Modeling Priorities as Gene Drive Mosquito
Projects Transition from Lab to Field
John M. Marshalla,* and Ace R. Northb,*
aDivisions of Epidemiology & Biostatistics, School of Public Health, University of
California, Berkeley, California, USA
bDepartment of Zoology, University of Oxford, Oxford, UK
Despite significant reductions in malaria incidence and prevalence over the last
decade following the wide-spread distribution of long-lasting insecticide-treated
nets (LLINs), malaria is not expected to be eliminated with currently available
tools - LLINs, indoor residual spraying with insecticides (IRS), and artemisinin
combination therapy drugs (ACTs) (Walker et al., 2016). Consequently, there is
interest in novel interventions that complement existing ones, such as attractive
targeted sugar baits (ATSBs) (Traore et al., 2020), transmission-blocking vaccines
(Coelho et al., 2019), and gene drive-modified mosquitoes. Gene drive
mosquitoes have been described as playing a potentially transformative role
toward malaria elimination as, provided that societal and regulatory approval can
be gained, they are not hindered by human compliance issues that other
interventions face and they should be capable of spreading beyond their site of
application, potentially impacting disease transmission on a wide scale (James et
al., 2018). These interventions are synergistic with currently available ones as, for
example, reducing the malaria parasite population through the distribution of
ACTs, and gene drive mosquitoes engineered with disease-refractory genes
results in fewer opportunities for the evolution of parasite resistance to either
intervention, more than would be the case for intervention in isolation (Marshall
et al., 2019).
Mathematical modeling has a central role to play in determining the
impact that gene drive systems could have, alongside other interventions, toward
the goal of malaria elimination. Predicting the spread of genes through
populations and their impacts on mosquito populations requires an understanding
of the dynamics of mosquitoes, humans, and parasites, with specific attention to
genetic inheritance, mosquito life history, and pathogen transmission.
Mathematical models provide a means to integrate the knowledge of each of these
components of vector-borne disease transmission, including a mechanistic
understanding of the processes involved and data that could be used to validate
these models. Given the potential irreversibility of a release of gene drive-
modified organisms, models provide a means to address questions regarding
safety and efficacy prior to a release based on the best available data. Such
models may be used as a basis for risk assessment, field trial design, and to
explore hypothetical intervention scenarios.
In this chapter, we survey modeling priorities as gene drive mosquito
projects advance from the lab to the field. We begin by highlighting priorities in
model building, namely (i) capturing nuances in the inheritance-biasing impacts
of gene drive systems, (ii) incorporating data and insights on mosquito vector
ecology, including life history, habitat distribution, and movement patterns, and
(iii) aligning entomological models with detailed models of malaria transmission,
including the impacts of currently available and novel interventions. We then
highlight several priorities in the model application as gene drive products
advance from the lab to the field. These include informing target product profiles
(TPPs) for gene drive products to assess when they satisfy safety and efficacy
criteria, and informing the design of cage trials, field trials, and eventually vector
and disease control interventions. Other priorities include developing monitoring
programs to assess the safety and efficacy of trials and interventions, developing
surveillance programs to detect unintended spread, and addressing risk and
regulatory questions requiring a quantitative analysis.
We focus on CRISPR-based homing gene drive systems, as these
currently have the most promise to contribute to the malaria eradication agenda.
Indeed, three of the most advanced malaria vector gene drive projects at present—
Target Malaria, the UC Irvine Malaria Initiative, and Transmission Zero—are
developing CRISPR-based homing gene drive systems to drive either a fitness
load or disease-refractory gene into a mosquito population. Homing-based gene
drive systems are able to spread through a population despite a fitness cost due to
their overrepresentation in the gametes of a heterozygote. This is achieved by
expressing an endonuclease which creates a double-stranded break at a highly
specific site chosen as a target for the drive integration (Esvelt et al., 2014).
Homology-directed repair (HDR) then copies the drive allele to the cut
chromosome (Rong and Golic, 2003). If this occurs in the germline, it effectively
converts a heterozygote into a homozygote in terms of inheritance.
Two general classes of CRISPR-based homing gene drive systems have
been proposed for the control of malaria vectors: (i) constructs that aim to
suppress vector populations by introducing fitness costs or a sex bias, and (ii)
constructs that aim to modify vector populations by introducing traits that reduce
disease transmission. Additionally, some constructs are intended to be self-
sustaining, whereby they spread from one population to another with the goal of
disease control over a wide area, and others are designed to be self-limiting,
whereby their spread is limited in both space and time. Gene drive systems exist
that fall into each pair of categories, and have been reviewed by others (Sinkins
and Gould, 2006; Alphey, 2014; Burt, 2014; Godfray et al., 2017; Raban et al.,
2020). Here, we provide an overview of modeling considerations that apply to the
development of several gene drive designs, with an emphasis on homing-based
systems intended for wide-scale malaria control.
7.2 Model Building
Good models should satisfy the principle of parsimony and be tailored to the
questions they are designed for. In the words of physicist Albert Einstein,
“Everything should be made as simple as possible, but no simpler,” and in the
words of statistician George Box, “All models are wrong, but some are useful.”
When gene drive systems were first proposed as a novel approach to control
mosquitoes, the models used to explore the idea were appropriately abstract and
generic (Burt, 2003; Deredec et al., 2008). These models focused on population
genetics—considering changes in gene frequencies in mostly randomly mixing
populations—and ignored most details of mosquito ecology and parasite
transmission. Such models are also used for new technologies, such as CleaveR
(Oberhofer et al., 2019) and TARE (Champer et al., 2020), which have only
recently been proposed. But as the earlier technologies have advanced and data
have become available, models with increasing levels of detail have been
developed for specific gene drive systems in specific mosquito species intended
for release in specific environments (North et al., 2019, 2020; Eckhoff et al.,
2017). As potential field trials edge closer, models capable of addressing a myriad
of logistical questions will be required, and increasing detail will be needed to
address the nuances of biased inheritance, mosquito vector ecology, and local
7.2.1 Population Genetics Models
The early conceptual models of homing-based gene drive preceded the discovery
of CRISPR as a gene-editing tool and described the population genetics of a gene
drive system, H, and a wildtype allele, W (Burt, 2003; Deredec et al., 2008). In
particular, the model of Deredec et al. (2008) defined homing rate, e, to be the
probability that a wildtype allele in the germline of a heterozygote is converted to
a gene drive allele, fitness load, s, to be the fitness penalty incurred by
homozygotes (HH), and dominance, h, to be the extent to which this fitness cost is
imposed on heterozygotes (HW). Depending on the parameter values, this model
predicted a number of possible outcomes following the introduction of a gene
drive system into a population: (i) the inheritance bias exceeds the fitness load
and the drive allele spreads into the population from low initial frequencies,
eventually eliminating the wildtype allele completely, (ii) the drive allele spreads
to a stable equilibrium frequency at which both alleles coexist, (iii) the drive allele
either spreads to fixation or is lost depending on its initial frequency in the
population, and (iv) the drive allele is invariably lost from the population (Burt,
2003; Deredec et al., 2008) (Fig. 7.1).
