disease vectors. This includes exploratory modeling of novel
genetic constructs, assessment of candidate constructs against TPPs and PPCs, and field trial
planning as constructs progress through the development pipeline. Current functionality pres-
ents a new opportunity to explore modeling-based research topics such as the invasiveness of
threshold-dependent drive systems in the presence of climate fluctuations, seasonal source-
sink dynamics and evolution towards smaller fitness costs. Future functionality that we are
planning includes: i) modeling of mosquito traps to address questions related to monitoring
and surveillance, and ii) more detailed epidemiological models addressing phenomena impor-
tant to malaria and arbovirus transmission—for instance, dengue models that incorporate
multiple serotypes with temporary cross-protective immunity and complications related to
antibody-dependent enhancement [40], and malaria models that incorporate age-structure,
immunity, asymptomatic infection and superinfection [41].
Additionally, we are exploring numerical sampling algorithms that can increase computa-
tional efficiency and speed, facilitated by separation of model specification and simulation in
the software. The complexity of models that can be developed in MGDrivE 2 means that sensi-
tivity analyses can become extremely computationally intensive, and the ability of the SPN
framework to leverage efficient algorithms in these circumstances will be highly valuable. We
also continue to be interested in developing a corresponding individual-based model capable
of efficient modeling when the number of possible states exceeds the number of individuals in
the population—for instance, for multi-locus systems such as daisy-drive [42] and multiplex-
ing schemes in which a single gene is targeted at multiple locations to reduce the rate of resis-
tance allele formation [43], and for epidemiological models in which age structure, immunity
and mosquito biting heterogeneity become prohibitive for population models [41].
As gene drive technology matures, potential species of interest are not limited to arthropod
vectors of disease. In addition to public health applications, gene drive has been proposed as a
technique to help address problems in agriculture and conservation, with target species includ-
ing insect agricultural pests [44] and invasive rodents that predate native birds [45]. While
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MGDrivE 1 was not designed with non-arthropod species in mind, it has been adapted for
application to invasive rodents on islands [46]. We expect MGDrivE 2 to be easier to adapt to
other insect or mammalian species due to the separation of model specification from simula-
tion, meaning there is no need to adapt code to numerically simulate trajectories. To adapt
model specification, the set of places and transitions for the SPN will need to be updated
according to the life stages and development and mortality rates for the species of interest.
New SPN transitions may be needed for behaviors not currently included, such as multiple
mating in adults, while redundant transitions may be removed.
Supporting information
S1 Table. Model parameters describing the gene drive construct, mosquito bionomics and
malaria epidemiology for simulations resembling releases on Grand Comore, Union of the
Comoros.
(PDF)
S1 Text. Description of the modeling framework. A description of the mathematical equa-
tions that govern the inheritance, life history, landscape and epidemiology modules and the
stochastic Petri net model formulation.
(PDF)
Acknowledgments
We thank Sandra Hui for discussions on software development and Fausto Bustos for input
on the epidemiological model.
Author Contributions
Conceptualization: Sean L. Wu, John M. Marshall.
Data curation: Toma
´s M. Leo
´n.
Formal analysis: Sean L. Wu, Andrew J. Dolgert.
Funding acquisition: John M. Marshall.
Investigation: Sean L. Wu, Jared B. Bennett, He
´ctor M. Sa
´nchez C., Toma
´s M. Leo
´n.
Methodology: Sean L. Wu, Jared B. Bennett, He
´ctor M. Sa
´nchez C., Andrew J. Dolgert, Toma
´s
M. Leo
´n.
Project administration: John M. Marshall.
Resources: John M. Marshall.
Software: Sean L. Wu, Jared B. Bennett, Andrew J. Dolgert.
Supervision: John M. Marshall.
Validation: Sean L. Wu, Jared B. Bennett.
Visualization: He
´ctor M. Sa
´nchez C.
Writing – original draft: Sean L. Wu, John M. Marshall.
Writing – review & editing: Sean L. Wu, Jared B. Bennett, He
´ctor M. Sa
´nchez C., Andrew J.
Dolgert, Toma
´s M. Leo
´n, John M. Marshall.
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References
1. Kyrou K, Hammond AM, Galizi R, Kranjc N, Burt A, Beaghton AK, et al. A CRISPR-Cas9 gene drive tar-
geting doublesex causes complete population suppression in caged Anopheles gambiae mosquitoes.
