A dynamic model of typhoid fever with optimal control analysis

Abstract

In this study, a deterministic mathematical model of Typhoid fever dynamics with control strategies; vaccination, hygiene practice, sterilization and screening is studied. The model is first analyzed for stability in terms of the control reproduction number, Rc, with constant controls. The disease-free equilibrium and endemic equilibrium of the model exist and are shown to be stable whenever Rc1 respectively. The model by investigation shows a forward bifurcation and the sensitivity analysis conducted revealed the most biological parameters to be targeted by policy health makers for curtailing the spread of the disease. The optimal control problem is obtained through the application of the Pontryagin maximum principle with respect to the above-mentioned control strategies. Simulations of the optimal control system and sensitivity of the constant control system confirm that hygiene practice with sterilization could be the best strategy in controlling the disease.