Modelling and analysis of a model for Chlamydia Trachomatis transmission dynamics

Abstract

Chlamydia infection, one of the commonest sexually transmitted infections (STIs), remain a public health challenge in both underdeveloped and developed countries of the world. Chlamydia trachomatis has been observed to have negative health consequences hence much research work is needed to be done to curb the spread of the disease in the population. In this paper, a mathematical model for studying the impact of condom usage and treatment on the transmission dynamics and control of Chlamydia in the population is presented. Qualitative analysis of the model shows that it undergoes the phenomenon of backward bifurcation. In the absence of this phenomenon (which is showntooccurasaresult of the reinfection of recovered individuals), the disease-free equilibrium of the modelis globally asymptotically stable whenever the associated reproduction number is less than unity. Further, for the same scenario as above, it is shown that the unique endemic equilibrium of the model exists whenever the reproduction number is greater than unity. Numerical results show a relationship between the progression rate, treatment rate and the reproduction number. Results from the sensitivity analysis of the model, using the reproduction number, Rc reveal that the top parameters that significantly drive the dynamics of Chlamydia in the population are the efficacy of condoms, condom compliance, a fraction of treated individuals who recover due to effective treatment and treatment rate. Numerical simulations of the model suggest that infected persons after treatment should wait for at least 7 days before engaging in any form of sexual activity or, if not possible use condoms correctly (to avoid reinfection) in order to effectively control the spread of the disease in the population. Keywords:Chlamydia; reproduction number; reinfection; stability; bifurcation