Modelling releases of sterile mosquitoes with different strategies

On the impact of re-mating and residual fertility on the Sterile Insect Technique efficacy: Case study with the medfly, Ceratitis capitata

The sterile insect technique (SIT) can be an efficient solution for reducing or eliminating certain insect pest populations. It is widely used in agriculture against fruit flies, including the Mediterranean fruit fly (medfly), Ceratitis capitata. The re-mating tendency of medfly females and the fact that the released sterile males may have some residual fertility could be a challenge for the successful implementation of the SIT. Obtaining the right balance between sterility level and sterile male quality (competitiveness, longevity, etc) is the key to a cost-efficient program. Since field experimental approaches can be impacted by many environmental variables, it is difficult to get a clear understanding on how specific parameters, alone or in combination, may affect the SIT efficiency. The use of models not only helps to gather knowledge, but it allows the simulation of a wide range of scenarios and can be easily adapted to local populations and sterile male production. In this study, we consider single- and double-mated females. We first show that SIT can be successful only if the residual fertility is less than a threshold value that depends on the basic offspring number of the targeted pest population, the re-mating rates, and the parameters of double-mated females. Then, we show how the sterile male release rate is affected by the parameters of double-mated females and the male residual fertility. Different scenarios are explored with continuous and periodic sterile male releases, with and without ginger aromatherapy, which is known to enhance sterile male competitiveness, and also taking into account some biological parameters related to females that have been mated twice, either first by a wild (sterile) male and then a sterile (wild) male, or by two wild males only. Parameter values were chosen for peach as host fruit to reflect what could be expected in the Corsican context, where SIT against the medfly is under consideration. Our results suggest that ginger aromatherapy can be a decisive factor determining the success of SIT against medfly. We also emphasize the importance of estimating the duration of the refractory period between matings depending on whether a wild female has mated with a wild or sterile male. Further, we show the importance of parameters, like the (hatched) eggs deposit rate and the death-rate related to all fertile double-mated females. In general, re-mating is considered to be detrimental to SIT programs. However, our results show that, depending on the parameter values of double-mated females, re-mating may also be beneficial for SIT. Our model can be easily adapted to different contexts and species, for a broader understanding of release strategies and management options.

About contamination by sterile females and residual male fertility on the effectiveness of the sterile insect technique. Impact on disease vector control and disease control

The sterile insect technique (SIT) is a technique to control pests and vectors of diseases by releasing mainly sterile males. Several challenges need to be solved before large-scale field application in order to guarantee its success. In this paper we intend to focus on two important issues: residual fertility in released (sterile) males and contamination of each release by sterile females. Indeed, sterile males are never 100% sterile, that is there is always a small proportion, ɛ, of fertile males (sperm of) within the sterile males population. Among the sterile insects that are released, a certain proportion, ϵF, of them are sterile females due to imperfect mechanical sex-separation technique. This can be particularly problematic when arthropod viruses are circulating, because mosquito females, even sterile, are vectors of diseases. Various upper bound values are given in the entomological literature for ϵF and ɛ without clear explanations. In this work, we aim to show that these values are related to the biological parameters of the targeted vector, the sterile insects release rate, and the epidemiological parameters of a vector-borne disease, like Dengue. We extend results studied separately in Aronna and Dumont (2020), Dumont and Yatat-Djeumen (2022). To study the impact of both issues, we develop and study a SIT-entomological-epidemiological mathematical model, with application to Dengue. Qualitative analysis of the model is carried out to highlight threshold values that shape the overall dynamics of the system. We show that vector elimination is possible only when Nɛ<1, where N is the basic-offspring number related to the targeted wild population. To ensure the success of SIT control, we recommend that the issue of residual fertility be addressed as a priority and then that contamination by sterile females be minimized with each release.

Modelling and analysis of periodic impulsive releases of the Nilaparvata lugens infected with wStri-Wolbachia

In this paper, we formulate a population suppression model and a population replacement model with periodic impulsive releases of Nilaparvata lugens infected with wStri. The conditions for the stability of wild-N . l u g e n s -eradication periodic solution of two systems are obtained by applying the Floquet theorem and comparison theorem. And the sufficient conditions for the persistence in the mean of wild N . l u g e n s are also given. In addition, the sufficient conditions for the extinction and persistence of the wild N . l u g e n s in the subsystem without wLug are also obtained. Finally, we give numerical analysis which shows that increasing the release amount or decreasing the release period are beneficial for controlling the wild N . l u g e n s , and the efficiency of population replacement strategy in controlling wild populations is higher than that of population suppression strategy under the same release conditions.

A mosquito population suppression model with a saturated Wolbachia release strategy in seasonal succession

Releasing Wolbachia-infected male mosquitoes to suppress wild female mosquitoes through cytoplasmic incompatibility has shown great promise in controlling and preventing mosquito-borne diseases. To make the release logistically and economically feasible, we propose a saturated release strategy, which is only implemented during the epidemic season of mosquito-borne diseases. Under this assumption, the model becomes a seasonally switching ordinary differential equation model. The seasonal switch brings rich dynamics, including the existence of a unique periodic solution or exactly two periodic solutions, which are proved by using the qualitative property of the Poincaré map. Sufficient conditions are also obtained for determining the stability of the periodic solutions.

