No file available
To read the file of this research,
you can request a copy directly from the authors.
Minimal cost-time strategies for population replacement using the IIT
Preprints and early-stage research may not have been peer reviewed yet.
Abstract
Vector control plays a central role in the fight against vector-borne diseases and, in particular, arboviruses. The use of the endosymbiotic bacterium Wolbachia has proven effective in preventing the transmission of some of these viruses between mosquitoes and humans, making it a promising control tool. The Incompatible Insect Technique (IIT) consists in replacing the wild population by a population carrying the aforementioned bacterium, thereby preventing outbreaks of the associated vector-borne diseases. In this work, we consider a two species model incorporating both Wolbachia infected and wild mosquitoes. Our system can be controlled thanks to a term representing an artificial introduction of Wolbachia-infected mosquitoes. Under the assumption that the birth rate of mosquitoes is high, we may reduce the model to a simpler one on the proportion of infected mosquitoes. We investigate minimal cost-time strategies to achieve a population replacement both analytically and numerically for the simplified 1D model and only numerically for the full 2D system
ResearchGate has not been able to resolve any citations for this publication.
In the fight against vector-borne arboviruses, an important strategy of control of epidemic consists in controlling the population of the vector, Aedes mosquitoes in this case. Among possible actions, two techniques consist either in releasing sterile mosquitoes to reduce the size of the population (Sterile Insect Technique) or in replacing the wild population by one carrying a bacteria, called Wolbachia, blocking the transmission of viruses from insects to humans. This article addresses the issue of optimizing the dissemination protocol for each of these strategies, in order to get as close as possible to these objectives. Starting from a mathematical model describing population dynamics, we study the control problem and introduce the cost function standing for population replacement and sterile insect technique. Then, we establish some properties of the optimal control and illustrate them with numerical simulations.
International audience
We present a model of infection by Wolbachia of an Aedes aegypti population. This model is designed to take into account both the biology of this infection and any available experimental data obtained in the field. The objective is to use this model for predicting the sustainable introduction of this bacteria. We provide a complete mathematical analysis of the model proposed and give the basic reproduction ratio R0 for Wolbachia. We observe a bistability phenomenon. Two equilibria are asymptotically stable : an equilibrium where all the population is uninfected and an equilibrium where all the population is infected. A third unstable equilibrium exists. We provide an lower bound for the basin of attraction of the desired infected equilibrium. We are in a backward bifurcation situation. The bistable situations occurs with natural biological values for the parameters.
Nous proposons un modèle d'infection par Wolbachia d'une population d'Aedes aegypti. Ce modèle est conçu pour prendre en compte à la fois l'histoire naturelle de cette infection et aussi l'introduction de données disponibles obtenues expérimentalement sur le terrain. Nous donnons un analyse complète du modèle ainsi que le taux de reproduction de base R0 pour Wolbachia. On observe un phénomène de bistabilité. Deux équilibres sont stables : un équilibre où toute la population est non infectée et un équilibre où toute la population est infectée. Un troisième équilibre (instable) existe. On donne des bornes inférieures pour l'équilibre recherché de complète infestation. On est dans une situation de bifurcation rétrograde. Cette situation de bistabilité est obtenue avec les valeurs des paramètres biologiquement normales.
The control of the spread of dengue fever by introduction of the
intracellular parasitic bacterium Wolbachia in populations of the vector Aedes
aegypti, is presently one of the most promising tools for eliminating dengue,
in the absence of an efficient vaccine. The success of this operation requires
locally careful planning to determine the adequate number of individuals
carrying the Wolbachia parasite that need to be introduced into the natural
population. The introduced mosquitoes are expected to eventually replace the
Wolbachia-free population and guarantee permanent protection against the
transmission of dengue to human.
In this study, we propose and analyze a model describing the fundamental
aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes
free of the parasite. We then use feedback control techniques to devise an
introduction protocol which is proved to guarantee that the population
converges to a stable equilibrium where the totality of mosquitoes carry
Wolbachia.
Use of the bacterium Wolbachia is an innovative new strategy designed to break the cycle of dengue transmission. There are two main mechanisms by which Wolbachia could achieve this: by reducing the level of dengue virus in the mosquito and/or by shortening the host mosquito’s lifespan. However, although Wolbachia shortens the lifespan, it also gives a breeding advantage which results in complex population dynamics. This study focuses on the development of a mathematical model to quantify the effect on human dengue cases of introducing Wolbachia into the mosquito population. The model consists of a compartment-based system of first-order differential equations; seasonal forcing in the mosquito population is introduced through the adult mosquito death rate. The analysis focuses on a single dengue outbreak typical of a region with a strong seasonally-varying mosquito population. We found that a significant reduction in human dengue cases can be obtained provided that Wolbachia-carrying mosquitoes persist when competing with mosquitoes without Wolbachia. Furthermore, using the Wolbachia strain WMel reduces the mosquito lifespan by at most 10% and allows them to persist in competition with non-Wolbachia-carrying mosquitoes. Mosquitoes carrying the WMelPop strain, however, are not likely to persist as it reduces the mosquito lifespan by up to 50%. When all other effects of Wolbachia on the mosquito physiology are ignored, cytoplasmic incompatibility alone results in a reduction in the number of human dengue cases. A sensitivity analysis of the parameters in the model shows that the transmission probability, the biting rate and the average adult mosquito death rate are the most important parameters for the outcome of the cumulative proportion of human individuals infected with dengue.
