Optimal control of Typhoid fever transmission under environmental and public health interventions

This study investigates the transmission dynamics of typhoid fever and assesses the impact of environmental factors and public health interventions on disease spread. Typhoid fever, caused by Salmonella Typhi, remains a major public health concern in regions with poor sanitation, high population density, and limited access to clean water. Although environmental contamination plays a critical role in sustaining transmission, its contribution is often under explored in mathematical modeling studies.

We developed a deterministic compartmental model incorporating environmental transmission pathways to better understand the role of contaminated water sources and human-environment interactions in the spread of typhoid fever. The model is formulated as a system of nonlinear ordinary differential equations. The basic reproduction number, R0 was derived using the next-generation matrix approach to determine the threshold conditions for disease persistence. We analyzed the existence and stability of the disease-free and endemic equilibrium points, establishing local and global stability results for [Formula: see text] and R0 > 1, respectively. Sensitivity analysis on the reproduction number and the endemic equilibrium was conducted to identify parameters with the greatest influence on disease transmission. Furthermore, the model was extended to an optimal control framework incorporating two intervention strategies: public health education campaigns and treatment of contaminated water bodies. Pontryagin's Maximum Principle was applied to characterize the optimal controls and derive the associated optimality system. Model parameters were estimated using reported typhoid fever data from Ethiopia obtained through the World Health Organization. Numerical simulations were performed to evaluate the impact of individual and combined intervention strategies.

Simulation results indicate that the combined implementation of environmental sanitation measures and educational interventions significantly reduces disease burden, particularly during outbreak periods.

These findings highlight the importance of integrating environmental management and community-based public health strategies in typhoid control programs.