On the efficiency of optimal vaccination, environmental sanitation and treatment controls for typhoid fever: a mathematical study approach

Abstract

Typhoid fever (TF) is a widespread infectious disease caused primarily by contaminated food, inadequate
sanitation, and poor hygiene. Our research study has not only developed an optimal control model for the dynamics of TF transmission in the population, but has also provided practical recommendations for its man-agement. The proposed model incorporates four control variables that account for vaccination, sanitation, proper hygiene, treatment, and disinfection and sterilization of the environment. The analytical solution to the optimal control problem is derived using Pontryagin’s maximum principle. At the same time, numerical simulations and efficiency analyses have identified a strategy that effectively stops the spread of TF in en-demic countries. Combining optimal sanitation and proper hygiene, treatment, disinfection, and sterilization of the environment has proven to be the most effective among the seven strategies examined, offering tangi- ble solutions for policymakers, public health officials, and researchers. However, the combination of all four controls must be taken into account in order to reduce the risk of TF in a population.