Modelling pulsed releases for sterile insect techniques: fitness costs of sterile and transgenic males and the effects on mosquito dynamics

Dynamics analysis of stage-structured wild and sterile mosquito interaction impulsive model

In this paper, we study a stage-structured wild and sterile mosquito interaction impulsive model. The aim is to study the feasibility of controlling the population of wild mosquitoes by releasing sterile mosquitoes periodically. The existence of trivial periodic solutions is obtained, and the corresponding local stability and global stability conditions are proved by Floquet theory and Lyapunov stability theorem, respectively. And we prove the existence conditions of non-trivial periodic solutions and their local stability. We can find that the system has the bistable phenomenon in which the trivial periodic solution and the non-trivial periodic solution can coexist under certain threshold conditions. All the results show that the appropriate release period and release amount of sterile mosquitoes can control the wild mosquito population within a certain range and even make them extinct. Finally, numerical simulation verifies our theoretical results.

Existence and stability of two periodic solutions for an interactive wild and sterile mosquitoes model

In this paper, we study the periodic and stable dynamics of an interactive wild and sterile mosquito population model with density-dependent survival probability. We find a release amount upper bound G∗, depending on the release waiting period T, such that the model has exactly two periodic solutions, with one stable and another unstable, provided that the release amount does not exceed G∗. A numerical example is also given to illustrate our results.

All-in-One Mosquito Containers: From the Laboratory to the Release Sites

Integrated vector control programs that use a Sterile Insect Technique approach require the production and release of large numbers of high quality, sterile male insects. In pilot projects conducted worldwide, sterile males are usually kept in containers at low densities until their manual release on the ground. Although the quality of the released insects is high, these containers are only suitable for small-scale projects, given the fact that the manual labor required for release is significant and therefore untenable in large-scale projects. This study will compare and contrast the quality of the males reared in the proposed “all-in-one” containers which considerably reduce both the handling of the insects and the manual labor required for release. As a result, project costs are lower. The design of these “all-in-one” containers incorporates two important features: ventilation and the density of the vertical resting surface. Having evaluated both features, it can be concluded that ventilation does not directly affect the quality of the insects, at least in the range of dimensions tested. However, the quality of the male insects is reduced in relation to an increase in the number of mosquitoes, with 500 being the optimum quantity of mosquitoes per “all-in-one” container.

Demographic feedbacks can hamper the spatial spread of a gene drive

This paper is concerned with a reaction-diffusion system modeling the fixation and the invasion in a population of a gene drive (an allele biasing inheritance, increasing its own transmission to offspring). In our model, the gene drive has a negative effect on the fitness of individuals carrying it, and is therefore susceptible of decreasing the total carrying capacity of the population locally in space. This tends to generate an opposing demographic advection that the gene drive has to overcome in order to invade. While previous reaction-diffusion models neglected this aspect, here we focus on it and try to predict the sign of the traveling wave speed. It turns out to be an analytical challenge, only partial results being within reach, and we complete our theoretical analysis by numerical simulations. Our results indicate that taking into account the interplay between population dynamics and population genetics might actually be crucial, as it can effectively reverse the direction of the invasion and lead to failure. Our findings can be extended to other bistable systems, such as the spread of cytoplasmic incompatibilities caused by Wolbachia.

Impulsive release strategies of sterile mosquitos for optimal control of wild population

To investigate the release strategies of sterile mosquitoes for the wild population control, we propose mathematical models for the interaction between two-mosquito populations incorporating impulsive releases of sterile ones. The long-term control model is first studied, and the existence and stability of the wild mosquito-extinction periodic solution are exploited. Thresholds of the release amount and release period which can guarantee the elimination of the wild mosquitos are obtained. Then for the limited-time control model, three different optimal strategies in impulsive control are investigated. By applying a time rescaling technique and an optimization algorithm based on gradient, the optimal impulsive release timings and amounts of sterile mosquitoes are obtained. Our results show that the optimal selection of release timing is more important than the optimal selection of release amount, while mixed optimal control has the best comprehensive effect.

Mark-release-recapture of male Aedes aegypti (Diptera: Culicidae): Use of rhodamine B to estimate movement, mating and population parameters in preparation for an incompatible male program

Rapid advances in biological and digital support systems are revolutionizing the population control of invasive disease vectors such as Aedes aegypti. Methods such as the sterile and incompatible insect techniques (SIT/IIT) rely on modified males to seek out and successfully mate with females, and in doing so outcompete the wild male population for mates. Currently, these interventions most frequently infer mating success through area-wide population surveillance and estimates of mating competitiveness are rare. Furthermore, little is known about male Ae. aegypti behaviour and biology in field settings. In preparation for a large, community scale IIT program, we undertook a series of mark- release-recapture experiments using rhodamine B to mark male Ae. aegypti sperm and measure mating interactions with females. We also developed a Spatial and Temporally Evolving Isotropic Kernel (STEIK) framework to assist researchers to estimate the movement of individuals through space and time. Results showed that ~40% of wild females captured daily were unmated, suggesting interventions will need to release males multiple times per week to be effective at suppressing Ae. aegypti populations. Males moved rapidly through the landscape, particularly when released during the night. Although males moved further than what is typically observed in females of the species, survival was considerably lower. These unique insights improve our understanding of mating interactions in wild Ae. aegypti populations and lay the foundation for robust suppression strategies in the future.

