Analysis of a Chlamydia Epidemic Model

In this paper, we have developed a five-compartmental epidemic model with Chlamydia infection. We have divided the total population into five classes, namely susceptible, exposed, infective in asymptomatic phase, infective in symptomatic phase and recovered class. The basic reproduction number (R 0 ) is calculated using the next-generation matrix method. The stability analysis of the model shows that the system is locally asymptotically stable at the disease-free equilibrium (DFE) E 0 when R 0 < 1. When R 0 > 1, an endemic equilibrium E 1 exists and the system becomes locally asymptotically stable at E 1 under some conditions. We have also discussed the Chlamydia epidemic model with two treatment controls. An objective functional is considered which is based on a combination of minimizing the number of exposed and infective individuals and the cost of treatment. Then an optimal control pair is obtained which minimizes the objective functional. Our numerical findings are illustrated through computer simulations using MATLAB, which show the reliability of our model from the practical point of view. Epidemiological implications of our analytical findings are addressed critically.