A MATHEMATICAL MODELING OF THE DYNAMICS OF TYPHOID FEVER

Résumé

A comprehensive mathematical model of typhoid fever was developed to investigate the complex transmission dynamics of the disease, shedding light on the intricate relationships between various factors influencing its spread. The model assumes a replenished population through birth and leverages existing data to validate its accuracy, ensuring a reliable representation of the disease’s behavior. The primary objective of this modeling exercise is to inform and enhance strategies for preventing, controlling, and eradicating typhoid fever, ultimately leading to improved public health policy and a better quality of life. Through mathematical analysis, it was revealed that the basic reproductive number ????0 plays a crucial role in determining the global dynamics of the disease. ????0 is less than 1, the disease-free equilibrium is locally stable, indicating that the disease will eventually die out. Conversely, if ????0 exceeds 1, an endemic equilibrium exists, and the disease will persist at a stable level. A thorough sensitivity analysis of the model parameters was conducted, providing valuable insights into the impact of various factors on the spread of typhoid fever. This knowledge enables informed decision-making and effective disease management. The model was solved using the Runge-Kutta scheme of order four, with a 40-year time horizon, and implemented in MATLAB. This study showcases the potency of mathematical modeling in understanding the transmission dynamics of typhoid fever, enabling policymakers and healthcare professionals to develop evidence-based strategies for disease control and prevention.