Mathematical Analysis of Efficacy of Condom as a Contraceptive on the Transmission of Chlamydia Disease

Chlamydia disease caused by the Chlamydia trachomatis is one of the major sexually transmitted infectious diseases globally. The progression of this disease has deadly effects cumulating into millions of death. Chlamydia causes numerous complications such as infertility in female, chronic pelvic pain and inflammation. Previous studies did not consider the effects of undetected infected individuals on the dynamic spread of the disease. Hence, this work investigated the effects of undetected infected individuals and efficacy of condom as a contraceptive in the dynamic spread of the disease. A six compartmental model to study the dynamic spread of chlamydia disease was developed using system of ordinary differential equation. The population was divided into susceptible, exposed, infected undetected symptomatic, infected detected symptomatic, infected asymptomatic and recovered individuals. The well-posedness of the model was investigated by the positivity of solution technique. Basic reproduction number (R0) was computed using Next Generation Matrix Method. The endemic equilibrium was investigated by the use of Lyapunov function. The results showed that the disease free equilibrium was stable whenever the basic reproduction number is less than unity (R0<1). The endemic equilibrium was found to be stable as a results of constructed Lyapunov function being negative definite. Numerical analysis showed that increasing in the undetected infected individuals enhanced the spread of the disease. Findings showed that undetected infected individuals played a vital role in the spread of Chlamydia disease. Moreover, using condom as a contraceptive reduced the spread of the disease.