Nat Biotechnol. 2018; 36: 1062–1066. https://doi.org/10.1038/nbt.4245 PMID: 30247490
2. Li M, Yang T, Kandul NP, Bui M, Gamez S, Raban R, et al. Development of a confinable gene drive sys-
tem in the human disease vector. Elife. 2020; 9. https://doi.org/10.7554/eLife.51701 PMID: 31960794
3. Carballar-Lejarazu
´R, Ogaugwu C, Tushar T, Kelsey A, Pham TB, Murphy J, et al. Next-generation
gene drive for population modification of the malaria vector mosquito,. Proc Natl Acad Sci U S A. 2020;
117: 22805–22814. https://doi.org/10.1073/pnas.2010214117 PMID: 32839345
4. Adolfi A, Gantz VM, Jasinskiene N, Lee H-F, Hwang K, Bulger EA, et al. Efficient population modifica-
tion gene-drive rescue system in the malaria mosquito Anopheles stephensi. https://doi.org/10.1038/
s41467-020-19426-0 PMID: 33144570
5. James S, Collins FH, Welkhoff PA, Emerson C, Godfray HCJ, Gottlieb M, et al. Pathway to Deployment
of Gene Drive Mosquitoes as a Potential Biocontrol Tool for Elimination of Malaria in Sub-Saharan
Africa: Recommendations of a Scientific Working Group †. The American Journal of Tropical Medicine
and Hygiene. 2018. pp. 1–49. https://doi.org/10.4269/ajtmh.18-0083 PMID: 29882508
6. James SL, Marshall JM, Christophides GK, Okumu FO, Nolan T. Toward the Definition of Efficacy and
Safety Criteria for Advancing Gene Drive-Modified Mosquitoes to Field Testing. Vector Borne Zoonotic
Dis. 2020; 20: 237–251. https://doi.org/10.1089/vbz.2019.2606 PMID: 32155390
7. Mordecai EA, Caldwell JM, Grossman MK, Lippi CA, Johnson LR, Neira M, et al. Thermal biology of
mosquito-borne disease. Ecol Lett. 2019; 22: 1690–1708. https://doi.org/10.1111/ele.13335 PMID:
31286630
8. White MT, Griffin JT, Churcher TS, Ferguson NM, Basa
´ñez M-G, Ghani AC. Modelling the impact of
vector control interventions on Anopheles gambiae population dynamics. Parasit Vectors. 2011; 4: 153.
https://doi.org/10.1186/1756-3305-4-153 PMID: 21798055
9. HMS C., Sa
´nchez C. HM, Wu SL, Bennett JB, Marshall JM. MGDrivE: A modular simulation framework
for the spread of gene drives through spatially-explicit mosquito populations. https://doi.org/10.1101/
350488
10. Champer J, Liu J, Oh SY, Reeves R, Luthra A, Oakes N, et al. Reducing resistance allele formation in
CRISPR gene drive. Proc Natl Acad Sci U S A. 2018; 115: 5522–5527. https://doi.org/10.1073/pnas.
1720354115 PMID: 29735716
11. Goss PJ, Peccoud J. Quantitative modeling of stochastic systems in molecular biology by using sto-
chastic Petri nets. Proc Natl Acad Sci U S A. 1998; 95: 6750–6755. https://doi.org/10.1073/pnas.95.12.
6750 PMID: 9618484
12. Bortolussi L, Hillston J, Latella D, Massink M. Continuous approximation of collective system behaviour:
A tutorial. Performance Evaluation. 2013. pp. 317–349. https://doi.org/10.1016/j.peva.2013.01.001
13. Deredec A, Godfray HCJ, Burt A. Requirements for effective malaria control with homing endonuclease
genes. Proc Natl Acad Sci U S A. 2011; 108: E874–80. https://doi.org/10.1073/pnas.1110717108
PMID: 21976487
14. Beck-Johnson LM, Nelson WA, Paaijmans KP, Read AF, Thomas MB, Bjørnstad ON. The importance
of temperature fluctuations in understanding mosquito population dynamics and malaria risk. R Soc
Open Sci. 2017; 4: 160969. https://doi.org/10.1098/rsos.160969 PMID: 28405386
15. Muriu SM, Coulson T, Mbogo CM, Godfray HCJ. Larval density dependence in Anopheles gambiae s.
s., the major African vector of malaria. J Anim Ecol. 2013; 82: 166–174. https://doi.org/10.1111/1365-
2656.12002 PMID: 23163565
16. Zeidler MP, Tan C, Bellaiche Y, Cherry S, Ha
¨der S, Gayko U, et al. Temperature-sensitive control of
protein activity by conditionally splicing inteins. Nat Biotechnol. 2004; 22: 871–876. https://doi.org/10.