Incompatible insect techniques for controlling populations of the dengue vector, Aedes aegypti, utilize the mating biology of adult male mosquitoes to achieve suppression through a sterilization process. As the study of Ae. aegypti control has typically focused on adult female mosquitoes, knowledge on male movement, survival and mating interactions in the field is lacking. Here we undertook several mark-release-recapture experiments on adult male Ae. aegypti in Innisfail, Australia, and measured important biological parameters. For the first time in large field experiments, we employed rhodamine B as a marker that when fed to adult males, identified both marked males and the wild females they mated with. We observed males moving further through the landscape, but surviving for a shorter period, than previous measurements undertaken on females in a field setting. A high proportion (~40%) of unmated females suggests individuals are constantly available for mating. As such, sterile male strategies may need to release at regular intervals to achieve effective population suppression. The unique insights provided by this study will assist in designing future sterile male field interventions.

Comparing sterile male releases and other methods for integrated control of the tiger mosquito in temperate and tropical climates

The expansion of mosquito species worldwide is creating a powerful network for the spread of arboviruses. In addition to the destruction of breeding sites (prevention) and mass trapping, methods based on the sterile insect technique (SIT), the autodissemination of pyriproxyfen (ADT), and a fusion of elements from both of these known as boosted SIT (BSIT), are being developed to meet the urgent need for effective vector control. However, the comparative potential of these methods has yet to be explored in different environments. This is needed to propose and integrate informed guidelines into sustainable mosquito management plans. We extended a weather-dependent model of Aedes albopictus population dynamics to assess the effectiveness of these different vector control methods, alone or in combination, in a tropical (Reunion island, southwest Indian Ocean) and a temperate (Montpellier area, southern France) climate. Our results confirm the potential efficiency of SIT in temperate climates when performed early in the year (mid-March for northern hemisphere). In such a climate, the timing of the vector control action was the key factor in its success. In tropical climates, the potential of the combination of methods becomes more relevant. BSIT and the combination of ADT with SIT were twice as effective compared to the use of SIT alone.

Study of the sterile insect release technique for a two-sex mosquito population model

In this paper, to study the large-scale time control and limited-time control of mosquito population in a field, a two-sex mosquito population model with stage structure and impulsive releases of sterile males is proposed. For the large-scale time control, a wild mosquito-free periodic solution is given and conditions under which it is globally stable are obtained by the use of the monotone system theory. Besides, based on the stability analysis, threshold conditions under which the wild mosquito population is eliminated or not are obtained. Then we study three different optimal release strategies for the limited-time control, which takes into account both of the population control level of wild mosquitoes and the economic input. To solve technical problems in optimal impulsive control, a time rescaling technique is applied and the gradients of cost function with respect to all control parameters are obtained. In addition, by the aid of numerical simulation, we get the optimal release amounts and release timings for each release strategy. Our study indicates that the optimal release timing control is superior to the optimal release amount control. However, simultaneous optimal selection of release amount and release timing leads to the best control performance.

Stability analysis in a mosquito population suppression model

In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold [Formula: see text] for the number of sterile mosquitoes and provide a sufficient condition for the origin [Formula: see text] to be globally asymptotically stable based on the threshold [Formula: see text]. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin [Formula: see text] is globally asymptotically stable if and only if the constant number [Formula: see text] of sterile mosquitoes released in the field is above [Formula: see text].

The economic impact and cost-effectiveness of combined vector-control and dengue vaccination strategies in Thailand: results from a dynamic transmission model

BACKGROUND AND AIMS

Dengue fever is a major public health problem in tropical/subtropical regions. Prior economic analyses have predominantly evaluated either vaccination or vector-control programmes in isolation and do not really consider the incremental benefits and cost-effectiveness of mixed strategies and combination control. We estimated the cost-effectiveness of single and combined approaches in Thailand.

METHODS

The impacts of different control interventions were analysed using a previously published mathematical model of dengue epidemiology and control incorporating seasonality, age structure, consecutive infection, cross protection, immune enhancement and combined vector-host transmission. An economic model was applied to simulation results to estimate the cost-effectiveness of 4 interventions and their various combinations (6 strategies): i) routine vaccination of 1-year olds; ii) chemical vector control strategies targeting adult and larval stages separately; iii) environmental management/ public health education and awareness [EM/ PHEA]). Payer and societal perspectives were considered. The health burden of dengue fever was assessed using disability-adjusted life-years (DALYs) lost. Costs and effects were assessed for 10 years. Costs were discounted at 3% annually and updated to 2013 United States Dollars. Incremental cost-effectiveness analysis was carried out after strategies were rank-ordered by cost, with results presented in a table of incremental analysis. Sensitivity and scenario analyses were undertaken; and the impact and cost-effectiveness of Wolbachia was evaluated in exploratory scenario analyses.

RESULTS

From the payer and societal perspectives, 2 combination strategies were considered optimal, as all other control strategies were dominated. Vaccination plus adulticide plus EM/ PHEA was deemed cost-effective according to multiple cost-effectiveness criteria. From the societal perspective, incremental differences vs. adulticide and EM/ PHEA resulted in costs of $157.6 million and DALYs lost of 12,599, giving an expected ICER of $12,508 per DALY averted. Exploratory scenario analyses showed Wolbachia to be highly cost-effective ($343 per DALY averted) vs. other single control measures.

CONCLUSIONS

Our model shows that individual interventions can be cost-effective, but that important epidemiological reductions and economic impacts are demonstrated when interventions are combined as part of an integrated approach to combating dengue fever. Exploratory scenario analyses demonstrated the potential epidemiological and cost-effective impact of Wolbachia when deployed at scale on a nationwide basis. Our findings were robust in the face of sensitivity analyses.

