Analysis of a delayed Chlamydia epidemic model with pulse vaccination

Abstract

In this paper, we have considered a dynamical model of Chlamydia disease with varying total population size, saturation incidence rate and discrete time delay to become infectious. It is assumed that there is a time lag (τ) to account for the fact that an individual infected with bacterium Chlamydia trachomatis is not infectious until after some time after exposure. The probability that an individual remains in the latency period (exposed class) at least t time units before becoming infectious is given by a step function with value 1 for 0⩽t<τ and value zero for t>τ. The probability that an individual in the latency period has survived is given by e-μτ, where μ denotes the natural mortality rate in all epidemiological classes. Pulse vaccination is an effective and important strategy for the elimination of infectious diseases and so we have analyzed this model with pulse vaccination. We have defined two positive numbers R1 and R2. It is proved that there exists an infection-free periodic solution which is globally attractive if R1<1 and the disease is permanent if R2>1. Our analytical findings are illustrated through computer simulation using MATLAB, which show the reliability of our model from the epidemiological point of view.