1038/nbt979 PMID: 15184905
17. Dissmeyer N. Conditional Modulation of Biological Processes by Low-Temperature Degrons. Methods
Mol Biol. 2017; 1669: 407–416. https://doi.org/10.1007/978-1-4939-7286-9_30 PMID: 28936674
18. Le Goff G, Damiens D, Ruttee A-H, Payet L, Lebon C, Dehecq J-S, et al. Field evaluation of seasonal
trends in relative population sizes and dispersal pattern of Aedes albopictus males in support of the
design of a sterile male release strategy. Parasit Vectors. 2019; 12: 81. https://doi.org/10.1186/s13071-
019-3329-7 PMID: 30755268
19. Ross SR. The Prevention of Malaria. 1910.
20. Macdonald G. The Epidemiology and Control of Malaria. 1957.
21. Smith DL, Dushoff J, Ellis McKenzie F. The Risk of a Mosquito-Borne Infectionin a Heterogeneous Envi-
ronment. PLoS Biology. 2004. p. e368. https://doi.org/10.1371/journal.pbio.0020368 PMID: 15510228
PLOS COMPUTATIONAL BIOLOGY
MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009030 May 21, 2021 15 / 17
22. Robinson M, Conan A, Duong V, Ly S, Ngan C, Buchy P, et al. A Model for a Chikungunya Outbreak in
a Rural Cambodian Setting: Implications for Disease Control in Uninfected Areas. PLoS Neglected
Tropical Diseases. 2014. p. e3120. https://doi.org/10.1371/journal.pntd.0003120 PMID: 25210729
23. Kucharski AJ, Funk S, Eggo RM, Mallet H-P, John Edmunds W, Nilles EJ. Transmission dynamics of
Zika virus in island populations: a modelling analysis of the 2013–14 French Polynesia outbreak. https://
doi.org/10.1371/journal.pntd.0004726 PMID: 27186984
24. Stoddard ST, Forshey BM, Morrison AC, Paz-Soldan VA, Vazquez-Prokopec GM, Astete H, et al.
House-to-house human movement drives dengue virus transmission. Proc Natl Acad Sci U S A. 2013;
110: 994–999. https://doi.org/10.1073/pnas.1213349110 PMID: 23277539
25. Gantz VM, Bier E. The dawn of active genetics. Bioessays. 2016; 38: 50–63. https://doi.org/10.1002/
bies.201500102 PMID: 26660392
26. Xu X-RS, Bulger EA, Gantz VM, Klanseck C, Heimler SR, Auradkar A, et al. Active Genetic Neutralizing
Elements for Halting or Deleting Gene Drives. Mol Cell. 2020. https://doi.org/10.1016/j.molcel.2020.09.
003 PMID: 32949493
27. Oberhofer G, Ivy T, Hay BA. Cleave and Rescue, a novel selfish genetic element and general strategy
for gene drive. Proc Natl Acad Sci U S A. 2019; 116: 6250–6259. https://doi.org/10.1073/pnas.
1816928116 PMID: 30760597
28. Champer J, Lee E, Yang E, Liu C, Clark AG, Messer PW. A toxin-antidote CRISPR gene drive system
for regional population modification. Nat Commun. 2020; 11: 1082. https://doi.org/10.1038/s41467-020-
14960-3 PMID: 32109227
29. Haas PJ. Stochastic Petri Nets: Modelling, Stability, Simulation. Springer Science & Business Media;
2006.
30. Gillespie DT. Stochastic Simulation of Chemical Kinetics. Annual Review of Physical Chemistry.
2007. pp. 35–55. https://doi.org/10.1146/annurev.physchem.58.032806.104637 PMID: 17037977
31. Gronewold A, Sonnenschein M. Event-based modelling of ecological systems with asynchronous cellu-
lar automata. Ecological Modelling. 1998. pp. 37–52. https://doi.org/10.1016/s0304-3800(98)00017-9
32. Wilkinson DJ. Stochastic Modelling for Systems Biology, Third Edition. 2018. https://doi.org/10.1201/
9781351000918
33. Soetaert K, Cash J, Mazzia F. Solving Ordinary Differential Equations in R. Solving Differential Equa-
tions in R. 2012. pp. 41–80. https://doi.org/10.1007/978-3-642-28070-2_3
34. Gillespie DT. Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chem-
istry. 1977. pp. 2340–2361. https://doi.org/10.1021/j100540a008
35. Gillespie DT. The multivariate Langevin and Fokker–Planck equations. American Journal of Physics.
1996. pp. 1246–1257. https://doi.org/10.1119/1.18387
36. Gillespie DT. Approximate accelerated stochastic simulation of chemically reacting systems. The Jour-
nal of Chemical Physics. 2001. pp. 1716–1733. https://doi.org/10.1063/1.1378322
37. Bayoh MN, Lindsay SW. Effect of temperature on the development of the aquatic stages of Anopheles
gambiae sensu stricto (Diptera: Culicidae). Bull Entomol Res. 2003; 93: 375–381. https://doi.org/10.
