ANALYTICAL SOLUTION OF A MATHEMATICAL MODEL OF TUBERCULOSIS WITH PASSIVELY IMMUNE COMPARTMENT

¹Abdullah Idris Enagi,²Mohammed Olanrewaju Ibrahim &³Fatima Sulayman.

¹Department of Mathematics, Federal University of Technology, Minna, Nigeria.

²Department of Mathematics, University of Ilorin,  Nigeria.

³Department of Mathematics, Ibrahim Badamasi Babangida University, Lapai, Nigeria

E-mail: enagi.idris@futminna.edu.ng

ABSTRACT

In this study, we proposed a Mathematical Model of tuberculosis dynamics. The model is a system of four first order ordinary differential equations. The population is partitioned into four compartments of passively immune infant class ,  Susceptible , Infected and Recovered . The analytical solutions using Homotopy Perturbation method (HPM) were obtained. Graphical profiles for each of the four compartments were obtained using MAPLE computer software package.  The results shows that the disease has a tendency of dying out with time when there is high recovery rate.

Key words: Tuberculosis, Analytical solution, Homotopy perturbation.