Human infertility due to undetected asymptomatic chlamydia infections: A mathematical modelling approach

Résumé

Chlamydia remains one of the commonest sexually transmitted infections (STIs) around the world, which has caused infertility and public health concern to many families and communities in both underdeveloped and developed countries. Chlamydia trachomatis has been observed to have negative health consequences in humans hence much research work is needed to avert the ugly trend of the disease in the population. In this work, a mathematical model for chlamydia, which splits the asymptomatic population into detected and undetected asymptomatic population is developed and analyzed. The reproduction number (Rc) was obtained using the next generation method. The model upon qualitative analysis exhibits the phenomenon of forward bifurcation near Rc = 1. The existence of forward bifurcation in the model shows that having the reproduction number less than one is enough pointer to guarantee the elimination of chlamydia in a community no matter the initial sizes of the infected subpopulation. Intuitively, this implies that the disease-free equilibrium of the model whenever Rc < 1 is globally asymptotically stable. Analytical and numerical results shows that the reproduction number (Rc) is a decreasing function of the treatment rate (τ1). Results from sensitivity analysis reveal that the chlamydia transmission rates and treatment rate are the prominent parameters that significantly drive the dynamics of chlamydia in the population. A close attention should be paid on these parameters in order to check the spread of the disease in the population. Numerical simulation results suggest that a low detection rate (10%) of the asymptomatic individuals (i.e., from undetected to detected state) is a potential threat to human
fertility, no matter the level of treatment given to the identified persons and thus not sufficient for Chlamydia elimination in about 40 years time. Further, it is also observed that a high detection rate (70%) of individuals infected with asymptomatic infection (from undetected to detected state) leads to the elimination of undetected asymptomatic individuals with the disease in the population in about 12 years time with the administration of sufficient treatment rate. Hence, identifying
more cases of undetected asymptomatic individuals immediately for treatment will help in reducing human infertility due to chlamydia infections in families and communities. In that light, preventive measures and optimized treatment was introduced into the basic model to formulate the optimal control model. The Pontrayagin′s maximum principle is utilized and the study shows that condom use and optimized treatment could be the best options for curbing the menace of chlamydia in the
family and community cycles.