Perturbation and bifurcation analysis of a gonorrhoea dynamics model with control

A model for the transmission dynamics of gonorrhoea with control incorporating passive immunity is formulated. We show that introduction of treatment or control parameters leads to transcritical bifurcation. The backward bifurcation coefficients were calculated and their numerical perturbation results to different forms of equilibria. The calculated effective reproduction number of the model with control is sufficiently small. This implies asymptotically stability of the solution, thus, the disease can be controlled in a limited time.