Abstract
Implement engineering approaches to solve medical problems which are known as biomedical engineering has gain great attention in recent decay. Of the most important engineering approaches which can be used to solve the medical problems are optimal control techniques. Where optimal control deals with the problem of finding a control law for a given system mathematical model, with some constraints, so that certain optimality criterion can be achieved. In this paper an optimal control technique called Pontryagin’s principle will be used to study of the impact of vaccination on the spread of infectious disease, seeking to reduce the infected group, a medical problem is mathematically modeled using SIR model approach. The obtained results are remarkably good.