MATHEMATICAL MODEL OF TUBERCULOSIS (TB) TRANSMISSION DYNAMICS INCORPORATING TREATMENT, ISOLATION AND VACCINATION

Abstract

In this thesis, we developed and analysed a mathematical model of Tuberculosis (TB) transmission dynamics incorporating treatment, isolation and vaccination. The total size of the population was partitioned into seven compartments. The model has two equilibria; the Diseases-Free Equilibrium (D.F.E) and Endemic Equilibrium (E.E). The equilibrium states were obtained for their stability relatively to the effective reproduction number. The result shows that, the disease-free equilibrium state was stable and the criteria for stability of the endemic equilibrium state are established. This thesis was able to show that the Tuberculosis (TB) infectious free equilibrium is locally and globally

asymptotically stable if

R0



1

. Using





0.075

,

m



0.300

,

i.

20

and N t   209,

042, 603,

S (t)  5000,

1850

1700 the number of quarantine human individual decreases

as the rate at which quarantine that becomes infected increases. The analytical solution was obtained using Homotopy perturbation Method (HPM) and effective reproduction number was computed in order to measure the relative impact for individual or combined intervention for effective disease control. Numerical simulations of the model show that, the combination of isolation and vaccination is the most effective way to combat the epidemiology of Tuberculosis (TB) virus.