Modeling Mosquito Population Suppression Based on Delay Differential Equations

Source abstract

Mosquito-borne diseases are threatening half of the world's population. A novel strategy of disease control is to suppress the mosquito population by releasing male mosquitoes infected by a special strain of Wolbachia. This bacterium induces cytoplasmic incompatibility so that eggs of wild females mated with released males fail to hatch. In this work, we introduce a model of delay differential equations to initiate a study on the mosquito suppression dynamics with the compensation policy that the loss of released males is compensated by new releasing, and the constant policy that a constant amount $c$ of infected males are released each time, $T$ days apart. We find the exact value of the threshold releasing intensity $r^*$ for the compensation policy and provide a reasonably sharp estimate of the threshold constant $c^*$ for the constant policy. In the first case, we also show that the model displays bistability with two stable steady-states and one unstable steady-state when the abundance of released males $R(t)\in (0, r^*)$. Our simulation reveals that some solutions may develop sustained oscillations with increasing magnitudes and suggests the existence of one or more stable periodic solutions. The simulation provides a theoretical support to the observation in the Guangzhou mosquito control program that a 5:1 releasing ratio between the releasing amount and the initial wild male abundance could be an optimal option. It also indicates that the suppression efficacy is insensitive to the waiting days between two consecutive releases. Several open mathematical questions are proposed in hope of stimulating more extensive explorations of the dynamic complexities of the model.