Dynamics And Optimal Control Of Two-group Epidemic Model

In order to reflect the different risk levels of disease transmission and infection to different individual,a two-group infectious disease model is established with limited resource in this paper.By utilizing Lyapunovfunctions,the global dynamics of the model with constant vaccination rates are obtained:the relationship between the basic reproductive number?₀and vaccination rates,the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium global attraction.Furthermore,when the disease is endemic,a time-varying epidemic model with two groups with limited immune resources is considered.Based on limited immune resources,the sum of accumulative number of the infected individuals and the cost in a fixed time span are selected as the objective function and the criteria for the existence and uniqueness of underlying optimal solutions are obtained via applying the optimal control theory.In addition,numerical simulations show the effects of both constant and variant vaccination rates on vaccine distribution strategy with limited immune resources.