Effects of Sterile Males and Fertility of Infected Mosquitoes on Mosquito-Borne Disease Dynamics

Abstract

By studying an infection-age structured model, we consider the effects of releasing sterile males and the fertility of infected mosquitoes on the mosquito-borne diseases transmission including the extinction of mosquitoes, the elimination and persistence of diseases. Firstly, equivalent integral equations are established to prove the well-posedness of solutions. Then, the main results of disease dynamics are given. By taking chikungunya as a numerical simulation example, an optimal releasing threshold is given according to our presupposed control standard. When the fertility disturbance of infected mosquitoes is small, the high releasing amount plays a main role on the control of the disease; however, when the fertility disturbance is large, the initial distributions and the fertility of infected mosquitoes are the key factors to control the disease. Mathematically, the fertility of infected mosquitoes makes the system have complex dynamics with multiple positive equilibria and bistability.

Keywords: Bistability; Chikungunya; Infection-age; Initial distributions; Releasing strategy.