Stability analysis of a class of SIS model with vertical infection rate. (Chinese. English summary) Zbl 07267335

Dou, Zhongli; Wang, Rui

Math. Pract. Theory 50, No. 1, 324-328 (2020).

Summary: This article studies an SIS model with vertical infection rate. It firstly calculates the basic reproduction number and equilibrium of the model, analyzes local asymptotic stability and global stability of the model at the disease-free equilibrium, builds Lyapunov function to prove global stability of the endemic equilibrium. Finally it is concluded that the infectious disease may disappear when the basic reproduction number is less than 1; while the infectious disease may be epidemic and finally develop into an endemic disease when the basic reproduction number is greater than 1.

MSC:

34D20	Stability of solutions to ordinary differential equations
92D30	Epidemiology

Keywords:

basic reproduction number; local asymptotic stability; global stability