MATHEMATICAL MODELING OF THE DYNAMICS OF INFECTIOUS DISEASES WITH RELAPSE
HALSON OGETO NYABERI *
Department of Mathematics, Kenyatta University, P.O. Box 43844-00100 Nairobi, Kenya.
VICTOR WANGILA WAKWABUBI
Department of Mathematics, Kenyatta University, P.O. Box 43844-00100 Nairobi, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we have formulated a mathematical model based on a series of ordinary dierential equations to study the transmission dynamics of infectious diseases that exhibit relapse. The basic reproduction number of the model was computed using the next generation matrix method. The existence of the equilibrium points of the model was investigated and stability analysis carried out. The disease free equilibrium point was found to be locally asymptotically stable when R0 < 1 and unstable when R0 > 1 and globally asymptotically stable when R0 < 1 and unstable when R0 > 1. The endemic equilibrium point was found to be locally and globally asymptotically stable when R0 > 1. The center manifold theory was used to investigate the type of bifurcation at R0 = 1.
Keywords: Dynamics, relapse, reproduction number, stability.