A study of the global properties and optimal control of dengue disease transmission model

Abstract

In this work, we formulate a nonlinear system of differential equations that models the transmission dynamics of dengue fever. The model exhibits the classical threshold behavior. We prove that when the basic reproduction number is less than one, the disease-free equilibrium is locally and globally asymptotically stable and when the basic reproduction number is greater than one the endemic equilibrium is globally asymptotically stable under certain conditions. The stability of equilibria is derived through the use of Lyapunov stability theory and LaSalle's invariance principle. In addition we formulate an optimal control problem involving preventive measures, the investment in vaccination of susceptible humans and the investment related to insecticide treatment. Numerical simulations are provided to illustrate the theoretical results.