Lyapunov stability analysis and optimization measures for a dengue disease transmission model

Abstract

In this paper, we study a dengue model governed by an eight-dimensional autonomous system of ordinary differential equations using dynamical system theory. Appropriate Lyapunov functions are used to carry out an extensive investigation of the global asymptotic dynamics of the model around the dengue-free and dengue-present equilibria. The model is shown to exhibit a forward bifurcation phenomenon using Center Manifold Theory. Sensitivity analysis is carried out to determine the relative importance of the model parameters to the spread of the disease. Using optimal control theory, the model is further extended to a nonlinear optimal control model to explore the impact of four time-dependent control variables, namely, personal protection, treatment drug therapy for latently infected individuals, treatment control for symptomatic individuals and insecticide control for mosquito reduction, on dengue disease dynamics in a population. Cost-effectiveness analysis is conducted on various strategies with combinations of at least three optimal controls to determine the least costly and most effective strategy that can be implemented to contain the spread of dengue in a population.