Numerical Analysis of the Maximum Principle Boundary-Value Problem for the Influenza Virus Spread Model

Abstract

We consider the optimal control problem for a model of the spread of the influenza virus ignoring natural births and deaths. The problem is investigated by the Pontryagin maximum principle. A maximum principle boundary-value problem is constructed and it is analyzed numerically by the parameter continuation method. The best control is obtained in the class of piecewise-constant controls with one switching point, which is of definite interest in applications. The functional value under this control is worse by approximately 12.8% than the functional value under extremal control.