1079/ber2003259 PMID: 14641976
38. INSEED. Annuaire Statistique des Comores. Moroni, Union of the Comoros. National Institute of Statis-
tics and Economic and Demographic Studies (INSEED); 2015.
39. Pfeffer DA, Lucas TCD, May D, Harris J, Rozier J, Twohig KA, et al. malariaAtlas: an R interface to
global malariometric data hosted by the Malaria Atlas Project. Malaria Journal. 2018. https://doi.org/10.
1186/s12936-018-2500-5 PMID: 30290815
40. Wearing HJ, Rohani P. Ecological and immunological determinants of dengue epidemics. Proc Natl
Acad Sci U S A. 2006; 103: 11802–11807. https://doi.org/10.1073/pnas.0602960103 PMID: 16868086
41. Griffin JT, Deirdre Hollingsworth T, Okell LC, Churcher TS, White M, Hinsley W, et al. Reducing Plas-
modium falciparum Malaria Transmission in Africa: A Model-Based Evaluation of Intervention Strate-
gies. PLoS Medicine. 2010. p. e1000324. https://doi.org/10.1371/journal.pmed.1000324 PMID:
20711482
42. Noble C, Min J, Olejarz J, Buchthal J, Chavez A, Smidler AL, et al. Daisy-chain gene drives for the alter-
ation of local populations. Proc Natl Acad Sci U S A. 2019; 116: 8275–8282. https://doi.org/10.1073/
pnas.1716358116 PMID: 30940750
43. Prowse TAA, Cassey P, Ross JV, Pfitzner C, Wittmann TA, Thomas P. Dodging silver bullets: good
CRISPR gene-drive design is critical for eradicating exotic vertebrates. Proc Biol Sci. 2017; 284. https://
doi.org/10.1098/rspb.2017.0799 PMID: 28794219
PLOS COMPUTATIONAL BIOLOGY
MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009030 May 21, 2021 16 / 17
44. Buchman A, Marshall JM, Ostrovski D, Yang T, Akbari OS. Synthetically engineered Medea gene drive
system in the worldwide crop pest Drosophila suzukii. Proceedings of the National Academy of Sci-
ences USA. 2018; 18: 4725–4730 https://doi.org/10.1073/pnas.1713139115 PMID: 29666236
45. Leitschuh CM, Kanavy D, Backus GA, Valdez RX, Serr M, Pitts EA, et al. Developing gene drive tech-
nologies to eradicate invasive rodents from islands. Journal of Responsible Innovation. 2018; 5: S121–
S138.
46. Landis WG. The origin, development, appliction, lessons learned, and future regarding the Bayesian
network relative risk model for ecological risk assessment. Integrated Environmental Assessment and
Management. 2020; 17: 79–94. https://doi.org/10.1002/ieam.4351 PMID: 32997384
PLOS COMPUTATIONAL BIOLOGY
MGDrivE 2: A gene drive model incorporating seasonality and epidemiology
PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1009030 May 21, 2021 17 / 17
... Despite their prevalence and relative ease of use, the canonical ODE framework poorly represents population heterogeneity and time-delay caused by development 27,28 . Extensions have been made to incorporate realistic development time distributions by incorporating a series of sub-stages with identical exponentially distributed dwell times (also known as the linear chain trick) 27,29,30 . Delay differential equations (DDEs) have also been used to model insect population dynamics with true time delays in development [31][32][33] . ...
... We argue that in cases where development time distribution is fixed a priori (excluded from model calibration), the LCT framework provides a significant advantage over canonical ODEs. Although the framework has been used in the field of infectious disease epidemiology 64,65 , it has recently been applied to the modelling of vector population dynamics 30 . ...
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... These resistance alleles have the potential to slow or even stop the spread of a gene drive. The dynamics of such drives have been modeled extensively [40][41][42][43][44][45][46][47][48][49][50] , which is particularly important for predicting the outcome of a real-world drive release. ...
