Modeling the dynamics of tuberculosis in a coupled metapopulation

Abstract

Tuberculosis (TB) is currently one of the key health test in many developing countries, Kenya included. TB is a curable transmissible ailment caused by Mycobacterium tuberculosis. The formation of the tubercles in tissues of the body like in the lung tissues describes the disease. Interaction with transmissible individuals can make one acquire TB. The behavior of transmissible diseases, its impacts and possible future prediction about its spread has been best understood with the knowledge of mathematical epidemiology. In this study, delay differential equations were formulated for purposes of determining stability of both Disease Free Equilibrium (DFE) and endemic equilibrium( EE) .The delay component was incorporated into Susceptible-Exposed-Infectious- Recovered (SEIR) model. A parameter called the basic reproduction number was computed using next generation matrix approach. Sensitivity analysis was carried out with respect to model parameters. Finally, numerical simulation were done using MATLAB for validation of the analytical results. Parameter values were obtained from secondary data. From the numerical results it was found out that R0 at DFE was 0.5828 and it was 1.0095 at EE.