These early models of homing-based gene drive also considered resistant
alleles, R, which contain the coding frame and function of the target site but not
the gene drive recognition site, and thus are resistant to homing (Deredec et al.,
2008). These resistant alleles may already exist due to standing genetic variation
(SGV), or may form through (i) error-prone repair mechanisms such as non-
homologous end-joining (NHEJ) and microhomology-mediated end-joining
(MMEJ), or (ii) de novo mutation after the drive allele has been introduced
(Unckless et al., 2017). If the drive allele confers a fitness load while the drive-
resistant allele does not, then the drive-resistant allele is expected to prevail in the
end and the level of SGV, rate of resistant allele generation, and magnitude of
fitness advantage of the drive-resistant allele over the drive allele will determine
the timescale over which this occurs (Marshall et al., 2017; Noble et al., 2017).
Figure 7.1 Population genetics of a homing drive allele. Time-
series dynamics depending on the homing rate, e, fitness load, s,
dominance of the fitness load, h, and initial drive allele frequency,
qstart. The model, which assumes that homing occurs after gene
expression so that costs of being homozygous are not experienced
by individuals in which homing occurs, is described by Deredec et
Subsequent models of homing-based gene drive have incorporated two
varieties of alleles conferring resistance to homing: (i) in-frame resistance alleles
that preserve the function of the target gene, R (sometimes denoted as “R1”), and
(ii) in-frame or out-of-frame costly resistant alleles that disrupt target gene
function, B (sometimes denoted as “R2”). Some of these models also account for
the different stages at which wildtype alleles are converted to intact drive or
drive-resistant alleles, notably: (i) pre-fertilization, in which the allelic make-up of
gametes in either parent is distorted, and (ii) post-fertilization, in which wildtype
alleles in a fertilized embryo are converted to drive-resistant alleles following
deposition of Cas9 by a mother having the intact drive allele (Deredec et al.,
2008; Champer et al., 2017; Pham et al., 2019; Adolfi et al., 2020). Maternal
deposition of Cas9 produces a mosaic marker phenotype in some offspring, as
somatic allele conversions are manifest in some embryonic cells but not others,
and are heritable when occurring in embryonic germ cells.
When incorporating these details of CRISPR-based homing drive into a
model, parameters that need estimating include: (i) the proportion of W alleles
that are cleaved in the gametes of HW heterozygotes, either female or male, (ii)
the proportion of those cleaved that are subject to accurate HDR and become H
alleles, either in females or males, (iii) the proportion of resistance alleles that are
R versus B (or R1 versus R2), (iv) the proportion of W alleles among offspring of
mothers having the Cas9 allele that is cleaved through maternal deposition in the
fertilized embryo, and whether this depends on how many Cas9 alleles the mother
has, and (v) the proportion of those maternally cleaved alleles that become R
alleles versus B alleles in the fertilized embryo (Pham et al., 2019; Adolfi et al.,
2020). Paternal deposition of Cas9 in the fertilized embryo is also possible and
may be important. Fitness costs must be considered, including costs due to the H
and B (or R2) alleles, especially when no copy of a functional target gene is
Laboratory cage studies are useful for estimating the parameters of
population genetic models. These studies fall into two categories: (i) crossing
experiments, in which mosquitoes having different genotypes are crossed and
marker phenotypes (and corresponding genotypes) of offspring are tallied (Kyrou
et al., 2018), and (ii) cage experiments, in which populations are monitored over
several generations and the time-series of marker phenotypes (and hence
genotypes) provides insights into their generating inheritance and fitness
processes (Pollegioni et al., 2020; Adolfi et al., 2020). Crossing experiments may
be used to directly estimate parameters such as cleavage and HDR rates, while
large cage studies are useful to estimate fitness effects and to refine estimates of
rates of resistance allele generation, including their fitness effects. Both
approaches also allow 95% confidence or credible intervals to be estimated for
In addition to single-locus homing-based gene drives, multi-locus gene
drives are important to consider as many have properties that would enable them
to serve as intermediate technologies in a phased release pipeline (Li et al., 2020),
or as systems to remediate transgenes from the environment following a trial
period (Xu et al., 2020). For instance, in split drive systems, transient drive
activity is achieved by locating the Cas9 and guide RNA (gRNA) components at
separate loci (Li et al., 2020). Drive occurs at the gRNA locus when the Cas9 and
gRNA alleles co-occur in an organism; but this effect is transient as the Cas9
allele is gradually eliminated from the population due to a fitness cost, the two
alleles segregate across generations, and the gRNA allele is also gradually
eliminated due to a fitness cost. Modeling the population genetics of these
systems requires many more possible genotypes and crosses to be considered, as
the number of possible genotypes multiplies across loci. There are also additional
biological features that sometimes emerge. For instance, a split drive system in
Drosophila melanogaster displays “shadow drive” in addition to regular drive at
the gRNA locus, in which maternally-deposited Cas9 biases inheritance of the
gRNA allele for one extra generation, even if the Cas9 allele is not transmitted to
the offspring (Terradas et al., 2021).
7.2.2 Mosquito Vector Models
Mosquito vector models come in a variety of shapes and sizes, reflecting
differences in the population of interest and motivating questions. For instance, a
model describing an island mosquito population will have different requirements
to one describing spread across a region. Investigations requiring seasonality may
include detailed consideration of rainfall (Lambert et al., 2018) and/or
temperature (Beck-Johnson et al., 2013). Notwithstanding, there are basic
ingredients that are common to models of mosquito vectors of malaria. Next, we
discuss these commonalities while highlighting important points of divergence
between models. We pay particular attention to how models address three major
details of mosquito biology: (i) density dependence in the mosquito life cycle, (ii)
mosquito movement behavior, and (iii) mosquito dry season biology.
