The Stability Analysis of the Mathematical Model of Tuberculosis Transmission Dynamics

Godswill U. Achi, Okafor, J.U, Kenneth Chimereucheya

Abstract: In this paper, we present the stability analysis of the mathematical model of Tuberculosis transmission dynamics based on SEI model. The analysis is derived from the principles of compartmental modeling showing the rates at which susceptible S move to latent class E and to the infectious class I. We used assumption and schematic presentation to get a system of three non-linear ordinary equations that govern the transmission of the disease guided by the work in [3] The steady state solution was computed and the basic reproduction number R_0 was obtained as (2+ (1+P)) / (+) (+). A stability analysis was done and the disease free equilibrium is shown to be stable if (2+ (1+P)) / (+) (+) <1 and unstable if (2+ (1+P)) / (+) (+) >1.

Keywords: Latent infection, Stability Analysis, Disease free equilibrium, Reproduction number and non-linear ordinary equation