Abstract: The dynamical behavior and optimal control problem of a class of infectious disease models with age structure were studied.The susceptible population was divided into two categories:non-elderly and elderly.The basic reproduction number of the model was derived by using the next-generation matrix method.Then,by constructing a Lyapunov function and applying LaSalle's invariance principle,the stability of the equilibrium point was strictly proved.Further,the vaccination rate,the implementation rate of personal protective measures,and the treatment rate were introduced as control variables to minimize the number of infections and the cost of social intervention.The Pontryagin's maximum principle was applied to give the optimal control strategy.The numerical simulation results show that,compared with the single universal prevention and control,the control strategy of implementing additional intervention for the elderly population can not only more effectively reduce the infection peak but also significantly shorten the duration of disease transmission.

Key words: age structure, infectious disease, optimal control, Pontryagin's maximum principle