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.

Mosquito Control Based on Pesticides and Endosymbiotic Bacterium Wolbachia

Mosquito-borne diseases, such as dengue fever and Zika, have posed a serious threat to human health around the world. Controlling vector mosquitoes is an effective method to prevent these diseases. Spraying pesticides has been the main approach of reducing mosquito population, but it is not a sustainable solution due to the growing insecticide resistance. One promising complementary method is the release of Wolbachia-infected mosquitoes into wild mosquito populations, which has been proven to be a novel and environment-friendly way for mosquito control. In this paper, we incorporate consideration of releasing infected sterile mosquitoes and spraying pesticides to aim to reduce wild mosquito populations based on the population replacement model. We present the estimations for the number of wild mosquitoes or infection density in a normal environment and then discuss how to offset the effect of the heatwave, which can cause infected mosquitoes to lose Wolbachia infection. Finally, we give the waiting time to suppress wild mosquito population to a given threshold size by numerical simulations.

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.

Wolbachia infection enhancing and decaying domains in mosquito population based on discrete models

In this article, we formulate and study a discrete equation model depicting the pattern of Wolbachia infection in a mosquito population. A domain in [Formula: see text] is called a Wolbachia infection enhancing (or decaying) domain if in which the Wolbachia infection frequency of the next generation is always bigger (or smaller) than that of the current generation. We first give a complete analysis of the equivalent Wolbachia infection frequency curves. And then we clearly characterize the Wolbachia infection enhancing domain and decaying domain for all of the parameters, respectively. Finally, some numerical examples are also provided to illustrate our theoretical results.

Implementation of control strategies for sterile insect techniques

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.

Modeling the impact of sterile males on an Aedes aegypti population with optimal control

We use partial differential equations to describe the dynamics of an Aedes aegypti mosquito population on an island, and the effects of a sterile male release. The model includes mosquito movement and an Allee effect to capture extinction events. We apply optimal control theory to identify the release strategy that eliminates the mosquitoes most rapidly, conditional on a limited availability of sterile males. The optimal solution for a single location is to initially release a substantial number of mosquitoes and to subsequently release fewer sterile males proportionally to the decreasing female population. The optimal solution for the whole island is intractable given a constraint on the total daily release of sterile males. The best approximation to the spatial optimal control strategy is to focus on the high mosquito density areas first and then move outwards (in both directions along the periphery of the island), until all areas have been covered, retaining throughout sufficient release intensity to prevent reintroduction in the already cleared areas.

Optimal control for disease vector management in SIT models: an integrodifference equation approach

Vector-borne diseases are a major public health concern inflicting high levels of disease morbidity and mortality. Vector control is one of the principal methods available to manage infectious disease burden. One approach, releasing modified vectors (such as sterile or GM mosquitoes) Into the wild population has been suggested as an effective method of vector control. However, the effects of dispersal and the spatial distribution of disease vectors (such as mosquitoes) remain poorly studied. Here, we develop a novel mathematical framework using an integrodifference equation (discrete in time and continuous in space) approach to understand the impact of releasing sterile insects into the wild population in a spatially explicit environment. We prove that an optimal release strategy exists and show how it may be characterized by defining a sensitivity variable and an adjoint system. Using simulations, we show that the optimal strategy depends on the spatially varying carrying capacity of the environment.

Characterization of Wolbachia enhancing domain in mosquitoes with imperfect maternal transmission

A novel method to reduce the burden of dengue is to seed wild mosquitoes with Wolbachia-infected mosquitoes in dengue-endemic areas. Concerns in current mathematical models are to locate the Wolbachia introduction threshold. Our recent findings manifest that the threshold is highly dependent on the initial population size once Wolbachia infection alters the logistic control death rate of infected females. However, counting mosquitoes is beyond the realms of possibility. A plausible method is to monitor the infection frequency. We propose the concept of Wolbachia enhancing domain in which the infection frequency keeps increasing. A detailed description of the domain is presented. Our results suggest that both the initial population size and the infection frequency should be taken into account for optimal release strategies. Both Wolbachia fixation and extinction permit the oscillation of the infection frequency.

Modeling the spreading and interaction between wild and transgenic mosquitoes with a random dispersal

Due to recent advances in genetic manipulation, transgenic mosquitoes may be a viable alternative to reduce some diseases. Feasibility conditions are obtained by simulating and analyzing mathematical models that describe the behavior of wild and transgenic populations living in the same geographic area. In this paper, we present a reaction-diffusion model in which the reaction term is a nonlinear function that describes the interaction between wild and transgenic mosquitoes, considering the zygosity, and the diffusive term that represents a nonuniform spatial spreading characterized by a random diffusion parameter. The resulting nonlinear system of partial differential equations is numerically solved using the sequential operator splitting technique, combining the finite element method and Runge-Kutta method. This scheme is numerically implemented considering uncertainty in the diffusion parameters of the model. Several scenarios simulating spatial release strategies of transgenic mosquitoes are analyzed, demonstrating an intrinsic association between the transgene frequency in the total population and the strategy adopted.

Diffusing wild type and sterile mosquitoes in an optimal control setting

This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations.

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.

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 Wolbachia infection in a sex-structured mosquito population carrying West Nile virus

Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number [Formula: see text] is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.