A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy

Main Article Content

Phineas Z. Mawira
David M. Malonza

Abstract

Tuberculosis, an airborne infectious disease, remains a major threat to public health in Kenya. In this study, we derived a system of non-linear ordinary differential equations from the SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analyzed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease-free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1.  Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can help
in controlling TB disease if incorporated effectively.

Keywords:
Tuberculosis, reproduction number, stability, numerical simulation.

Article Details

How to Cite
Mawira, P. Z., & Malonza, D. M. (2020). A Mathematical Modeling of Tuberculosis Dynamics with Hygiene Consciousness as a Control Strategy. Journal of Advances in Mathematics and Computer Science, 35(7), 38-48. https://doi.org/10.9734/jamcs/2020/v35i730302
Section
Original Research Article

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