Optimal control of Chlamydia model with vaccination

Abstract

In this work, a vaccination model for Chlamydia trachomatis with cost-effectiveness optimal control analysis is developed and analyzed. The disease free equilibrium of model is shown to be locally asymptotically stable when the reproduction number is less than unity. The disease-free equilibrium of the model was proven not to be globally asymptotically stable. The model is also shown to undergo the phenomenon of backward bifurcation when the associated reproduction number is less than unity. The necessary conditions for the existence of optimal control and the optimality system for the model are established using the Pontryagin’s Maximum Principle. Global Sensitivity analysis is also carried out to determine parameters which most affect the dynamics of the disease, when the reproduction number, exposed, infectious and treated populations are used as response functions. The parameters that strongly drive the dynamics of the disease when the infectious class is used as the response function are the natural death rate \(\mu \), the treatment failure rate \(\varphi \), and the fraction of people that failed treatment p. Simulations of the optimal control system reveal that the strategy that combines Chlamydia trachomatis prevention and treatment is the most cost-effective strategy in the fight against the disease.