Modelling the dynamics of bubonic plague with Yersinia pestis in the environment

Abstract

Bubonic plague is an infectious disease that is caused by the bacteria Yersinia pestis when it affect a part of circulatory system namely lymphatic system. It is mainly transferred between populations through flea bites. In this paper we develop a deterministic model that includes four compartments namely Human, Rodent, Flea and pathogens in the environment to study the dynamics and spread of bubonic plague. The model is analyzed to determine the role and magnitude of the involvement of the four sub-populations in the transmission and spread of the disease. We use the next generation method to find the disease threshold R0which is then used to examine the local stability of the equilibrium points. A sensitivity analysis is carried out to determine the most, medium and least sensitive model parameters that affect negatively or positively the basic reproduction number. The result call for attention to most sensitive parameter which is the progression rate of flea from susceptible state to infected state (β). Other significant parameters are adequate contact rates (Γfh), (Γhf), (Γfr), (Γfr) and (Γrf); progression rates (α1), (α2), (γ1) and (γ2); and the pathogens in the environment under the condition that the their survival is favored by the environment. The numerical simulation also support the analytical solution which then cement the argument that the fruitful strategy to combat bubonic plague disease will be the one that will consider the factors that have shown to have a significant contribution to the increase of the basic reproduction number.