Mathematical Modelling of Typhoid Fever Disease Incorporating Protection against Infection
J. K. Nthiiri *
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
G. O. Lawi
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
C. O. Akinyi
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
D. O. Oganga
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
W. C. Muriuki
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
M. J. Musyoka
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
P. O. Otieno
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
L. Koech
Department of Mathematics, Masinde Muliro University of Science and Technology, P.O.Box 190-50100, Kakamega, Kenya.
*Author to whom correspondence should be addressed.
Abstract
In this study, we have formulated a mathematical model based on a system of ordinary differential equations to study the dynamics of typhoid fever disease incorporating protection against infection. The existence of the steady states of the model are determined and the basic reproduction number is computed using the next generation matrix approach. Stability analysis of the model is carried out to determine the conditions that favour the spread of the disease in a given population. Numerical simulation of the model carried showed that an increase in protection leads to low disease prevalence in a population.
Keywords: Reproduction number, protection, typhoid fever.