18.104.22.168 Mosquito life cycle
The first step to building a mosquito population model is to decompose the
mosquito life cycle into distinct life stages. While most models incorporate an
aquatic juvenile and terrestrial adult stage, the inclusion of further life-history
detail is more variable. For Anopheles gambiae s.l, it is well documented that the
juvenile stage is composed of eggs (2-3 days), followed by four larval instars (7-
10 days in total), followed by pupae (2-3 days) (Silver, 2007). Some models treat
these stages distinctly (Lunde et al., 2013; Eckhoff et al., 2017), while others
distinguish eggs from larvae from pupae but lump all larval stages together
(Deredec et al., 2011), or into two larval stages (White et al., 2011), or lump all
the juvenile stages together (North and Godfray, 2018; Ermert et al., 2011).
Adults are typically categorized by sex, and it is common to distinguish unmated
from mated females (Deredec et al., 2011). Among mated females, some models
decompose the stages of the gonotrophic cycle, for instance into host-seeking and
ovipositing sub-stages (North et al., 2013), while others assume all mated females
oviposit a number of eggs each day (Ermert et al., 2011; North and Godfray,
In addition to classifying mosquitoes by life stage, more detailed models
also classify adult mosquitoes by chronological age, which allows consideration
of age-dependent mortality, in particular “senescence,” whereby the mortality rate
increases with age. While senescence is often observed in laboratory conditions
(Dawes et al., 2009; Benedict et al., 2009), there is less evidence that it is
important in natural populations (Clements and Paterson, 1981). Senescence may
be rare in wild mosquito populations because mosquitoes face many age-
independent hazards, including predation, meaning that few individuals live long
enough for age itself to impact mortality. Models of natural mosquito populations,
therefore, tend to assume that adult mosquitoes have a constant mortality rate,
which produces exponentially-distributed lifespans. Female mosquito lifespan is
an important parameter in malaria epidemiology because it affects both vectorial
capacity and the population growth rate (Macdonald, 1957). Several methods are
available to estimate this parameter, including inference from decaying collection
numbers in mark-release-recapture (MRR) studies, and dissections that are able to
estimate the number of gonotrophic cycles that a female mosquito has completed
(Detinova et al., 1945; Polovodova, 1949).
22.214.171.124 Spatial population structure
Spatially-explicit models of mosquito population dynamics are needed to model
the spread of gene drives through spatially-structured populations. Two broad
approaches that have been applied to study this are: (i) metapopulation models,
which consist of a set of randomly mixing populations connected by migration,
and (ii) models that describe the movement of individuals through continuous
space, either using a reaction-diffusion or individual-based approach. The
simplest metapopulation model is a two-patch model, whereby two distinct
populations exchange migrants. The two-patch model has been used to investigate
modifications that are not intended to spread beyond their release population. For
instance, Sudweeks et al. (2019) used a two-patch model to investigate the
potential of gene drives to suppress island populations of invasive rodents by
targeting alleles that are fixed on the island but not present on the mainland.
Various threshold-dependent drive systems have also been studied in this way
(Dhole et al., 2019; Burt and Deredec, 2018; Marshall and Hay, 2012).
Metapopulation models generalize the two-patch model to two or more
randomly mixing populations connected by migration. The most abstract
metapopulation models assume the local populations can be defined by
equilibrium states, such as wildtype, gene drive, or empty, without explicitly
considering individuals within populations (Fig. 7.2A). These models can help to
illustrate some abstract principles, for instance that spatial structure can result in
wildtype and driving genes coexisting in a metapopulation, even when local
Figure 7.2 A population-based metapopulation model describing
the spatial population dynamics of a suppression gene drive allele.
A. It is assumed that the gene drive will rapidly spread to fixation
in wildtype populations (“takeover” events, which occur at rate
meWS for every wildtype patch), while gene drive populations
become extinct more readily than wildtype populations (μs > μw)
and are less efficient at recolonizing empty habitat (δ < 1). Except
for extinction, these processes are all mediated by the migration
rate, m, among populations, and the predicted equilibrium state of
the metapopulation depends critically upon this parameter. B. As
migration rate increases from zero, the metapopulation transitions
from extinct (m < 0.4) to exclusively wildtype (the gene drive
cannot invade, 0.4 < m < 1.52) to coexistence (1.52 < m < 3.9), to
exclusively gene drive (m > 3.9). The model parameters are: e =
1.5, μs = 2, μw = 0.4, and δ = 0.8. Full details of the simulation are
provided in Bull et al. (2019).
coexistence is not possible (Bull et al., 2019). This outcome is predicted to occur
for intermediate rates of migration between local populations. By contrast, low
migration rates are predicted to prevent the gene drive from establishing, while
high rates allow the gene drive to eliminate the wildtype (Fig. 7.2B). While these
models can be instructive, metapopulation models that consider the internal
dynamics of local populations reveal further complexity in how spatial structure
may affect gene drive dynamics in real landscapes (North et al., 2019, 2020).
A variety of models have been created to describe both the metapopulation
and local population dynamics of mosquito vectors. Over a decade ago, the
Skeeter Buster model was created (Magori et al., 2009; Legros et al., 2012) by
extending the CIMSiM model of spatial mosquito ecology (Focks et al., 1995) to
model the spread of gene drive systems through spatially-explicit Ae. aegypti
populations. Soon after, the EMOD malaria model (Eckhoff, 2011) was used to
simulate the spread of homing-based gene drive systems through national-scale
An. gambiae populations (Eckhoff et al., 2017). While both model frameworks
describe mosquito populations on a grid, migration rates between populations
may vary arbitrarily, meaning that the grid may represent a more complex
geographical space. The MGDrivE framework (Sanchez et al., 2020; Wu et al.,
2020) has recently been created to simulate the spread of user-defined gene drive
systems through a network of populations arbitrarily arranged in space, and the
framework of North and Godfray (2018) describes An. gambiae populations
distributed in populations coinciding with human settlements on the basis that An.
gambiae is anthropophilic. The decision on which approach is best to use depends
on a number of factors, including mosquito species, knowledge of the study area,
and available computational power.
