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.
