具有疫苗接种和潜伏期的传染病模型的最优控制分析

Analysis of optimal control for infectious disease models with vaccination and incubation periods

建立了具有疫苗接种和潜伏期的传染病最优控制模型,得到了基本再生数R_(0),构造了Lyapunov函数.当R_(0)<1时,无病平衡点是全局渐近稳定的;当R_(0)>1时,地方病平衡点是全局渐近稳定的.利用最优控制理论和Pontryagin原理分析了最优控制策略,使得疾病控制过程中的成本最低.用数值模拟验证了理论结果的正确性.

The optimal control of epidemic model with vaccination and latency period is established,and the basic reproduction number R_(0)is obtained.By constructing the Lyapunov function,it is shown that the disease-free equilibrium point is globally asymptotically stable when R_(0)<1,and the endemic disease equilibrium point is globally asymptotically stable when R_(0)>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.