Dynamics of a two-sex model for the population ecology of dengue mosquitoes in the presence of Wolbachia

The release of Wolbachia-infected mosquitoes into the population of wild mosquitoes is one of the promising biological control method for combating the population abundance of mosquitoes that cause deadly diseases, such as dengue. In this study, a new two-sex mathematical model for the population ecology of dengue mosquitoes and disease is designed and used to assess the population-level impact of the periodic release of Wolbachia-infected mosquitoes. Rigorous analysis of the model, which incorporates many of the lifecycle features of dengue disease and the cytoplasmic incompatibility property of Wolbachia bacterium in mosquitoes, reveal that the disease-free equilibrium of the model is locally-asymptotically stable whenever a certain epidemiological threshold, known as the reproduction number of the model (denoted by R_0W), is less than unity. The model is shown, using centre manifold theory, to undergo the phenomenon of backward bifurcation at R_0W=1. The consequence of this bifurcation is that Wolbachia may not persist, or dengue disease may not be effectively-controlled, when R_0W is less than unity. Such persistence and elimination will depend on the initial sizes of the sub-populations of the model. Two mechanisms were identified for which the backward bifurcation phenomenon can be removed. When backward bifurcation does not occur, the associated non-trivial disease-free equilibrium is shown to be globally-asymptotically stable when the reproduction number of the model is less than unity. Numerical simulations, using data relevant to dengue transmission dynamics in northern Queensland, Australia, shows that releasing Wolbachia-infected mosquitoes every three weeks, for a one-year duration, can lead to the effective control of the population abundance of the local wild mosquitoes, and that such effective control increases with increasing number of Wolbachia-infected mosquitoes released (resulting in the reduction of over 90% of the wild mosquito population from their baseline values). Furthermore, simulations show that releasing only adult male Wolbachia-infected mosquitoes provide more beneficial population-level impact (in terms of reducing the population abundance of the wild mosquitoes), in comparison to releasing adult female Wolbachia-infected mosquitoes. Increasing the frequency of Wolbachia release (e.g., from the default release frequency of every three weeks to weekly) does not significantly affect the effectiveness of the Wolbachia-based control program in curtailing the local abundance of the wild mosquitoes. Finally, it was shown that the cytoplasmic incompatibility property of Wolbachia bacterium does not significantly affect the effectiveness of the Wolbachia-based mosquito control strategy implemented in the community.

MATHEMATICAL MODELING OF THE IMPACT OF PERIODIC RELEASE OF STERILE MALE MOSQUITOES AND SEASONALITY ON THE POPULATION ABUNDANCE OF MALARIA MOSQUITOES

This study presents a new mathematical model for assessing the impact of sterile insect technology (SIT) and seasonal variation in local temperature on the population abundance of malaria mosquitoes in an endemic setting. Simulations of the model, using temperature data from Kipsamoite area of Kenya, show that a peak abundance of the mosquito population is attained in the Kipsamoite area when the mean monthly temperature reaches [Formula: see text]. Furthermore, in the absence of seasonal variation in local temperature, our results show that releasing more sterile male mosquitoes (e.g., 100,000) over a one year period with relatively short duration between releases (e.g., weekly, bi-weekly or even monthly) is more effective than releasing smaller numbers of the sterile male mosquitoes (e.g., 10,000) over the same implementation period and frequency of release. It is also shown that density-dependent larval mortality plays an important role in determining the threshold number of sterile male mosquitoes that need to be released in order to achieve effective control (or elimination) of the mosquito population in the community. In particular, low(high) density-dependent mortality requires high(low) numbers of sterile male mosquitoes to be released to achieve such control. In the presence of seasonal variation in local temperature, effective control of the mosquito population using SIT is only feasible if a large number of the sterile male mosquitoes (e.g., 100,000) is periodically released within a very short time interval (at most weekly). In other words, seasonal variation in temperature necessitates more frequent releases (of a large number) of sterile male mosquitoes to ensure the effectiveness of the SIT intervention in curtailing the targeted mosquito population.

Revisiting Alkali Metals As a Tool to Characterize Patterns of Mosquito Dispersal and Oviposition

Mark-recapture methods constitute a set of classical ecological tools that are used to collect information on species dispersal and population size. These methods have advanced knowledge in disparate scientific fields, from conservation biology to pest control. Gathering information on the dispersal of mosquito species, such as Aedes aegypti, has become critical since the recognition of their role as vectors of pathogens. Here, we evaluate a method to mark mosquitoes that exploits the rare alkali metals rubidium (Rb) and caesium (Cs), which have been used previously to mark adult insects through feeding. We revised this method by adding Rb and Cs directly to water in which the immature stages of Ae. aegypti were allowed to develop. We then assessed the effect of Rb- and Cs-enriched water on fitness, survival and bioaccumulation in both adult females and their eggs. Results indicated that Cs had adverse effects on Ae. aegypti, even at low concentrations, whereas Rb at low concentrations had no measured effects on exposed individuals and accumulated at detectable levels in adult females. The method described here relies on passive uptake of Rb during immature stages, which has the benefit of avoiding handling or manipulation of the dispersive adults, which enables purer measurement of movement. Moreover, we demonstrated that Rb was transferred efficiently from the marked females to their eggs. To our knowledge, Rb is the only marker used for mosquitoes that has been shown to transfer vertically from females to eggs. The application of Rb rather than more traditional markers may therefore increase the quality (no impact on released individuals) and quantity (both adults and eggs are marked) of data collected during MR studies. The method we propose here can be used in combination with other markers, such as stable isotopes, in order to maximize the information collected during MR experiments.