Experiments and field trials have shown that the intracellular bacterium Wolbachia may be introduced into populations of the mosquito Aedes aegypti, the primary vector for dengue fever. In the absence of Wolbachia, a mosquito acquiring the dengue virus from an infected human enters an exposed (infected but not infectious) period before becoming infectious itself. A Wolbachia-infected mosquito that acquires dengue (i) may have a reduced lifespan, so that it is less likely to survive the exposed period and become infectious, and (ii) may have a reduced ability to transmit dengue, even if it has survived the exposed period. Wolbachia introduction has therefore been suggested as a potential dengue control measure. We set up a mathematical model for the system to investigate this suggestion and to evaluate the desirable properties of the Wolbachia strain to be introduced. We show that Wolbachia has excellent potential for dengue control in areas where R 0 is not too large. However, if R 0 is large, Wolbachia strains that reduce but do not eliminate dengue transmission have little effect on endemic steady states or epidemic sizes. Unless control measures to reduce R 0 by reducing mosquito populations are also put in place, it may be worth the extra effort in such cases to introduce Wolbachia strains that eliminate dengue transmission completely.
Dengue fever, a viral disease spread by the mosquito Aedes aegypti, affects 50-100 million people a year in many tropical countries. Because the virus must incubate within mosquito hosts for two weeks before being able to transmit the infection, shortening the lifespan of mosquitoes may curtail dengue transmission. We developed a continuous time reaction-diffusion model of the spatial spread of Wolbachia through a population of A. aegypti. This model incorporates the lifespan-shortening effects of Wolbachia on infected A. aegypti and the fitness advantage to infected females due to cytoplasmic incompatibility (CI). We found that local establishment of the Wolbachia infection can occur if the fitness advantage due to CI exceeds the fitness reduction due to lifespan-shortening effects, in accordance with earlier results concerning fecundity reduction. However, spatial spread is possible only if the fitness advantage due to CI is twice as great as the fitness reduction due to lifespan shortening effects. Moreover, lifespan-shortening and fecundity-reduction can have different effects on the speed of wave-retreat. Using data from the literature, we estimated all demographic parameters for infected and uninfected mosquitoes and computed the velocities of spread of infection. Our most optimistic estimates suggest that the spatial spread of lifespan-shortening Wolbachia may be so slow that efficient spatial spread would require a prohibitively large number of point releases. However, as these estimates of demographic parameters may not accurately reflect natural conditions, further research is necessary to corroborate these predictions.
Genetic manipulations of insect populations for pest control have been advocated for some time, but there are few cases where manipulated individuals have been released in the field and no cases where they have successfully invaded target populations. Population transformation using the intracellular bacterium Wolbachia is particularly attractive because this maternally-inherited agent provides a powerful mechanism to invade natural populations through cytoplasmic incompatibility. When Wolbachia are introduced into mosquitoes, they interfere with pathogen transmission and influence key life history traits such as lifespan. Here we describe how the wMel Wolbachia infection, introduced into the dengue vector Aedes aegypti from Drosophila melanogaster, successfully invaded two natural A. aegypti populations in Australia, reaching near-fixation in a few months following releases of wMel-infected A. aegypti adults. Models with plausible parameter values indicate that Wolbachia-infected mosquitoes suffered relatively small fitness costs, leading to an unstable equilibrium frequency <30% that must be exceeded for invasion. These findings demonstrate that Wolbachia-based strategies can be deployed as a practical approach to dengue suppression with potential for area-wide implementation.
