Global behavior and optimal control of a dengue transmission model with standard incidence rates and self‐protection

Abstract

It takes into account that conscious, susceptible individuals with self‐protection cannot be infected by mosquito bites, a seven‐dimensional dengue transmission model with self‐protection, and two different standard incidence rates are proposed. Our focus is on discussing the global behavior and the optimal control of the model. We first calculate the control reproduction number and determine that if , the model has a unique dengue equilibrium . Furthermore, we obtain the local stability of dengue‐free equilibrium and the dengue equilibrium by using the method of proof by contradiction. By utilizing the limit system of the model and the Lyapunov direct method, we acquire that is globally stable if ; is globally attractive if , and if , the model is weakly persistent with a thorough analysis, and then is globally stable. Finally, in order to minimize investment in dengue transmission, an optimal control strategy with four control variables is presented using Pontryagin's minimum principle.