TITLE:
Stability Analysis of Bubonic Plague Model with the Causing Pathogen Yersinia pestis in the Environment
AUTHORS:
Rigobert Charles Ngeleja, Livingstone Luboobi, Yaw Nkansah-Gyekye
KEYWORDS:
Disease Free Equilibrium, Endemic Equilibrium Stability Analysis, Bubonic Plague, Pathogens in the Environment
JOURNAL NAME:
Advances in Infectious Diseases,
Vol.6 No.3,
September
16,
2016
ABSTRACT: 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 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.