Models that describe the movement of gene drive organisms through
continuous space take either a reaction-diffusion or individual-based approach. A
reaction-diffusion framework that describes the spatial spread of gene drives as
traveling waves was proposed by Tanaka et al. (2017) as a spatial generalization
of a population genetics model (Unckless et al., 2015). This work suggested that,
for a drive system with a fitness cost within a certain range (i.e., 0.5 < s < 0.7), the
spread would occur for releases exceeding a critical population density, and a
barrier conferring a selective disadvantage to gene drive organisms could
potentially contain the spread. A reaction-diffusion model of a driving Y
chromosome has been used to investigate additional characteristics of spatial
spread, in particular the speed of spread (Beaghton et al., 2016). Finally, an
individual-based model that describes the spread of gene drive organisms in
continuous space, taking into account life history, was used by North et al. (2013)
to investigate the effects of fine-scale stochasticity and larval and feeding site
densities on gene drive spread. The computational requirements for these types of
individual-based models mean that they are best suited to analyses at small spatial
scales, while reaction-diffusion frameworks can explore less detailed models at
larger spatial scales.
126.96.36.199 Density dependence
As mosquitoes develop from egg to larva to pupa to adult, there are some life-
history processes that occur differently in sparse versus crowded populations.
These are referred to as “density-dependent” processes, and are especially
important to identify and characterize because they act to regulate populations,
preventing them from growing indefinitely. In mosquitoes, there are two life-
history processes that are widely accepted as being density-dependent: (i) larval
development and mortality, as crowding of larvae in pools of water increases
competition for space and resources, and (ii) mating, because the ease at which a
newly-emerged female finds a mate depends on the density of the adult male
population, and sometimes their ability to form swarms (Mozūraitis et al., 2020).
Larval density-dependence is widely regarded as the most significant
factor regulating population size for anopheline mosquitoes, and a number of lab
(Lyimo et al., 1992; Koenraadt and Takken, 2003) and field studies (Gimnig et
al., 2002; Muriu et al., 2013) have sought to quantify this by measuring larval
development and mortality at a range of densities. Based on these studies, three
broad effects of larval crowding have been identified: reduced survival, prolonged
development, and smaller adults. Uneven competition between the four instar
stages has also been observed, with fourth-stage instars predating on first-stage
instars under some circumstances (Koenraadt and Takken, 2003). Impacts on
larval development time and resulting adult size were seen in two field studies,
but the studies disagreed on whether larval density had an impact on mortality
(Gimnig et al., 2002; Muriu et al., 2013).
Theoretical ecologists have classified crowding competition that affects
survival along a spectrum from “contest” to “scramble” (Bellows, 1981). “Contest
competition” arises when some contestants acquire their required resources at the
expense of others who perish. “Scramble competition” arises when resources are
equally shared. The limited empirical evidence suggests that contest competition
is a better model for anopheline larvae (Muriu et al., 2013; White et al., 2011),
and most models use a contest functional form to model larval survival. Under
contest competition, populations converge to a stable size in a given environment,
referred to as the “carrying capacity.” Anopheline larvae tend to develop in
temporary water bodies created by recent rainfall (Gimnig et al., 2001; Shililu et
al., 2003), motivating some models to assume that larval competition reduces with
recent rainfall (Ermert et al., 2011; Lambert et al., 2018; North and Godfray,
2018; Lunde et al., 2013; Wu et al., 2020). Some models include temperature
effects in the contest competition function (Ermert et al., 2011; Lunde et al.,
2013), or include additional effects such as asymmetric competition between
larval instars at different stages (Lunde et al., 2013; Eckhoff et al., 2017). We are
unaware of population models that incorporate density-dependent effects for
larval development time or resulting adult size. The difficulty of including these
factors is not so much building the model as estimating the parameters from
limited data. We advocate for more research to deepen our understanding of these
While larval competition is an example of negative density dependence,
mating is an example of positive density dependence, as female mosquitoes find
mates more easily at higher population densities (Moziaraitis et al., 2020). As
such, density-dependent mating is unlikely to be important in large populations,
where most females will mate within a day or two of emerging; however, it may
be important in small populations that could be driven to extinction if males
become so rare that most females fail to mate, an example of an Allee effect
(Courchamp et al., 1999). This may be important in highly seasonal environments
where population density becomes very low in the dry season, and in populations
suppressed by suppression gene drive systems. Density-dependent mating can be
incorporated into models by assuming females mate at slower rates in smaller
populations leading to a significant risk of death before finding a mate (North and
188.8.131.52 Movement ecology
Models of mosquito movement are crucial to gain an informed prediction of how
transgenes may spread spatially. Understanding of mosquito movement patterns is
limited due to the fact that mosquito flight is difficult to observe directly, and so
movement patterns are inferred from indirect evidence, primarily MRR studies
and genetic data. In MRR studies, dispersal of captured and released mosquitoes
is inferred from their recapture locations. These studies are best suited to inferring
small-scale movement patterns, and typically take place within a single village,
although a handful of experiments have recaptured mosquitoes outside the release
village, allowing the frequency of inter-village movements to be estimated
(Thomson et al., 1995; Taylor et al., 2001; Costantini et al., 1996). These studies
indicate that movements between neighboring villages occur at rates in the region
of 0.5–3% per adult mosquito per day (North and Godfray, 2018), though caution
is needed in extrapolating from so few data, and such rates will be highly
dependent on the local geography and distance between villages.
Little is known about the limits of local mosquito flight distances
(Verdonschot and Besse-Lototskaya, 2014), or about long-range movements that
may occur if adult mosquitoes “hitchhike” in high-altitude seasonal winds
(Huestis et al., 2019) or in human vehicles. These movements are not suited to
MRR studies, however genetic or genomic data could be leveraged to obtain some
estimates of their scale and rates. For instance, the An. gambiae 1000 Genomes
Project has shown that insecticide-resistant haplotypes have, in recent decades,
spread over large parts of sub-Saharan Africa from a small number of origins
(Anopheles gambiae 1000 Genomes Consortium et al., 2017). Other approaches
to infer intermediate and large-scale movement based on genetic data include
Wright’s fixation index, FST, using a variety of genetic markers such as single
nucleotide polymorphisms (SNPs) and repeat sequences such as microsatellites
(Marsden et al., 2013; Taylor et al., 2001), and novel methods utilizing the theory
of identity-by-descent, which provide an estimate of effective dispersal averaged
over several generations (Novembre and Slatkin, 2009). We hope that the
growing interest in gene drive technology will spur further studies of anopheline
genomic data, and further MRR experiments, to gain additional insights into both
fine-scale and large-scale movement patterns.
