Mathematical Modeling of Typhoid Fever Transmission Dynamics: A Sensitivity Analysis and Implications for Public Health Strategies
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201-224
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10.58578/mjaei.v3i2.9377
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Authors:Hassan Muhammad1*, Auwal Abdullahi2, Gambo Yakubu3, Adamu Ishiyaku4, O. O. Niyi5, Alagbe S. O6
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Abstract
A comprehensive mathematical model of typhoid fever was developed to investigate the complex transmission dynamics of the disease and clarify the relationships among factors influencing its spread. The model assumes population replenishment through births and uses existing data to validate its accuracy, thereby supporting a reliable representation of disease behavior. This study aims to inform and strengthen strategies for the prevention, control, and possible eradication of typhoid fever in order to support improved public health policy and quality of life. Mathematical analysis revealed that the basic reproductive number, R₀, plays a central role in determining the global dynamics of the disease. When R₀ is less than 1, the disease-free equilibrium is locally stable, indicating that the disease will eventually die out. Conversely, when R₀ exceeds 1, an endemic equilibrium exists, suggesting that the disease will persist at a stable level. Sensitivity analysis of the model parameters provided valuable insights into the relative influence of different factors on typhoid fever transmission, thereby supporting informed decision-making and effective disease management. The model was solved using the fourth-order Runge–Kutta scheme over a 40-year time horizon and implemented in MATLAB. The study concludes that mathematical modeling is a powerful tool for understanding the transmission dynamics of typhoid fever and for guiding evidence-based strategies for disease control and prevention. This study contributes to infectious disease modeling by demonstrating how equilibrium analysis, reproductive number estimation, and parameter sensitivity assessment can support public health planning aimed at reducing the burden of typhoid fever.
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