Dengue fever is the most important mosquito-borne viral disease of humans with more than 50 million cases estimated annually in more than 100 countries. Disturbingly, the geographic range of dengue is currently expanding and the severity of outbreaks is increasing. Control options for dengue are very limited and currently focus on reducing population abundance of the major mosquito vector, Aedes aegypti. These strategies are failing to reduce dengue incidence in tropical communities and there is an urgent need for effective alternatives. It has been proposed that endosymbiotic bacterial Wolbachia infections of insects might be used in novel strategies for dengue control. For example, the wMelPop-CLA Wolbachia strain reduces the lifespan of adult A. aegypti mosquitoes in stably transinfected lines. This life-shortening phenotype was predicted to reduce the potential for dengue transmission. The recent discovery that several Wolbachia infections, including wMelPop-CLA, can also directly influence the susceptibility of insects to infection with a range of insect and human pathogens has markedly changed the potential for Wolbachia infections to control human diseases. Here we describe the successful transinfection of A. aegypti with the avirulent wMel strain of Wolbachia, which induces the reproductive phenotype cytoplasmic incompatibility with minimal apparent fitness costs and high maternal transmission, providing optimal phenotypic effects for invasion. Under semi-field conditions, the wMel strain increased from an initial starting frequency of 0.65 to near fixation within a few generations, invading A. aegypti populations at an accelerated rate relative to trials with the wMelPop-CLA strain. We also show that wMel and wMelPop-CLA strains block transmission of dengue serotype 2 (DENV-2) in A. aegypti, forming the basis of a practical approach to dengue suppression.
Wolbachia are maternally inherited intracellular bacterial symbionts that are estimated to infect more than 60% of all insect species. While Wolbachia is commonly found in many mosquitoes it is absent from the species that are considered to be of major importance for the transmission of human pathogens. The successful introduction of a life-shortening strain of Wolbachia into the dengue vector Aedes aegypti that halves adult lifespan has recently been reported. Here we show that this same Wolbachia infection also directly inhibits the ability of a range of pathogens to infect this mosquito species. The effect is Wolbachia strain specific and relates to Wolbachia priming of the mosquito innate immune system and potentially competition for limiting cellular resources required for pathogen replication. We suggest that this Wolbachia-mediated pathogen interference may work synergistically with the life-shortening strategy proposed previously to provide a powerful approach for the control of insect transmitted diseases.
The mosquito Aedes aegypti was recently transinfected with a life-shortening strain of the endosymbiont Wolbachia pipientis (wMelPop) as the first step in developing a biocontrol strategy for dengue virus transmission. In addition to life-shortening, the wMelPop-infected mosquitoes also exhibit increased daytime activity and metabolic rates. Here we sought to quantify the blood-feeding behaviour of Wolbachia-infected females as an indicator of any virulence or energetic drain associated with Wolbachia infection.
In a series of blood-feeding trials in response to humans, we have shown that Wolbachia-infected mosquitoes do not differ in their response time to humans, but that as they age they obtain fewer and smaller blood meals than Wolbachia-uninfected controls. Lastly, we observed a behavioural characteristic in the Wolbachia infected mosquitoes best described as a "bendy" proboscis that may explain the decreased biting success.
Taken together the evidence suggests that wMelPop infection may be causing tissue damage in a manner that intensifies with mosquito age and that leads to reduced blood-feeding success. These behavioural changes require further investigation with respect to a possible physiological mechanism and their role in vectorial capacity of the insect. The selective decrease of feeding success in older mosquitoes may act synergistically with other Wolbachia-associated traits including life-shortening and viral protection in biocontrol strategies.
Effective vector control, and more specifically mosquito control, is a complex and difficult problem, as illustrated by the continuing prevalence (and spread) of mosquito-transmitted diseases. The sterile insect technique and similar methods control certain agricultural insect pest populations in a species-specific, environmentally sound, and effective manner; there is increased interest in applying this approach to vector control. Such an approach, like all others in use and development, is not a one-size-fits-all solution, and will be more appropriate in some situations than others. In addition, the proposed release of pest insects, and more so genetically modified pest insects, is bound to raise questions in the general public and the scientific community as to such a method's efficacy, safety, and sustainability. This article attempts to address these concerns and indicate where sterile-insect methods are likely to be useful for vector control.
In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing sufficient conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with the releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, under which the release size is adjusted in accordance with the wild population size estimate. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.
Vector control is critical to limit the circulation of vector-borne diseases, like chikungunya, dengue or zika, which have become important issues around the world. Among them, the Sterile Insect Technique (SIT) and the Incompatible Insect Technique (IIT) have recently aroused a renewed interest. In this paper we derive and study a minimalistic mathematical model designed for Aedes mosquito population elimination by SIT/IIT. Contrary to most of the previous models, it is bistable in general, allowing simultaneously for elimination of the population and for its survival. We consider different types of releases (constant, periodic or impulsive) and show necessary conditions to reach elimination in each case. We also estimate both sufficient and minimal treatment times. Biological parameters are estimated from a case study of an Aedes polynesiensis population, for which extensive numerical investigations illustrate the analytical results. The applications of this work are two-fold: to help identifying some key parameters that may need further field investigations, and to help designing release protocols.