184.108.40.206 Dry season ecology
Much of sub-Saharan Africa undergoes seasonal cycling between dry and rainy
conditions; a duality that is particularly pronounced in the Sahel where the dry
season may last up to ten months (Nicholson, 2013). Sahelian dry conditions are
hostile to mosquito populations, which seem to disappear during these times only
to reappear at the onset of each rainy season (Dao et al., 2014). How mosquito
species achieve this remains the subject of debate, despite decades of research.
The most prominent explanations are: (i) adult mosquitoes aestivate by hiding in
shelters and re-emerge when rains begin (Omer and Cloudsley-Thompson, 1970;
Dao et al., 2014), (ii) extinct areas are recolonized each year by adult mosquitoes
dispersing from nearby locations with permanent larval habitat (Ramsdale et al.,
1970; Jawara et al., 2008), and (iii) adult mosquitoes recolonize after being
carried large distances by high-altitude seasonal winds (Garrett-Jones, 1962;
Huestis et al., 2019). Evidence for each of these hypotheses, which are not
mutually exclusive, is limited to indirect observations. For example, the recapture
of a single An. gambiae female that was marked in the previous rainy season in a
village in Mali is suggestive of aestivation (Lehmann et al., 2010), while the
capture of small numbers of An. coluzzii females on sticky panels that were raised
to 40–290 meters nightly in Mali are suggestive of wind-borne migration (Huestis
et al., 2019). Genomic analyses offer hope for further insights.
To investigate how dry season ecology may influence a gene drive vector
suppression program, North et al. implemented each of these hypotheses within a
model of gene drive in West Africa (North et al., 2019, 2020). A number of subtle
effects of dry season ecology were reported. For example, simulations suggest
long-distance migration speeds up the spread of gene drives to remote locations,
yet may also facilitate the recolonization of populations that have been extirpated
by the drive allele in the case of a population suppression strategy. Aestivation
was generally predicted to slow the rate of gene drive spread because it results in
fewer active mosquito generations per year (it was assumed that mosquitoes
aestivate in all locations, including those with permanent larval habitat).
Additional modeling could explore the impact of dry season ecology on the use of
different varieties of gene drive systems.
7.2.3 Malaria Transmission Models
Models of disease transmission are becoming increasingly relevant to models of
gene drive, as: (i) the readiness of a gene drive system for field trials will be
determined in 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 (James et al., 2020). Given the
potential for a non-localized gene drive system to spread widely, it has been
acknowledged that drive systems at the trial stage should be expected to cause a
significant reduction in disease transmission. Therefore, readiness for field trials
should be determined by alignment with a TPP that includes the expected impact
on disease transmission (James et al., 2018). Models that incorporate both gene
drive and epidemiological dynamics are also important for the design of
monitoring protocols, so that epidemiological outcomes can be inferred from
entomological field measurements.
Vector-borne disease models can be more complicated than those for
diseases transmitted directly from human to human as they require consideration
of the vector, host, and pathogen. However, the dynamics simplify when disease
progression in humans and mosquitoes is considered in parallel, with the
interaction between the two occurring according to “force of infection” (FOI)
terms, the FOI in humans (per capita rate at which susceptible humans become
infected), λH and the FOI in vectors (per capita rate at which susceptible
mosquitoes become infected), λV. Malaria infection in mosquitoes is reasonably
described by an SEI model (susceptible-exposed-infectious), in which adult
mosquitoes emerge from pupae in the susceptible state, become exposed and
latently infected at a per capita rate equal to λV, and progress to infectiousness
after an “extrinsic incubation period” (EIP) (Ross, 1910; Macdonald, 1957) (Fig.
7.3A). The FOI in mosquitoes is proportional to the fraction of humans that are
infectious. 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 probability of zero (Fig. 7.3B).
The simplest model of human malaria is the Ross-Macdonald model
(Ross, 1910; Macdonald, 1957), in which, alongside the SEI model in mosquitoes,
human disease progression is described by an SIS model (Fig. 7.3A). Here,
humans become infected at rate, λH, and recover at a rate, r. The FOI in humans,
λH, is proportional to the size of the mosquito population and the fraction of
mosquitoes that are infectious. This is a significant simplification of malaria
transmission dynamics and hence may only be used to obtain ballpark estimates
of transmission level. A number of more detailed models have been developed
that concisely describe malaria transmission dynamics and may be used to obtain
more accurate predictions. These include models developed by the malaria
modeling group at Imperial College London (Griffin et al., 2010; Walker et al.,
2016), and the Infectious Disease Modeling Unit at the Swiss Tropical and Public
Health Institute. Important details that contribute to the accuracy of these models
include acquired and maternal immunity, symptomatic and asymptomatic
infection, variable parasite density and superinfection in humans, human age
structure, mosquito biting heterogeneity, and antimalarial drug therapy and
prophylaxis. It is important that these models are calibrated to the setting of
Figure 7.3 Integrating models of gene drive and malaria
transmission. A. In the Ross-Macdonald model of malaria
transmission, susceptible humans (SH) become infected/infectious
(IH) at a rate equal to the force of infection in humans, λH, and
recover at rate r, becoming susceptible again. Female mosquitoes
emerge as susceptible adults (SV), become exposed/latently
infected (EV) at a rate equal to the force of infection in mosquitoes,
λV, and progress to infectiousness (IV) through the extrinsic
incubation period (EIP = 1/γV). The mortality rate, μF, is the same
for female mosquitoes in each of these states. B. Example
simulations from the MGDrivE 2 modeling framework of a split
gene drive system and linked malaria-refractory gene introduced
into an Anopheles gambiae population with implications for
malaria transmission inferred from the Ross-Macdonald model.
Following releases of the drive system at year two, 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 proportion of infected/infectious humans (solid
green line) declines until it reaches near undetectable levels by
year four. Full details of the simulation are provided in Wu et al.
interest, and that historical intervention coverage is accounted for so that modeled
levels of immunity are accurate.
