Global Stability Analysis of a General Model of Zika Virus

Nonautonomous Dynamical Systems

Zhang J.¹  Rebaza J.²  Bessey K.³  Mavis M.⁴ 

[1] Department of Mathematics, Johns Hopkins University;Department of Mathematics, Missouri State University;Department of Mathematics, University of NorthGeorgia;Rosenstiel School of Marine and Atmospheric Science, University of Miami;

关键词: disease epidemics;    dynamical systems;    global stability;    lyapunov functions;    37n25;    92d25;   

DOI  :  10.1515/msds-2019-0002

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown