Perturbation and bifurcation analysis of a gonorrhoea dynamics model with control

TL;DR

This paper develops a gonorrhoea transmission model with control measures, analyzing how treatment affects disease stability and bifurcation behavior, demonstrating potential for disease eradication.

Contribution

It introduces a gonorrhoea model incorporating passive immunity and control, analyzing bifurcations and stability, which is a novel approach in understanding disease control dynamics.

Findings

Introduction of control leads to transcritical bifurcation.

Effective reproduction number is sufficiently small for stability.

Disease can be controlled within a limited time.

Abstract

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.