Alongside a detailed model of human malaria transmission, a detailed
model of mosquito life history allows genetic control technologies to be assessed
in combination with currently available vector control tools such as LLINs and
IRS, as well as emerging technologies such as ATSBs. The elaborated feeding
and gonotrophic cycle model proposed by Le Menach et al. (Le Menach et al.,
2007) has been adapted and widely used (Griffin et al., 2010; White et al., 2011;
Chitnis et al., 2010) to describe how LLINs and IRS reduce malaria transmission
by: (i) increasing the death rate of adult female mosquitoes, (ii) increasing the
proportion of bites taken on livestock rather than people, and (iii) decreasing the
egg laying rate by increasing the time taken for female mosquitoes to obtain a
blood meal. With growing awareness of the limitations of LLINs and IRS, interest
has shifted to integrated vector management, and this model has been extended to
include the impact of ATSBs, spatial repellents, spatial spraying, odor-baited
traps, ovitraps, and livestock treated with systemic or topical insecticides
(Marshall et al., 2013; Kiware et al., 2017).
Which malaria transmission model is most suited to the analysis will
depend on a number of factors, including the data available to parameterize the
model and the required specificity of the output. For analyses that seek to provide
qualitative results for a generic setting, the Ross-Macdonald model may suffice;
however, for models being applied to specific settings where interventions history
is available, a parsimonious model such as the Imperial College London model
(Griffin et al., 2010) or OpenMalaria may be well-suited. Models that need to
include a high degree of spatial resolution and interventions such as reactive case
detection or reactive spraying with insecticides may require an individual-based
approach. Comparison of several models can help to build consensus where there
is agreement, and to better understand the consequences of model assumptions
when projections differ (Eaton et al., 2015).
7.3 Model Application
As gene drive mosquito projects transition from lab to field, a wide range of
research questions arise that stand to benefit from modeling input (Fig. 7.4).
Regulatory approval for environmental releases of gene drive mosquitoes will
depend on a demonstration of product safety and efficacy, both of which have
aspects suited to modeling analyses. Product efficacy may be apparent from
laboratory and cage studies; however, modeling analyses allow us to extrapolate
an expected impact to the population level, including impacts on human disease
incidence. Likewise, many questions in an environmental risk assessment (ERA)
may be addressed empirically by laboratory or cage studies, while other risks
Figure 7.4 Models as a means of data integration. As gene drive
mosquito projects progress from lab to field, models may be used
to combine data from disparate sources including gene drive cage
trials, field studies of mosquito vectors, and clinical malaria
incidence from healthcare centers. These data inform models
describing gene drive inheritance, mosquito ecology, and malaria
transmission, which may be combined into an integrated modeling
framework. This integrated framework, or components thereof,
may be used to address a range of project-related modeling
questions regarding gene drive product safety and efficacy, and
planning and analysis of cage trials, field trials, and interventions.
involve complex, interacting factors or become apparent at the population level
are well suited to modeling analyses. Models will also be useful in planning field
trials or interventions of gene drive mosquitoes. In these cases, models can
explore possible outcomes prior to a release being performed based on data from
laboratory or cage experiments and a quantitative understanding of local mosquito
ecology and malaria transmission. We explore these and other model applications
in the following section.
7.3.1 Target Product Profiles
TPPs are valuable planning tools for determining whether a product is likely to
have its desired effect in practice. For low-threshold gene drive systems, TPPs
will likely play a role in deciding whether a product should be advanced from
contained laboratory testing to semi-field or field testing, given the possibility that
transgenes may become established in the local mosquito population following a
release. While some aspects of TPPs for novel genetic technologies may be
addressed empirically with data from molecular biologists, ecologists, and other
specialists, other aspects require a quantitative approach that uses modeling to
integrate data from multiple sources and make population-level inferences
(Carballar-Lejarazú and James, 2017). Target outcomes will be both
entomological, e.g., reducing the number of malaria-competent mosquitoes to less
than 10% of their expected population size over a given time period, and
epidemiological, e.g., reducing clinical malaria incidence by at least 20–50%
within a given timeframe.
Addressing modeling questions related to TPPs entails: (i) defining the
desired outcomes, and (ii) exploring regions of parameter space that achieve
them. Primary outcomes of interest to regulatory agencies are likely to be
epidemiological in nature. At a recent meeting organized by the Foundation for
the National Institutes of Health (FNIH), it was discussed that a 20–50%
reduction in the clinical incidence of malaria will likely be required prior to field
testing of low-threshold gene drive systems in inhabited areas (James et al.,
2020). The eventual incidence target is likely to represent a balance between
demonstrating significant public health benefits, while also having an achievable
goal that will enable the technology to be approved for use. This highlights the
need for models to predict epidemiological impacts prior to a release based on
In addition to the 20–50% reduction in the clinical incidence of malaria,
other desired outcomes discussed at the FNIH meeting on TPPs include: (i) a
minimum duration of epidemiological impact of three years, (ii) an entomological
impact that would result in the required epidemiological impact, perhaps as
measured by vectorial capacity, and (iii) a rate of spread that would produce the
desired epidemiological impact within an acceptable time frame for a field trial
(perhaps within two years) (James et al., 2020). Achievement of these outcomes
depends on the field trial setting, which would be chosen, at least in part, for
consistency with the objectives. TPPs may also include requirements regarding
confinement and remediation, assessments of which benefit from modeling input.
Modeling analyses that support TPPs explore parameter value ranges that
achieve these outcomes. To best scope such analyses, the parameter space capable
of achieving these outcomes should be narrowed down as much as possible based
on data from laboratory gene drive experiments, ecological and epidemiological
characterization of the field site, and release schemes possible given feasible
production capabilities. Construct parameters to be explored include: (i) rates of
cleavage and accurate homology-directed repair, (ii) rates of resistant allele
generation through NHEJ and other mechanisms, (iii) the proportion of resistant
alleles that are in-frame and functional versus out-of-frame or otherwise costly,
(iv) fitness costs of the various homing and resistant alleles, (v) efficacy of the
anti-pathogen effector gene and its robustness to pathogen evolution (for
population replacement strategies), and (vi) levels of standing genetic variation at
the construct target site. Wide ranges of parameter space should be explored to
determine those collectively satisfying TPP criteria. Sensitivity analyses should
also be conducted where there is inadequate data to accurately specify input
parameters. This activity can provide a basis for prioritizing field data to be
collected by entomologists.
