Optimal control of vaccination and treatment for an SIR epidemiological model

摘要

We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and treatment strategies that will minimize the cost of the two control measures as well as the number of infectives. Our model analyses show that the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity while the endemic equilibrium exists and it is globally asymptotically stable whenever the basic reproduction number is greater than unity. We used Pon-tryagin's maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of vaccination and treatment strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simulation is discussed.