(Meta)population dynamics determine effective spatial distributions of mosquito-borne disease control

Recent epidemics of mosquito-borne dengue and Zika viruses demonstrate the urgent need for effective measures to control these diseases. The best method currently available to prevent or reduce the size of outbreaks is to reduce the abundance of their mosquito vectors, but there is little consensus on which mechanisms of control are most effective, or when and where they should be implemented. Although the optimal methods are likely context dependent, broadly applicable strategies for mosquito control, such as how to distribute limited resources across a landscape in times of high epidemic risk, can mitigate (re)emerging outbreaks. We used mathematical simulations to examine how the spatial distribution of larval mosquito control affects the size of disease outbreaks, and how mosquito metapopulation dynamics and demography might impact the efficacy of different spatial distributions of control. We found that the birth rate and mechanism of density-dependent regulation of mosquito populations affected the average outbreak size across all control distributions. These factors also determined whether control distributions favoring the interior or the edges of the landscape most effectively reduced human infections. Thus, understanding local mosquito population regulation and dispersion can lead to more effective control strategies.

Uncovering mechanisms behind mosquito seasonality by integrating mathematical models and daily empirical population data: Culex pipiens in the UK

BACKGROUND

Many mosquito-borne diseases exhibit substantial seasonality, due to strong links between environmental variables and vector and pathogen life-cycles. Further, a range of density-dependent and density-independent biotic and abiotic processes affect the phenology of mosquito populations, with potentially large knock-on effects for vector dynamics and disease transmission. Whilst it is understood that density-independent and density-dependent processes affect seasonal population levels, it is not clear how these interact temporally to shape the population peaks and troughs. Due to this, the paucity of high-resolution data for validation, and the difficulty of parameterizing density-dependent processes, models of vector dynamics may poorly estimate abundances, which has knock-on effects for our ability predict vector-borne disease outbreaks.

RESULTS

We present a rich dataset describing seasonal abundance patterns of each life stage of Culex pipiens, a widespread vector of West Nile virus, at a field site in southern England in 2015. Abundance of immature stages was measured three times per week, whilst adult traps were run four nights each week. This dataset is integrated with an existing delay-differential equation model predicting Cx. pipiens seasonal abundance to improve understanding of observed seasonal abundance patterns. At our field site, the outcome of our model fitting suggests interspecific predation on mosquito larvae and temperature-dependent larval mortality combine to act as the main sources of population regulation throughout the active season, whilst competition for resources is a relatively small source of larval mortality.

CONCLUSIONS

The model suggests that density-independent mortality and interspecific predation interact to shape patterns of mosquito seasonal abundance in a permanent aquatic habitat and we propose that competition for resources is likely to be important where periods of high rainfall create transient habitats. Further, we highlight the importance of challenging population abundance models with data from across all life stages of the species of interest if reliable inferences are to be drawn from these models, particularly when considering mosquito control and vector-borne disease transmission.

Toward Implementation of Mosquito Sterile Insect Technique: The Effect of Storage Conditions on Survival of Male Aedes aegypti Mosquitoes (Diptera: Culicidae) During Transport

Sterile insect technique (SIT) is a promising, environmentally friendly alternative to the use of pesticides for insect pest control. However, implementing SIT with Aedes aegypti (Linnaeus) mosquitoes presents unique challenges. For example, during transport from the rearing facility to the release site and during the actual release in the field, damage to male mosquitoes should be minimized to preserve their reproductive competitiveness. The short flight range of male Ae. aegypti requires elaborate release strategies such as release via Unmanned Aircraft Systems, more commonly referred to as drones. Two key parameters during transport and release are storage temperature and compaction rate. We performed a set of laboratory experiments to identify the optimal temperatures and compaction rates for storage and transport of male Ae. aegypti. We then conducted shipping experiments to test our laboratory-derived results in a 'real-life' setting. The laboratory results indicate that male Ae. aegypti can survive at a broad range of storage temperatures ranging from 7 to 28°C, but storage time should not exceed 24 h. Male survival was high at all compaction rates we tested with a low at 40 males/cm3. Interestingly, results from our 'real-life' shipping experiment showed that high compaction rates were beneficial to survival. This study advances key understudied aspects of the practicalities of moving lab-reared insects into the field and lies the foundation for further studies on the effect of transport conditions on male reproductive fitness.

Optimal control of malaria: combining vector interventions and drug therapies

BACKGROUND

The sterile insect technique and transgenic equivalents are considered promising tools for controlling vector-borne disease in an age of increasing insecticide and drug-resistance. Combining vector interventions with artemisinin-based therapies may achieve the twin goals of suppressing malaria endemicity while managing artemisinin resistance. While the cost-effectiveness of these controls has been investigated independently, their combined usage has not been dynamically optimized in response to ecological and epidemiological processes.

RESULTS

An optimal control framework based on coupled models of mosquito population dynamics and malaria epidemiology is used to investigate the cost-effectiveness of combining vector control with drug therapies in homogeneous environments with and without vector migration. The costs of endemic malaria are weighed against the costs of administering artemisinin therapies and releasing modified mosquitoes using various cost structures. Larval density dependence is shown to reduce the cost-effectiveness of conventional sterile insect releases compared with transgenic mosquitoes with a late-acting lethal gene. Using drug treatments can reduce the critical vector control release ratio necessary to cause disease fadeout.

