Mathematical Analysis of a Non-Smooth Mosquitoes Control Model

Abstract

The sterilization method (SM) is a promising strategy for preventing the escalation of dengue fever, zika and malaria through controlling mosquitoes. A fractional-order SM non-smooth Filippov system with threshold policy control is proposed, which entails sterile mosquitoes releasing to control the population of wild mosquitoes. If the density of the wild population falls below a certain threshold, sterile release is prohibited. However, if the wild population exceeds the threshold, sterile mosquitoes are released. The dynamics of this model, including various types of equilibria existence and their stability, are investigated analytically and numerically. Sliding mode dynamics and pseudo-equilibrium are obtained by using the Filippov convex method; moreover, boundary node and boundary saddle bifurcations are discovered.