Mathematical Analysis of Typhoid Fever with Control Measures
Shior M.M.
Odo, C.E.
Agbata B.C.
Patrick, A. A. Mensah
Asante-Mensa F.
Fokuo M.O.
Chibuikem C.T.
Obeng-Denteh W.
Abstract
In this study, a typhoid fever model is developed using fundamental mathematical modeling techniques, resulting in a system of five ordinary differential equations (ODEs). A mathematical analysis of the model is then conducted to examine the existence and uniqueness of solutions, ensuring that the model is both mathematically and epidemiologically feasible within a well-defined region. The equilibrium points of the model are determined, and the stability of the disease-free equilibrium (DFE) is analyzed. To assess whether the disease will persist or die out, the basic reproduction number ( ) is derived using the next-generation matrix method. Sensitivity analysis is performed on to identify the most influential parameters affecting disease transmission. The results indicate that the contact rate has a positive sensitivity index, meaning that reducing human interaction with contaminated sources or infected individuals can significantly lower the spread of typhoid fever. A numerical simulation is carried out using MATLAB to visualize the behavior of the model under different intervention strategies. The simulation results suggest that prompt treatment of infected individuals and effective management of contaminated agents are the most effective approaches for controlling typhoid fever. By reducing exposure to contaminated water and food, improving sanitation, and ensuring early medical intervention, the spread of the disease can be minimized.
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