Author(s)

Rigobert Charles Ngeleja^1*, Livingstone Luboobi², Yaw Nkansah-Gyekye¹

¹School of Computational and Communication Science and Engineering, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania.
²Department of Mathematics, Makerere University, Kampala, Uganda.

Bubonic plague is a serious bacterial disease, mainly transmitted to human beings and rodents through flea bite. However, the disease may also be transmitted upon the interaction with the infected materials or surfaces in the environment. In this study, a deterministic model for bubonic plague disease with Yersinia pestis in the environment is developed and analyzed. Conditions for existence and stability of the equilibrium points are established. Using Jacobian method disease free equilibrium (DFE) point, E⁰ was proved to be locally asymptotically stable. The Metzler matrix method was used to prove that the DFE was globally asymptotically stable when R₀ < 1. By applying Lyapunov stability theory and La Salles invariant principle, we prove that the endemic equilibrium point of system is globally asymptotically stable when R₀ > 1. Numerical simulations are done to verify the analytical predictions. The results show that bubonic plague can effectively be controlled or even be eradicated if efforts are made to ensure that there are effective and timely control strategies.

Disease Free Equilibrium, Endemic Equilibrium Stability Analysis, Bubonic Plague, Pathogens in the Environment

Ngeleja, R. , Luboobi, L. and Nkansah-Gyekye, Y. (2016) Stability Analysis of Bubonic Plague Model with the Causing Pathogen Yersinia pestis in the Environment. Advances in Infectious Diseases, 6, 120-137. doi: 10.4236/aid.2016.63016.