MATHEMATICAL MODELING OF THE TRANSMISSION DYNAMICS OF TYPHOID FEVER AND ITS CONTROL

Abstract

In this research work, a mathematical model of the transmission dynamics of typhoid fever and its control was developed using a system of ordinary differential equations. Local stability analysis on the disease-free equilibrium was done using the Jacobian matrix approach. The semi-analytical solutions of the model were obtained using the Differential Transformation method and the solutions were plotted using Maple. The result of the findings shows that the Disease Free Equilibrium State (DFE) of the model is stable if R0˂1. The result of the numerical simulation shows that a reduction in the contact rate with infectious individuals reduces the transmission rate of the disease. The simulation also reveals that at high treatment rates for the infected individuals, the number of recovered individuals increases. Hence, as the vaccination rate increases, the population of the exposed class decreases. However, due to Typhoid fever’s connection with malaria and other febrile infections we recommend that those infections should be incorporated into the model.