CONCLUSIONS

Combining vector control and drug therapies is the most effective and efficient use of resources, and using optimized implementation strategies can substantially reduce costs.

Modelling and analysis of impulsive releases of sterile mosquitoes

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.

New revised simple models for interactive wild and sterile mosquito populations and their dynamics

Based on previous research, we formulate revised, new, simple models for interactive wild and sterile mosquitoes which are better approximations to real biological situations but mathematically more tractable. We give basic investigations of the dynamical features of these simple models such as the existence of equilibria and their stability. Numerical examples to demonstrate our findings and brief discussions are also provided.

Limited mobility of target pests crucially lowers controllability when sterile insect releases are spatiotemporally biased

The sterile insect technique (SIT) is a genetic pest control method wherein mass-reared sterile insects are periodically released into the wild, thereby impeding the successful reproduction of fertile pests. In Okinawa Prefecture, Japan, the SIT has been implemented to eradicate the West Indian sweet potato weevil Euscepes postfasciatus (Fairmaire), which is a flightless agricultural pest of sweet potatoes. It is known that E. postfasciatus is much less mobile than other insects to which the SIT has been applied. However, previous theoretical studies have rarely examined effects of low mobility of target pests and variation in the spatiotemporal evenness of sterile insect releases. To theoretically examine the effects of spatiotemporal evenness on the regional eradication of less mobile pests, we constructed a simple two-patch population model comprised of a pest and sterile insect moving between two habitats, and numerically simulated different release strategies (varying the number of released sterile insects and release intervals). We found that spatially biased releases allowed the pest to spatially escape from the sterile insect, and thus intensively lowered its controllability. However, we showed that the temporally counterbalancing spatially biased releases by swapping the number of released insects in the two habitats at every release (called temporal balancing) could greatly mitigate this negative effect and promote the controllability. We also showed that the negative effect of spatiotemporally biased releases was a result of the limited mobility of the target insect. Although directed dispersal of the insects in response to habitats of differing quality could lower the controllability in the more productive habitat, the temporal balancing could promote and eventually maximize the controllability as released insects increased.

Mechanistic model for predicting the seasonal abundance of Culicoides biting midges and the impacts of insecticide control

BACKGROUND

Understanding seasonal patterns of abundance of insect vectors is important for optimisation of control strategies of vector-borne diseases. Environmental drivers such as temperature, humidity and photoperiod influence vector abundance, but it is not generally known how these drivers combine to affect seasonal population dynamics.

METHODS

In this paper, we derive and analyse a novel mechanistic stage-structured simulation model for Culicoides biting midges-the principle vectors of bluetongue and Schmallenberg viruses which cause mortality and morbidity in livestock and impact trade. We model variable life-history traits as functional forms that are dependent on environmental drivers, including air temperature, soil temperature and photoperiod. The model is fitted to Obsoletus group adult suction-trap data sampled daily at five locations throughout the UK for 2008.

RESULTS

The model predicts population dynamics that closely resemble UK field observations, including the characteristic biannual peaks of adult abundance. Using the model, we then investigate the effects of insecticide control, showing that control strategies focussing on the autumn peak of adult midge abundance have the highest impact in terms of population reduction in the autumn and averaged over the year. Conversely, control during the spring peak of adult abundance leads to adverse increases in adult abundance in the autumn peak.

CONCLUSIONS

The mechanisms of the biannual peaks of adult abundance, which are important features of midge seasonality in northern Europe and are key determinants of the risk of establishment and spread of midge-borne diseases, have been hypothesised over for many years. Our model suggests that the peaks correspond to two generations per year (bivoltine) are largely determined by pre-adult development. Furthermore, control strategies should focus on reducing the autumn peak since the immature stages are released from density-dependence regulation. We conclude that more extensive modelling of Culicoides biting midge populations in different geographical contexts will help to optimise control strategies and predictions of disease outbreaks.

Stage-structured wild and sterile mosquito population models and their dynamics

To study the impact of the sterile insect technique and effects of the mosquitoes' metamorphic stage structure on the transmission dynamics of mosquito-borne diseases, we formulate stage-structured continuous-time mathematical models, based on systems of differential equations, for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for the releases of sterile mosquitoes in the models and investigate the model dynamics, including the existence of positive equilibria and their stability. Numerical examples are provided to demonstrate the dynamical features of the models.

Modelling sterile insect technique to control the population of Anopheles gambiae

Background

There is a renewed effort to develop novel malaria control strategies as even well-implemented existing malaria control tools may fail to block transmission in some regions. Currently, transgenic implementations of the sterile insect technique (SIT) such as the release of insects with a dominant lethal, homing endonuclease genes, or flightless mosquitoes are in development. These implementations involve the release of transgenic male mosquitoes whose matings with wild females produce either no viable offspring or no female offspring. As these technologies are all in their infancy, little is known about the relative efficiencies of the various implementations.

Methods

This paper describes agent-based modelling of emerging and theoretical implementations of transgenic SIT in Anopheles gambiae for the control of malaria. It reports on female suppression as it is affected by the SIT implementation, the number of released males, and competitiveness of released males.

Conclusions

The simulation experiments suggest that a late-acting bisex lethal gene is the most efficient of the four implementations we simulated. They demonstrate 1) the relative impact of release size on a campaign’s effectiveness 2) late-acting genes are preferred because of their ability to exploit density dependent larval mortality 3) late-acting bisex lethal genes achieve elimination before their female-killing counterparts.

