Mathematical analysis of a model for Chlamydia and Gonorrhea codynamics with optimal control

Abstract

Abstract A model for Chlamydia trachomatis (CT) and Gonorrhea codynamics, with optimal control analysis is studied and analyzed to assess the impact of targetted treatment for each of the diseases on their co-infections in a population. Analysis of the gonorrhea-only sub-model shows the existence of a stable disease free equilibrium (DFE) and a stable endemic equilibrium (EE) when the associated reproduction number is less than one. In the absence of re-infection, the DFE of the gonorrhea-only sub-model is shown to be globally asymptotically stable when the respective reproduction number is below one. The endemic equilibrium of the gonorrhea-only sub-model is also shown to be globally asymptotically stable when reproduction is greater than one. Applying the Centre Manifold Theory, the complete model is shown to undergo backward bifurcation when the associated reproduction number is less than unity. The optimality system for the co-infection model is established using the Pontryagin’s Maximum Principle. Implementing male CT treatment and male gonorrhea treatment cause a reduction in the total number of females and males co-infected with CT and gonorrhea. Also, implementing male CT treatment and female gonorrhea treatment leads to a decrease in the total number of females and males co-infected with CT and gonorrhea. Moreover, implementing female CT treatment and male gonorrhea treatment averts the highest co-infected cases, in comparison with all the intervention strategies.