The optimal control of epidemic model with vaccination and latency period is established,and the basic reproduction number R0 is obtained.By constructing the Lyapunov function,it is shown that the disease-free equilibrium point is globally asymptotically stable when R0<1,and the endemic disease equilibrium point is globally asymptotically stable when R0>1.The optimal control strategy is analyzed by using the optimal control theory and Pontryagin maximum principle to minimize the total cost of disease control.Numerical simulations were experimented to verify the correction of the results approached in this paper.
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