Until recently, TPPs for malaria vector control interventions have focused
on mosquito-centric analyses and outcomes. For instance, TPPs for odor-baited
traps and spatial repellents have utilized models of the mosquito life and feeding
cycle and derived outcomes such as the impact on the entomological inoculation
rate (EIR), which measures the number of infective bites that a person receives
per unit time but does not require a detailed understanding of parasite
transmission between mosquitoes and humans (Okumu et al., 2010; Killeen et al.,
2011; Killeen and Moore, 2012). As models of malaria transmission have become
more sophisticated, human-centric analyses and outcomes have become more
common. For instance, the Imperial College London and OpenMalaria models of
malaria transmission have been leveraged to explore the expected impact of
vaccines and novel vector control tools such as ATSBs on clinical malaria
incidence (Hogan et al., 2018; Fraser et al., 2021; Golumbeanu et al., 2021). Such
analyses will be essential for gene drive-modified mosquitoes, given the interest
in regulatory agencies in epidemiological end-points.
7.3.2 Monitoring and Surveillance
As several gene drive mosquito projects advance from contained laboratory
testing to semi-field testing and/or small-scale field trials, there is an urgent need
to assess both: (i) monitoring requirements to assess gene drive establishment and
persistence at the field site, and (ii) surveillance requirements to detect the
unintended spread of gene drive-modified mosquitoes beyond the testing or trial
site. This is of particular importance as, for non-localized gene drive mosquito
projects, the potential scale of intervention means that monitoring and
surveillance are expected to be more costly than research, development, and
deployment, perhaps even several times over.
Regarding surveillance of spread to unintended areas, open questions
related to the optimal density and placement of traps, and frequency of checking
traps, in order to detect gene drive-modified mosquitoes before they become too
numerous to be remediated. Lessons may be learned from invasive species
literature, in which early invasions may be halted through effective surveillance
efforts, and the influence of geography on an organism’s dispersal characteristics
has been shown to be important (Koch et al., 2020). Surveillance program costs
may be estimated based on unit costs for the purchase, distribution, and
monitoring of traps and analysis of trapped mosquitoes. Trade-offs may be
considered between the use of a larger number of cheaper BG-Sentinel traps,
which may require more frequent visitation, or a smaller number of “smart traps,”
such as those being developed by Microsoft Premonition, which is more
expensive but has increased functionality and may require less frequent visitation.
Regarding monitoring for gene drive establishment and persistence at field
sites, lessons may be learned from the experiences of the World Mosquito
Program with small-scale field trials of Wolbachia-transfected mosquitoes
(Hoffmann et al., 2011). An important detail here is the incorporation of
heterogeneity in spatial models, and the design of monitoring schemes capable of
detecting geographic locations having low transgene or Wolbachia frequency. For
low-threshold gene drive systems, monitoring requirements for detecting rare
resistant alleles should also be assessed, as these could greatly compromise
population suppression strategies. For population replacement strategies, a more
pressing concern is the resistance of malaria parasites to the effector gene.
Monitoring program costs may be estimated based on model parameters (e.g.,
density of traps, frequency of monitoring, number of mosquitoes analyzed) and
unit costs for the purchase, distribution, and monitoring of traps and analysis of
7.3.3 Risk and Regulatory Considerations
The first gene drive products to be considered for malaria control will likely
require stringent ERAs. Since field data on gene drives will not exist before
releases begin, evaluation of many potential risks will benefit from evidence
generated through modeling, in addition to evidence from laboratory studies, field
data collection, pre-existing literature, and combinations thereof. One approach to
conducting a rigorous ERA is the method of “problem formulation,” in which a
list of potential harms is generated, each of which is decomposed into a “risk
hypothesis” that describes the causal chain of events by which it may occur
(Raybould, 2006; Devos et al., 2019). This approach has recently been used to
map the potential risks associated with the releases of mosquitoes with a
population suppression gene drive (Connolly et al., 2021). Modeling can support
this process by examining risk hypotheses that involve complex, interacting
factors; for instance, those that are manifest at the population level.
Consider, for instance, the risk hypothesis that a population suppression
gene drive system carried by female mosquitoes induces higher vectorial capacity,
resulting in increased local malaria incidence following a release. A causal
pathway by which this risk may occur is: (i) the transgene becomes common in
the local mosquito population, (ii) transgenic females have a greater vectorial
capacity for malaria, and (iii) elevated vectorial capacity causes a greater increase
in malaria transmission than the reduction in transmission caused by mosquito
population suppression. To assess the probability of this outcome, researchers
would assess the probability of each step in the pathway. Laboratory studies
would determine whether transgenic females do indeed have a higher vectorial
capacity for malaria, and if this is true, modeling would be used to determine the
implications of this for malaria transmission at the population level. Models may
opt to explore the worst-case scenario by combining the largest reasonable
increase in vector competence with the smallest reasonable suppression caused by
the transgene. If malaria incidence is predicted to increase under this scenario, this
will be an important concern for an ERA to consider further.
Many risk hypotheses that modeling may help to inform concern disease
transmission outcomes, since these are generally extrapolated from pre-existing or
generated data (Hosack et al., 2021). Two examples that may apply to either
population suppression or population replacement gene drive strategies include:
(i) the risk that female mosquitoes, if included in a release, could transmit and
increase incidence of another vector-borne disease present in the community, such
as o’nyong’nyong virus or lymphatic filariasis, in the months following a release,
and (ii) the risk that a gene drive system only shows transient success, reducing
malaria immunity in the human population and resulting in increased malaria
susceptibility and incidence upon technology failure. These risks highlight the
importance of developing versatile disease transmission models alongside models
of mosquito ecology and gene drive inheritance.
