Global Stability and Cost-Effectiveness Analysis of a Nonlinear Dynamic Typhoid Fever Epidemic Model

Typhoid fever remains a significant public health concern, particularly in low- and middle-income countries where inadequate sanitation, unsafe water, and limited access to healthcare facilitate its transmission. Despite numerous mathematical models developed to study typhoid dynamics, there is a paucity of data-driven and control-oriented studies calibrated to African epidemiological settings, with limited integration of optimal intervention strategies and economic evaluation. In this research, we formulated a nonlinear model for typhoid fever that studied the transmission dynamics of the disease. The model is rigorously analyzed to establish the positivity and boundedness of solutions, and the local and global asymptotic stability of the disease-free and endemic equilibria is investigated using standard dynamical systems techniques. Using epidemiological yearly data from South Africa between 2004 and 2022, key model parameters are estimated via a least squares fitting approach, enabling reliable computation of the threshold R0 and supporting comprehensive global sensitivity, uncertainty, and robustness analyses to identify parameters that most strongly influence disease transmission. Further, the typhoid fever model was modified to a compartmentalized intervention model capturing the eradication strategies of personal protection and education, continuous vaccination, and treatment. The intervention model is solved analytically, and its associated numerical solution is provided. A cost-effectiveness analysis is conducted to determine the most economically efficient intervention for reducing the burden. The results provide data-driven insights into typhoid fever transmission in South Africa and offer quantitative guidance for designing effective and cost-efficient public health control strategies.