Mathematical Modeling and Cost-Effectiveness Analysis of an SeEeIeRe Typhoid Fever Model

The complications induced by typhoid fever in the host are a significant concern for public health, with most countries in Sub-Saharan Africa, Asia, and North America grappling with their worst typhoid cases and deaths owing to poor sanitation problems. We examined a nonlinear mathematical model for typhoid fever disease. This model explains how the disease spreads by testing its stability at both the typhoid-free and typhoid-present equilibriums. Thus, we used different mathematical tools to investigate the basic structure of the disease, such as Castillo–Chavez’s geometric method and the geometrical method of the Bendixson criterion for typhoid-present equilibrium’s global stability. To understand the influential parameters in the typhoid reproduction number R0, a local and global sensitivity analysis of the model is carried out. We further apply the optimal control theory to the model, examining the impact of time-dependent controls such as personal protection, vaccination, and treatment on disease dynamics. We provide the work’s simulated results as a framework for disease control. We then conducted a cost-effectiveness study to determine which of the listed strategies was the most cost-effective.