7.3.4 Cage Trials
The World Health Organization (WHO) recommends a phased approach to the
testing and release of gene drive-modified mosquitoes. Phase one comprises
small-scale laboratory studies followed by testing in larger population cages in a
laboratory setting, while phase two comprises confined field trials (Benedict et al.,
2014). The intermediate step of large cage studies is recommended as this enables
the observation of age-structured mosquito populations that undergo semi-natural
population dynamics, albeit in highly simplified environments. Mosquitoes in
cage studies live their entire lives in these populations, meaning fitness effects of
transgenes may be revealed that are difficult to detect using small-scale laboratory
studies alone. Following WHO guidelines, the Target Malaria project has used
large cage experiments to investigate both self-limiting An. gambiae
modifications (Valerio et al., 2016; Facchinelli et al., 2019; Pollegioni et al.,
2020) and a self-sustaining gene drive system that targets the doublesex gene
required for female fertility (Hammond et al., 2021). Modeling has been useful at
multiple stages of the design and analysis of these cage trials. To assist in
planning, models were constructed from pre-existing information, such as the
results of smaller-scale studies, to predict how cage population dynamics might
depend on the experimental set-up. After the experiments had run their course, the
same models were fitted to the cage data and used to help estimate key model
7.3.5 Field Trial Design
By integrating a fitted model from cage trial data with models of mosquito
ecology and malaria transmission tailored to a candidate field site, an integrated
model can be used to explore potential release scenarios and to contribute to field
trial design. Important considerations for an initial field trial of gene drive-
modified mosquitoes are: (i) whether the measured outcome of interest is
epidemiological, or entomological (with a modeled epidemiological outcome),
and (ii) whether an intermediate drive system such as a split drive (Li et al., 2020)
or an autosomal X-shredder (Facchinelli et al., 2019) be tested first, given
concerns over confinement of non-localized gene drive systems to field sites. As
such, key questions for models to explore are: (i) what release schemes are
achievable and lead to the gene drive mosquito having the intended outcome
within the timeframe of a field trial (1–3 years), and (ii) what checks and balances
need to be put in place to ensure that the gene drive product being trialed is
confined to the field site? Models may also be used to design remediation
strategies following a trial and to help to inform the distribution of traps to
monitor trial progress and confinement objectives.
The first field trial of a novel tool such as a gene drive-modified mosquito
is likely to involve a single release site and accompanying control site. This was
the case for initial trials of Aedes aegypti having the RIDL construct (releases of
insects carrying a dominant lethal allele) (Harris et al., 2012), for trials of ATSBs
to suppress An. gambiae in Mali (Müiler et al., 2010), and for trials of Wolbachia-
infected Ae. aegypti in Queensland, Australia (Hoffmann et al., 2011). In the
event that a trial is successful at a single field site, trials involving a collection of
intervention and control sites may be pursued. For instance, ATSBs were recently
trialed in seven of 14 study villages in Mali (the other seven being control sites)
where LLINs are in widespread use (Traore et al., 2020) and discussions are now
proceeding toward randomized controlled trials (RCTs). For Wolbachia-infected
Ae. aegypti, an RCT was recently conducted in Yogyakarta, Indonesia in which
the intervention was shown to have a statistically significant impact on reducing
dengue incidence (Indriani et al., 2020). Modeling and analysis of RCTs are
statistical in nature, but may be paired with mathematical models, especially at the
7.3.6 Intervention Design
In the event that a gene drive mosquito product is ultimately approved for use, a
number of logistical questions will emerge regarding how it should be deployed.
Past modeling has indicated the spread of gene drives will be affected by
environmental conditions, including the distribution of mosquito resources across
a landscape (North et al., 2013) and seasonality (Lambert et al., 2018; Eckhoff et
al., 2017; North et al., 2020). For instance, North et al. (2013) found that the
establishment of a population suppression gene drive system is more challenging
in a spatially-clustered population as compared to a uniformly-distributed one
because, in the presence of spatial clustering, the drive allele is at risk of locally
extinguishing parts of the population and thereby becoming locally extinct itself.
To prevent this from happening, population suppression gene drive mosquitoes
should be released throughout a landscape rather than at a single site (North et al.,
We anticipate that models will play a critical role in the planning and
implementation of future gene drive mosquito interventions. Models will be
useful in assessing the merits of a variety of release schemes, including: (i) the
frequency, size, and number of releases, (ii) the spatial distribution of releases,
(iii) the life stage of release, and (iv) whether to release males only or also
females with a disease-refractory gene (Sánchez et al., 2020; Winskill et al.,
2014). Additional factors to consider include the logistics of release infrastructure,
e.g., the locations of lab rearing facilities, the rate at which gene drive mosquitoes
can be produced, and transportation from rearing facilities to release sites. As
low-threshold gene drive mosquitoes are self-sustaining, another option to
consider, particularly for population replacement strategies, is sourcing gene drive
mosquitoes from one of the release sites where they have become prevalent and
distributing larvae from these sites widely.
In addition to release logistics, a large component of a gene drive
mosquito intervention will be the accompanying monitoring and surveillance
effort, and modeling will help to inform the distribution of mosquito traps and
frequency of monitoring, as described earlier. Data collected from these traps will
then be used to ensure that the release is proceeding as intended, and to
parameterize and validate the model iteratively. For a large-scale intervention,
rare events such as the generation of uncommon resistance alleles are more likely
to occur, and so surveillance efforts should monitor for these, and models should
be prepared to address their emergence. Models of remediation plans should also
be iteratively updated as an intervention progresses, in the event of unwanted
effects or a shift in public opinion.
As gene drive mosquito projects transition from lab to field in support of the
wider malaria elimination agenda, mathematical and computational modeling is
expected to play a growing role, in parallel with other project components such as
community engagement, regulatory approval, and intervention delivery. In
preparation for this role, it is important that models continue to be developed and
iteratively refined based on the best available data regarding gene drive
inheritance, vector ecology, malaria epidemiology, and other project components.
Key data required to improve these models include those concerning mosquito
life history, habitat distribution, and movement patterns, as well as those
quantifying rare molecular events, such as the formation of drive-resistant alleles
that may occur in large populations. Given the surging interest in the
epidemiological implications of gene drive mosquitoes, transmission dynamics at
locations of interest should be well studied.
Priorities regarding model application will evolve as these projects
progress. Given the potential for low-threshold gene drive systems to spread,
alignment with TPP criteria and an ERA is especially important prior to any open
release. Some of these criteria and risks will require formal mathematical and
computational analyses. Given that monitoring and surveillance are expected to
be a significant cost driver for gene drive mosquito projects, models are needed to
design cost-efficient monitoring strategies to ensure each project is having its
intended effect, as well as cost-efficient surveillance strategies to detect
unintended spread while it can still be remediated. Modeling priorities will then
progress from designing and analyzing cage trials to designing and analyzing field
trials, with the eventual goal of supporting a wide-scale intervention. We foresee
the continued need for modeling efforts to ensure that gene drive mosquito
technology can be deployed safely and effectively in line with regulatory
requirements and the wishes of affected communities, and toward the eventual
goal of malaria eradication.
The authors thank Dr. Héctor M. Sánchez C. for help in preparing Fig. 7.3.
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