Optimal Control of a Class of Reaction-diffusion SIQR Epidemic Models
In order to investigate how to control the disease faster when it occurs and to avoid spreading and epidemics,this paper investigated the optimal control problem for a class of susceptible-infectious-quarantined-recovered(SIQR)reaction-diffusion epidemic models.Firstly,the truncation method was used to prove the existence of the solution y=(S,I,Q,R)T of the state equation.Secondly,the minimisation sequence was used to prove the existence of the optimal control pair(S*,I*,Q*,R*,u*).Finally,the Lagrange method was used to obtain the first-order necessary condition and the expression of the optimal control u*.The results showed that when the control u=u* was optimal,the given objective function was minimised.This study is of great significance to the problem of optimal control of infectious disease models with partial differential equations.
epidemic modelreaction-diffusion equationexistence and uniqueness of solutionsoptimal controlfirst-order necessary condition
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