Optimal Control And Dynamic Behavior Of HFMD Model

Hand,foot and mouth disease(HFMD)is a global infectious disease caused by pathogens,because of many pathogens,spread wide,so often occur.In recent years,symptomatic HFMD has brought bad effects on children’s health and caused serious losses to the national economy.In order to provide effective control and prevention strategies,a mathematical model to describe the internal mechanism of transmission of HFMD has been applied in the study of HFMD.Therefore,the research content of this article mainly includes the following two aspects:1.The long-term dynamic behavior of the reaction-diffusion model of HFMD in the bounded spatial domain was studied.By considering the high infectivity of HFMD,the model to be studied in the second chapter is established.Firstly,the adaptability of the model is analyzed,and the existence of the global solution and the uniform boundedness of the solution are proved,Then the basic regeneration number ?0 is given.The kinetic properties are proved.Finally,the Hamilton-Jacobi-Bellman equation is given by using Bellmans optimality principle,and the existence of its solution is proved.The correctness of the theory is verified by numerical simulation.2.A pulse vaccination strategy is introduced into a random HFMD model with Markov switching.The problem of near-optimal control for randomized HFMD system is studied,in which the objective function is the cost required for the treatment of HFMD.According to the estimation of adjoint equations,the error estimate of near-optimal control is further given,and sufficient conditions for the existence of near-optimal control are established by using the Hamiltonian function.Based on the principle of random maximum,the necessary conditions for the existence of near-optimal control are proved.The results are verified by numerical examples.