Fitness cost implications of PhiC31-mediated site-specific integrations in target-site strains of the Mexican fruit fly, Anastrepha ludens (Diptera: Tephritidae)

Site-specific recombination technologies are powerful new tools for the manipulation of genomic DNA in insects that can improve transgenesis strategies such as targeting transgene insertions, allowing transgene cassette exchange and DNA mobilization for transgene stabilization. However, understanding the fitness cost implications of these manipulations for transgenic strain applications is critical. In this study independent piggyBac-mediated attP target-sites marked with DsRed were created in several genomic positions in the Mexican fruit fly, Anastrepha ludens. Two of these strains, one having an autosomal (attP_F7) and the other a Y-linked (attP_2-M6y) integration, exhibited fitness parameters (dynamic demography and sexual competitiveness) similar to wild type flies. These strains were thus selected for targeted insertion using, for the first time in mexfly, the phiC31-integrase recombination system to insert an additional EGFP-marked transgene to determine its effect on host strain fitness. Fitness tests showed that the integration event in the int_2-M6y recombinant strain had no significant effect, while the int_F7 recombinant strain exhibited significantly lower fitness relative to the original attP_F7 target-site host strain. These results indicate that while targeted transgene integrations can be achieved without an additional fitness cost, at some genomic positions insertion of additional DNA into a previously integrated transgene can have a significant negative effect. Thus, for targeted transgene insertions fitness costs must be evaluated both previous to and subsequent to new site-specific insertions in the target-site strain.

Antipathogen genes and the replacement of disease-vectoring mosquito populations: a model-based evaluation

Recently, genetic strategies aimed at controlling populations of disease-vectoring mosquitoes have received considerable attention as alternatives to traditional measures. Theoretical studies have shown that female-killing (FK), antipathogen (AP), and reduce and replace (R&R) strategies can each decrease the number competent vectors. In this study, we utilize a mathematical model to evaluate impacts on competent Aedes aegypti populations of FK, AP, and R&R releases as well as hybrid strategies that result from combinations of these three approaches. We show that while the ordering of efficacy of these strategies depends upon population life history parameters, sex ratio of releases, and switch time in combination strategies, AP-only and R&R/AP releases typically lead to the greatest long-term reduction in competent vectors. R&R-only releases are often less effective at long-term reduction of competent vectors than AP-only releases or R&R/AP releases. Furthermore, the reduction in competent vectors caused by AP-only releases is easier to maintain than that caused by FK-only or R&R-only releases even when the AP gene confers a fitness cost. We discuss the roles that density dependence and inclusion of females play in the order of efficacy of the strategies. We anticipate that our results will provide added impetus to continue developing AP strategies.

A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti

We present a simple mathematical model to replicate the key features of the sterile insect technique (SIT) for controlling pest species, with particular reference to the mosquito Aedes aegypti, the main vector of dengue fever. The model differs from the majority of those studied previously in that it is simultaneously spatially explicit and involves pulsed, rather than continuous, sterile insect releases. The spatially uniform equilibria of the model are identified and analysed. Simulations are performed to analyse the impact of varying the number of release sites, the interval between pulsed releases and the overall volume of sterile insect releases on the effectiveness of SIT programmes. Results show that, given a fixed volume of available sterile insects, increasing the number of release sites and the frequency of releases increases the effectiveness of SIT programmes. It is also observed that programmes may become completely ineffective if the interval between pulsed releases is greater that a certain threshold value and that, beyond a certain point, increasing the overall volume of sterile insects released does not improve the effectiveness of SIT. It is also noted that insect dispersal drives a rapid recolonisation of areas in which the species has been eradicated and we argue that understanding the density dependent mortality of released insects is necessary to develop efficient, cost-effective SIT programmes.

On an integro-differential model for pest control in a heterogeneous environment

Insect pests pose a major threat to a balanced ecology as it can threaten local species as well as spread human diseases; thus, making the study of pest control extremely important. In practice, the sterile insect release method (SIRM), where a sterile population is introduced into the wild population with the aim of significantly reducing the growth of the population, has been a popular technique used to control pest invasions. In this work we introduce an integro-differential equation to model the propagation of pests in a heterogeneous environment, where this environment is divided into three regions. In one region SIRM is not used making this environment conducive to propagation of the insects. A second region is the eradication zone where there is an intense release of sterile insects, leading to decay of the population in this region. In the final region we explore two scenarios. In the first case, there is a small release of sterile insects and we prove that if the eradication zone is sufficiently large the pests will not invade. In the second case, when SIRM is not used at all in this region we show that invasions always occur regardless of the size of the eradication zone. Finally, we consider the limiting equation of the integro-differential equation and prove that in this case there is a critical length of the eradication zone which separates propagation from obstruction. Moreover, we provide some upper and lower bound for the critical length.

