Mathematical Modeling of Tuberculosis Dynamics With Hygiene Consciousness as a Control Strategy
Loading...
Date
2020
Authors
Zaberio, Mawira Phineas
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Tuberculosis, an air-borne 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 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 analysed 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
Description
A project submitted in partial fulfilment of the requirements of the award of
the degree of Master of Science in Applied Mathematics in the School of
Pure and Applied Sciences of Kenyatta University.
JUNE 2020
Keywords
Mathematical Modeling, Tuberculosis Dynamics, Hygiene Consciousness