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1.Malaria, dengue, Zika, and other mosquito‐borne diseases continue to pose a major global health burden through much of the world, despite the widespread distribution of insecticide‐based tools and antimalarial drugs. The advent of CRISPR/Cas9‐based gene editing and its demonstrated ability to streamline the development of gene drive systems has reignited interest in the application of this technology to the control of mosquitoes and the diseases they transmit. The versatility of this technology has enabled a wide range of gene drive architectures to be realized, creating a need for their population‐level and spatial dynamics to be explored. 2.We present MGDrivE (Mosquito Gene Drive Explorer): a simulation framework designed to investigate the population dynamics of a variety of gene drive architectures and their spread through spatially‐explicit mosquito populations. A key strength of the MGDrivE framework is its modularity: a) a genetic inheritance module accommodates the dynamics of gene drive systems displaying userdefined inheritance patterns, b) a population dynamic module accommodates the life history of a variety of mosquito disease vectors and insect agricultural pests, and c) a landscape module generates the metapopulation model by which insect populations are connected via migration over space. 3.Example MGDrivE simulations are presented to demonstrate the application of the framework to CRISPR/Cas9‐based homing gene drive for: a) driving a disease‐refractory gene into a population (i.e. population replacement), and b) disrupting a gene required for female fertility (i.e. population suppression), incorporating homing‐resistant alleles in both cases. Further documentation and use examples are provided at the project's Github repository. 4.MGDrivE is an open‐source R package freely available on CRAN. We intend the package to provide a flexible tool capable of modeling novel inheritance‐modifying constructs as they are proposed and become available. The field of gene drive is moving very quickly, and we welcome suggestions for future development.
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Mosquito‐borne diseases cause a major burden of disease worldwide. The vital rates of these ectothermic vectors and parasites respond strongly and nonlinearly to temperature and therefore to climate change. Here, we review how trait‐based approaches can synthesise and mechanistically predict the temperature dependence of transmission across vectors, pathogens, and environments. We present 11 pathogens transmitted by 15 different mosquito species – including globally important diseases like malaria, dengue, and Zika – synthesised from previously published studies. Transmission varied strongly and unimodally with temperature, peaking at 23–29ºC and declining to zero below 9–23ºC and above 32–38ºC. Different traits restricted transmission at low versus high temperatures, and temperature effects on transmission varied by both mosquito and parasite species. Temperate pathogens exhibit broader thermal ranges and cooler thermal minima and optima than tropical pathogens. Among tropical pathogens, malaria and Ross River virus had lower thermal optima (25–26ºC) while dengue and Zika viruses had the highest (29ºC) thermal optima. We expect warming to increase transmission below thermal optima but decrease transmission above optima. Key directions for future work include linking mechanistic models to field transmission, combining temperature effects with control measures, incorporating trait variation and temperature variation, and investigating climate adaptation and migration.
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If they are able to spread in wild populations, CRISPR-based gene-drive elements would provide new ways to address ecological problems by altering the traits of wild organisms, but the potential for uncontrolled spread tremendously complicates ethical development and use. Here, we detail a self-exhausting form of CRISPR-based drive system comprising genetic elements arranged in a daisy chain such that each drives the next. “Daisy-drive” systems can locally duplicate any effect achievable by using an equivalent self-propagating drive system, but their capacity to spread is limited by the successive loss of nondriving elements from one end of the chain. Releasing daisy-drive organisms constituting a small fraction of the local wild population can drive a useful genetic element nearly to local fixation for a wide range of fitness parameters without self-propagating spread. We additionally report numerous highly active guide RNA sequences sharing minimal homology that may enable evolutionarily stable daisy drive as well as self-propagating CRISPR-based gene drive. Especially when combined with threshold dependence, daisy drives could simplify decision-making and promote ethical use by enabling local communities to decide whether, when, and how to alter local ecosystems.
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CRISPR-Cas9-based gene drive systems possess the inherent capacity to spread progressively throughout target populations. Here we describe two self-copying (or active) guide RNA-only genetic elements, called e-CHACRs and ERACRs. These elements use Cas9 produced in trans by a gene drive either to inactivate the cas9 transgene (e-CHACRs) or to delete and replace the gene drive (ERACRs). e-CHACRs can be inserted at various genomic locations and carry two or more gRNAs, the first copying the e-CHACR and the second mutating and inactivating the cas9 transgene. Alternatively, ERACRs are inserted at the same genomic location as a gene drive, carrying two gRNAs that cut on either side of the gene drive to excise it. e-CHACRs efficiently inactivate Cas9 and can drive to completion in cage experiments. Similarly, ERACRs, particularly those carrying a recoded cDNA-restoring endogenous gene activity, can drive reliably to fully replace a gene drive. We compare the strengths of these two systems.