Ann Infect Dis Epidemiol | Volume 5, Issue 2 | Review Article | Open Access

Modeling the Dynamics of Tuberculosis in a Coupled Metapopulation

Mutai Wesley^1*, Kirui Wesley² and Mukuna Wilys³

¹Department of Mathematics and Computer Science, University of Kabianga, Kenya ²Department of Mathematics and Actuarial Science, South Eastern Kenya University, Kenya

^*Correspondance to: Mutai Wesley 

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Abstract

Tuberculosis (TB) is currently one of the key health tests 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 Disease Free Equilibrium (DFE). The delay component was incorporated into Susceptible-Exposed-Infectious-Recovered (SEIR) model. A parameter called the basic reproduction number was computed and sensitivity analysis carried out with respect to model parameters. Finally, numerical simulations were done using MATLAB for validation of the analytical results. Parameter values were obtained from secondary data.

Keywords:

TB; Reproduction number; Delay differential equations; Stability; Disease free equilibrium

Citation:

Wesley M, Wesley K, Wilys M. Modeling the Dynamics of Tuberculosis in a Coupled Metapopulation. Ann Infect Dis Epidemiol. 2020; 5(2): 1054.