Global Stability Analysis of a General Model of Zika Virus

Abstract

Mathematical models of Zika virus dynamics are relatively new, and they mostly focus on either vector and horizontal, or vector and vertical transmission only. In this work,we first revisit a recent model that considers vector and vertical transmission, and we provide an alternative proof on the global stability of the disease-free equilibrium point. Then, a new and general model is presented which includes vector, horizontal and vertical transmission. For this new model, existence of both a disease-free and an endemic equilibrium is studied. Using matrix and graph-theoretic methods, appropriate Lyapunov functions are constructed and results on the global stability properties of both equilibria are established.

Keywords

• disease epidemics
• dynamical systems
• global stability
• lyapunov functions
• 37n25
• 92d25