Population-level effects of fitness costs associated with repressible female-lethal transgene insertions in two pest insects

Genetic control strategies offer great potential for the sustainable and effective control of insect pests. These strategies involve the field release of transgenic insects with the aim of introducing engineered alleles into wild populations, either permanently or transiently. Their efficacy can therefore be reduced if transgene-associated fitness costs reduce the relative performance of released insects. We describe a method of measuring the fitness costs associated with transgenes by analyzing their evolutionary trajectories when placed in competition with wild-type alleles in replicated cage populations. Using this method, we estimated lifetime fitness costs associated with two repressible female-lethal transgenes in the diamondback moth and olive fly as being acceptable for field suppression programs. Furthermore, using these estimates of genotype-level fitness costs, we were able to project longer-term evolutionary trajectories for the transgenes investigated. Results from these projections demonstrate that although transgene-associated fitness costs will ultimately cause these transgenes to become extinct, even when engineered lethality is repressed, they may persist for varying periods of time before doing so. This implies that tetracycline-mediated transgene field persistence in these strains is unlikely and suggests that realistic estimates of transgene-associated fitness costs may be useful in trialing ‘uncoupled’ gene drive system components in the field.

The role of environmental variables on Aedes albopictus biology and chikungunya epidemiology

Aedes albopictus is a vector of dengue and chikungunya viruses in the field, along with around 24 additional arboviruses under laboratory conditions. As an invasive mosquito species, Ae. albopictus has been expanding in geographical range over the past 20 years, although the poleward extent of mosquito populations is limited by winter temperatures. Nonetheless, population densities depend on environmental conditions and since global climate change projections indicate increasing temperatures and altered patterns of rainfall, geographic distributions of previously tropical mosquito species may change. Although mathematical models can provide explanatory insight into observed patterns of disease prevalence in terms of epidemiological and entomological processes, understanding how environmental variables affect transmission is possible only with reliable model parameterisation, which, in turn, is obtained only through a thorough understanding of the relationship between mosquito biology and environmental variables. Thus, in order to assess the impact of climate change on mosquito population distribution and regions threatened by vector-borne disease, a detailed understanding (through a synthesis of current knowledge) of the relationship between climate, mosquito biology, and disease transmission is required, but this process has not yet been undertaken for Ae. albopictus. In this review, the impact of temperature, rainfall, and relative humidity on Ae. albopictus development and survival are considered. Existing Ae. albopictus populations across Europe are mapped with current climatic conditions, considering whether estimates of climatic cutoffs for Ae. albopictus are accurate, and suggesting that environmental thresholds must be calibrated according to the scale and resolution of climate model outputs and mosquito presence data.

Genetic control of Aedes aegypti: data-driven modelling to assess the effect of releasing different life stages and the potential for long-term suppression

BACKGROUND

Control of the world's most important vector-borne viral disease, dengue, is a high priority. A lack of vaccines or effective vector control methods means that novel solutions to disease control are essential. The release of male insects carrying a dominant lethal (RIDL) is one such approach that could be employed to control Aedes aegypti. To maximise the potential of RIDL control, optimum release strategies for transgenic mosquitoes are needed. The use of field data to parameterise models allowing comparisons of the release of different life-stages is presented together with recommendations for effective long-term suppression of a wild Ae. aegypti population.

METHODS

A compartmental, deterministic model was designed and fitted to data from large-scale pupal mark release recapture (MRR) field experiments to determine the dynamics of a pupal release. Pulsed releases of adults, pupae or a combination of the two were simulated. The relative ability of different release methods to suppress a simulated wild population was examined and methods to maintain long-term suppression of a population explored.

RESULTS

The pupal model produced a good fit to field data from pupal MRR experiments. Simulations using this model indicated that adult-only releases outperform pupal-only or combined releases when releases are frequent. When releases were less frequent pupal-only or combined releases were a more effective method of distributing the insects. The rate at which pupae eclose and emerge from release devices had a large influence on the relative efficacy of pupal releases. The combined release approach allows long-term suppression to be maintained with smaller low-frequency releases than adult- or pupal-only release methods.

CONCLUSIONS

Maximising the public health benefits of RIDL-based vector control will involve optimising all stages of the control programme. The release strategy can profoundly affect the outcome of a control effort. Adult-only, pupal-only and combined releases all have relative advantages in certain situations. This study successfully integrates field data with mathematical models to provide insight into which release strategies are best suited to different scenarios. Recommendations on effective approaches to achieve long-term suppression of a wild population using combined releases of adults and pupae are provided.

Genetic control of Aedes mosquitoes

Aedes mosquitoes include important vector species such as Aedes aegypti, the major vector of dengue. Genetic control methods are being developed for several of these species, stimulated by an urgent need owing to the poor effectiveness of current methods combined with an increase in chemical pesticide resistance. In this review we discuss the various genetic strategies that have been proposed, their present status, and future prospects. We focus particularly on those methods that are already being tested in the field, including RIDL and Wolbachia-based approaches.

Genetic control of mosquitoes

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.

Transient population dynamics of mosquitoes during sterile male releases: modelling mating behaviour and perturbations of life history parameters

The release of genetically-modified or sterile male mosquitoes offers a promising form of mosquito-transmitted pathogen control, but the insights derived from our understanding of male mosquito behaviour have not fully been incorporated into the design of such genetic control or sterile-male release methods. The importance of aspects of male life history and mating behaviour for sterile-male release programmes were investigated by projecting a stage-structured matrix model over time. An elasticity analysis of transient dynamics during sterile-male releases was performed to provide insight on which vector control methods are likely to be most synergistic. The results suggest that high mating competitiveness and mortality costs of released males are required before the sterile-release method becomes ineffective. Additionally, if released males suffer a mortality cost, older males should be released due to their increased mating capacity. If released males are of a homogenous size and size-assortative mating occurs in nature, this can lead to an increase in the abundance of large females and reduce the efficacy of the population-suppression effort. At a high level of size-assortative mating, the disease transmission potential of the vector population increases due to male releases, arguing for the release of a heterogeneously-sized male population. The female population was most sensitive to perturbations of density-dependent components of larval mortality and female survivorship and fecundity. These findings suggest source reduction might be a particularly effective complement to mosquito control based on the sterile insect technique (SIT). In order for SIT to realize its potential as a key component of an integrated vector-management strategy to control mosquito-transmitted pathogens, programme design of sterile-male release programmes must account for the ecology, behaviour and life history of mosquitoes. The model used here takes a step in this direction and can easily be modified to investigate additional aspects of mosquito behaviour or species-specific ecology.

