Global stability for delay SIR epidemic model with vertical transmission

Junli Liu, Tailei Zhang

School of Mathematics and Statistics Xi'an Jiaotong University Xi'an, China.
School of Science Xi'an Polytechnic University Xi'an, China.

DOI: 10.4236/ojapps.2012.24B001                

Abstract

A SIR epidemic model with delay, saturated contact rate and vertical transmission is considered. The basic reproduction number is calculated. It is shown that this number characterizes the disease transmission dynamics: if, there only exists the disease-free equilibrium which is globally asymptotically stable; if, there is a unique endemic equilibrium and the disease persists, sufficient cond- itions are obtained for the global asymptotic stability of the endemic equilibrium.

Keywords

delay; vertical transmission; saturated contact rate; global asymptotic stability; permanence

Conflicts of Interest

The authors declare no conflicts of interest.

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