OPTIMAL CONTROL ANALYZE AND EQUILIBRIUM EXISTENCE OF SEIR EPIDEMIC MODEL WITH BILINEAR INCIDENCE AND TIME DELAY IN STATE AND CONTROL VARIABLES

摘要

In this paper, we will formulate S E I R epidemic model with bilinear incidence and time delay as basic model. Then, we will investigate the optimal control strategy of our model with time delay in state and control variables. We use a vaccination program as optimal control strategy to minimize the number of susceptible and to maximize the recovered individuals. By mathematical analysis we find the existence of solution and optimal control of our model. We use Pontryagin’s maximum principle to characterize this optimal control.