MODELING THE ROLE OF VACCINATION, ENVIRONMENTAL SANITATION, AND SATURATED TREATMENT ON THE SPREAD OF TYPHOID FEVER

Abstract

A deterministic nonlinear mathematical model is developed for typhoid transmission dynamics in human hosts, coupled with multiple transmission routes. The model aims to examine the role of control interventions such as vaccination, environmental sanitation, and saturated treatment on the prevalence of typhoid. First, the qualitative analysis of the model with constant control interventions is performed. The model exhibits a backward bifurcation phenomenon. Sensitivity analysis is also conducted to identify impactful parameters for effective control of the disease. Then, the model is extended to a corresponding optimal control problem to investigate the optimum intervention strategies by assessing their effects on typhoid prevalence and economic load. The characterization of the optimal controls is determined using Pontryagin’s Maximum Principle, and the optimality system is developed. Numerical results suggest that, in the absence of treatment, the combination of vaccination and environmental sanitation controls plays an important role in reducing the typhoid burden and economic load. Moreover, the comprehensive use of the three control interventions is more effective than using any single or two combined control interventions. It reduces the number of infective humans and environmental bacteria as well as the cost burden associated with applied controls and opportunity loss. Thus, the comprehensive effect of the three control interventions is found to be more economical during typhoid outbreaks.