A Mathematical Model of a Tuberculosis Transmission Dynamics Incorporating First and Second Line Treatment

J Andrawus,F.Y Eguda,I.G Usman,T.G Urum,I.M Dibal,G.H Anka,S.I Maiwa

doi:10.4314/jasem.v24i5.29

Abstract

This paper presents a new mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment. We calculated a control reproduction number which plays a vital role in biomathematics. The model consists of two equilibrium points namely disease free equilibrium and endemic equilibrium point, it has been shown that the disease free equilibrium point was locally asymptotically stable if thecontrol reproduction number is less than one and also the endemic equilibrium point was locally asymptotically stable if the control reproduction number is greater than one. Numerical simulation was carried out which supported the analytical results. Keywords: Mathematical Model, Biomathematics, Reproduction Number, Disease Free Equilibrium, Endemic Equilibrium Point

Highlights

Tuberculosis (TB) is a protracted bacterial infectious disease caused by Mycobacterium tuberculosis which position a major health, social and economic burden globally, especially in low and middle income countries (WHO, 2013)
Tuberculosis is conveyed by tiny airborne droplets which are ejected into the air when a person with active pulmonary TB coughs or talks (Issarowa et al, 2015)
The purpose of this article is to formulate a mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment which provides insights into the drug resistant cases in first and second line treatment

Summary

Introduction

Tuberculosis (TB) is a protracted bacterial infectious disease caused by Mycobacterium tuberculosis which position a major health, social and economic burden globally, especially in low and middle income countries (WHO, 2013). The purpose of this article is to formulate a mathematical model of a tuberculosis transmission dynamics incorporating first and second line treatment which provides insights into the drug resistant cases in first and second line treatment.

Objectives

Results

Conclusion