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 necessary 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 releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, which is adjustable in accordance with reliable estimations of the wild population sizes. Under this control mode, global convergence to the mosquitofree equilibrium is proved on the grounds of another sufficient condition that relates not only the size and frequency of periodic releases but also the frequency of sparse measurements taken on wild populations. 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.

Wolbachia-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become less capable of getting viral infections and transmitting the virus to human hosts. In this paper, we propose an explicit sex-structured population model that describes an interaction of uninfected (wild) male and female mosquitoes and those deliberately infected with wMelPop strain of Wolbachia in the same locality. This particular strain of Wolbachia is regarded as the best blocker of dengue and other arboviral infections. However, wMelPop strain of Wolbachia also causes the loss of individual fitness in Aedes aegypti mosquitoes. Our model allows for natural introduction of the decision (or control) variable, and we apply the optimal control approach to simulate wMelPop Wolbachia infestation of wild Aedes aegypti populations. The control action consists in continuous periodic releases of mosquitoes previously infected with wMelPop strain of Wolbachia in laboratory conditions. The ultimate purpose of control is to find a tradeoff between reaching the population replacement in minimum time and with minimum cost of the control effort. This approach also allows us to estimate the number of Wolbachia-carrying mosquitoes to be released in day-by-day control action. The proposed method of biological control is safe to human health, does not contaminate the environment, does not make harm to non-target species, and preserves their interaction with mosquitoes in the ecosystem.

Wolbachia is a maternally transmitted bacterial symbiont which is known to reduce the vector competence of mosquitoes and other arthropod species. Therefore, Wolbachia-based biocontrol is regarded as a practicable method for prevention and control of dengue and other arboviral infections. In particular, a deliberate infection of Aedes aegypti females with wMelPop Wolbachia strain makes them almost incapable of transmitting dengue and other arboviruses. In this paper, we present and thoroughly analyze a population dynamics model of interaction between wild Aedes aegypti female mosquitoes and those infected with wMelPop Wolbachia strain, which compete for the same vital resources (food, breeding sites, etc.) and share the same locality. Using this model, we demonstrate that the final outcome of the competition essentially depends on the frequency of Wolbachia infection. Further, we apply the optimal control approach and design the control intervention programs based on periodic releases of Wolbachia-carrying females for establishing wMelPop Wolbachia infection in the target locality.

In this paper, we propose and thoroughly analyze the ODE model that describes the competition between wild Aedes aegypti female mosquitoes and those carrying Wolbachia bacterial symbiont in the same locality. Using this model in the context of optimal control, we further propose feasible strategies for replacing the wild population with Wolbachia-carriers.The latter is known as Wolbachia-based biocontrol aimed at prevention of various arboviral infections (such as dengue, chikungunya, and zika diseases), given that Wolbachia drastically reduces the mosquito ability to acquire arboviral infections.

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