Modelling Aedes aegypti mosquito control via transgenic and sterile insect techniques: endemics and emerging outbreaks

The invasion of pest insects often changes or destroys a native ecosystem, and can result in food shortages and disease endemics. Issues such as the environmental effects of chemical control methods, the economic burden of maintaining control strategies and the risk of pest resistance still remain, and mosquito-borne diseases such as malaria and dengue fever prevail in many countries, infecting over 100 million worldwide in 2010. One environmentally friendly method for mosquito control is the Sterile Insect Technique (SIT). This species-specific method of insect control relies on the mass rearing, sterilization and release of large numbers of sterile insects. An alternative transgenic method is the Release of Insects carrying a Dominant Lethal (RIDL). Our objective is to consider contrasting control strategies for two invasive scenarios via SIT and RIDL: an endemic case and an emerging outbreak. We investigate how the release rate and size of release region influence both the potential for control success and the resources needed to achieve it, under a range of conditions and control strategies, and we discuss advantageous strategies with respect to reducing the release resources and strategy costs (in terms of control mosquito numbers) required to achieve complete eradication of wild-type mosquitoes.

Assessing the feasibility of controlling Aedes aegypti with transgenic methods: a model-based evaluation

Suppression of dengue and malaria through releases of genetically engineered mosquitoes might soon become feasible. Aedes aegypti mosquitoes carrying a conditionally lethal transgene have recently been used to suppress local vector populations in small-scale field releases. Prior to releases of transgenic insects on a wider scale, however, most regulatory authorities will require additional evidence that suppression will be effective in natural heterogeneous habitats. We use a spatially explicit stochastic model of an Ae. aegypti population in Iquitos, Peru, along with an uncertainty analysis of its predictions, to quantitatively assess the outcome of varied operational approaches for releases of transgenic strains with conditional death of females. We show that population elimination might be an unrealistic objective in heterogeneous populations. We demonstrate that substantial suppression can nonetheless be achieved if releases are deployed in a uniform spatial pattern using strains combining multiple lethal elements, illustrating the importance of detailed spatial models for guiding genetic mosquito control strategies.

Mathematical studies on the sterile insect technique for the Chikungunya disease and Aedes albopictus

Chikungunya is an arthropod-borne disease caused by the Asian tiger mosquito, Aedes albopictus. It can be an important burden to public health and a great cause of morbidity and, sometimes, mortality. Understanding if and when disease control measures should be taken is key to curtail its spread. Dumont and Chiroleu (Math Biosc Eng 7(2):315-348, 2010) showed that the use of chemical control tools such as adulticide and larvicide, and mechanical control, which consists of reducing the breeding sites, would have been useful to control the explosive 2006 epidemic in Réunion Island. Despite this, chemical control tools cannot be of long-time use, because they can induce mosquito resistance, and are detrimental to the biodiversity. It is therefore necessary to develop and test new control tools that are more sustainable, with the same efficacy (if possible). Mathematical models of sterile insect technique (SIT) to prevent, reduce, eliminate or stop an epidemic of Chikungunya are formulated and analysed. In particular, we propose a new model that considers pulsed periodic releases, which leads to a hybrid dynamical system. This pulsed SIT model is coupled with the human population at different epidemiological states in order to assess its efficacy. Numerical simulations for the pulsed SIT, using an appropriate numerical scheme are provided. Analytical and numerical results indicate that pulsed SIT with small and frequent releases can be an alternative to chemical control tools, but only if it is used or applied early after the beginning of the epidemic or as a preventive tool.

Modeling the sterile insect technique for suppression of light brown apple moth (Lepidoptera: Tortricidae)

A population model was derived for light brown apple moth, Epiphyas postvittana (Walker) (Lepidoptera: Tortricidae), subject to the sterile insect technique (SIT). The model was parameterized from the literature and from recent laboratory studies conducted in New Zealand and Australia. Relationships were fitted for several model parameters that vary with irradiation dose, allowing the model to simulate effectively complete sterility at 300 Gy through inherited sterility occurring from lower doses. At 300 Gy, the model suggests that eventual population extinction is 95% probable when the ratio of released to wild males in monitoring traps exceeds 6.4. Higher overflooding rates would be required to achieve eradication more rapidly. The optimal release interval, in terms of minimizing the required rate of production of factory moths, is approximately weekly. There is little advantage in releasing males only compared with releasing both sexes. Female-only releases are unlikely to be a useful tool for inherited sterility eradication because there is no reduction in the fertility of F1 offspring. The critical release rate required to halt population increase declines with decreasing irradiation dose, but at doses of < 171 Gy there is a risk that irradiated-lineage moths may form a self-sustaining population, making eradication by SIT alone impossible. The model suggests that a dose of around 200 Gy may be optimal because the resulting inherited sterility would reduce by a third the number of factory moths required compared with 300 Gy.