Genetics can potentially provide new, species-specific, environmentally friendly methods for mosquito control. Genetic control strategies aim either to suppress target populations or to introduce a harm-reducing novel trait. Different approaches differ considerably in their properties, especially between self-limiting strategies, where the modification has limited persistence, and self-sustaining strategies, which are intended to persist indefinitely in the target population and may invade other populations. Several methods with different molecular biology are under development and the first field trials have been completed successfully. Expected final online publication date for the Annual Review of Entomology Volume 59 is January 07, 2014. Please see http://www.annualreviews.org/catalog/pubdates.aspx for revised estimates.
The Sterile Insect Technology (SIT) is a nonpolluting method of control of the invading insects that transmit disease. The method relies on the release of sterile or treated males in order to reduce the wild population of anopheles mosquito. We propose two mathematical models. The first model governs the dynamics of the anopheles mosquito. The second model, the SIT model, deals with the interaction between treated males and wild female anopheles. Using the theory of monotone operators, we obtain dynamical properties of a global nature that can be summarized as follows. Both models are dissipative dynamical systems on the positive cone . The value of the basic offspring number is a forward bifurcation for the model of the anopheles mosquito, with the trivial equilibrium being globally asymptotically stable (GAS) when , whereas becomes unstable and one stable equilibrium is born with well determined basins of attraction when . For the SIT model, we obtain a threshold number of treated male mosquitoes above which the control of wild female mosquitoes is effective. That is, for the equilibrium is GAS. When , the number of equilibria and their stability are described together with their precise basins of attraction. These theoretical results are rephrased in terms of possible strategies for the control of the anopheles mosquito and they are illustrated by numerical simulations.
The chikungunya (CHIK) outbreak that struck La Reunion Island in 2005 was preceded by few human cases of Dengue (DEN), but which surprisingly did not lead to an epidemic as might have been expected in a non-immune population. Both arboviral diseases are transmitted to humans by two main mosquito species, Aedes aegypti and Aedes albopictus. In the absence of the former, Ae. albopictus was the only species responsible for viral transmission on La Reunion Island. This mosquito is naturally super-infected with two Wolbachia strains, wAlbA and wAlbB. While Wolbachia does not affect replication of CHIK virus (CHIKV) in Ae. albopictus, a similar effect was not observed with DEN virus (DENV).
To understand the weak vectorial status of Ae. albopictus towards DENV, we used experimental oral infections of mosquitoes from La Reunion Island to characterize the impact of Wolbachia on DENV infection. Viral loads and Wolbachia densities were measured by quantitative PCR in different organs of Ae. albopictus where DENV replication takes place after ingestion. We found that: (i) Wolbachia does not affect viral replication, (ii) Wolbachia restricts viral density in salivary glands, and (iii) Wolbachia limits transmission of DENV, as infectious viral particles were only detected in the saliva of Wolbachia-uninfected Ae. albopictus, 14 days after the infectious blood-meal.
We show that Wolbachia does not affect the replication of DENV in Ae. albopictus. However, Wolbachia is able to reduce viral infection of salivary glands and limit transmission, suggesting a role of Wolbachia in naturally restricting the transmission of DENV in Ae. albopictus from La Reunion Island. The extension of this conclusion to other Ae. albopictus populations should be investigated.
Dengue fever and dengue haemorrhagic fever are important arthropod-borne viral diseases. Each year, there are ∼50 million dengue infections and ∼500,000 individuals are hospitalized with dengue haemorrhagic fever, mainly in Southeast Asia, the Pacific and the Americas. Illness is produced by any of the four dengue virus serotypes. A global strategy aimed at increasing the capacity for surveillance and outbreak response, changing behaviours and reducing the disease burden using integrated vector management in conjunction with early and accurate diagnosis has been advocated. Antiviral drugs and vaccines that are currently under development could also make an important contribution to dengue control in the future.
Wolbachia are maternally inherited bacteria that induce cytoplasmic incompatibility in mosquitoes, and are able to use these patterns of sterility to spread themselves through populations. For this reason they have been proposed as a gene drive system for mosquito genetic replacement, as well as for the reduction of population size or for modulating population age structure in order to reduce disease transmission. Here, recent progress in the study of mosquito Wolbachia is reviewed. We now have much more comprehensive estimates of the parameters that can affect the spread of Wolbachia through natural populations from low starting frequencies, and for waves of spread to be maintained in the face of partial barriers to gene flow. In Aedes albopictus these dynamics are extremely favourable, with very high maternal transmission fidelity and levels of incompatibility recorded. Correspondence between measurements taken in the lab and field is much better than in the Drosophila simulans model system. Important research goals are also discussed, including Wolbachia transformation, interspecific transfer and the elucidation of the mechanisms of incompatibility and rescue; all will be aided by a wealth of new Wolbachia genome information.
Shape Variation and Optimization
- A Henrot
- M Pierre
A. Henrot and M. Pierre. Shape Variation and Optimization, volume 28 of Tracts in Mathematics. European Mathematical Society, Zürich, 2018.