Mathematical analysis of a Chlamydia trachomatis with nonlinear incidence and recovery rates

Abstract

Chlamydia, one of the commonest sexually transmitted infections (STIs), remain a public health concern in both underdeveloped and developed countries of the world. Chlamydia has caused worrying public health consequences hence much research work is needed to check the spread of the disease in the population. In this paper, a mathematical model for Chlamydia is developed and analyzed with nonlinear incidence and recovery rates. Qualitative analysis of the model shows that the disease-free equilibrium is locally asymptotically stable using the method of linearization. Further, using the comparison theorem method, the disease-free equilibrium is found to be globally asymptotically stable whenever the associated reproduction number is less than unity. Furthermore, mathematical analysis of the reproduction number shows that the intervention levels and the maximum per capita recovery rate due to effective treatment has a significant impact in reducing the burden of Chlamydia in the population. Numerical results show a relationship between the transmission rate, intervention levels, maximum per capita recovery rate and the reproduction number. Sensitivity analysis was conducted on the parameters connected to the reproduction number, Rc and results reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the transmission rate, intervention levels and the maximum per capita recovery rate. These parameters need to be checked by healthcare policy makers if the disease must be controlled in the population.