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.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1515/msds-2019-0002

Rights Information

© 2019 The authors, published by De Gruyter. This work is licensed under the Creative Commons Attribution alone 4.0 License.

Keywords

Disease epidemics, dynamical systems, global stability, Lyapunov functions

Publication Date

1-1-2021

Journal Title

Nonautonomous Dynamical Systems

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