Analysis Of An SQEIAR Deterministic And Stochastic Epidemic Model With Media Coverage And Asymptomatic Infection

The ravages of infectious diseases not only endanger the safety of human lives,but also destroy national economies,the prevention and treatment of infectious diseases has always been a global issue.With the rapid development of information society,media coverage is more conducive to controlling the spread of infectious diseases,while the asymptomatic spread of infectious diseases will make the transmission of diseases more complicated and increase the difficulty of disease prevention and treatment.An SQEIAR model as well as an stochastic SQEIAR model with media coverage and asymptomatic infection is established and studied in this paper,the main contents are as follows:The research background and present situation,as well as the preliminary knowledge is introduced in the first chapter.In the second chapter,we propose an SQEIAR model with media coverage and asymptomatic infection.Firstly,the local and global stability of disease-free equilibrium and the local asymptotic stability of epidemic equilibrium,as well as the persistence of the system are proved and the basic reproductive number is sensitivity analysised.Furthermore,an optimal control model is established on the basis of deterministic model,the optimal control function based on the minimum control cost and the best control effect is found,the results are verified by numerical simulation in the end.In the third chapter,considering the stochastic perturbation,an SQEIAR stochastic model with media coverage and asymptomatic infection based on the deterministic model is established.Firstly,the existence and uniqueness of the global positive solution of the system is proved,then a sufficient condition for the disappearance of the disease is given,and the Lyapunov function is constructed to prove the existence of a unique stable distribution of the system and the distribution is ergodic by using the Has' Minskii theory.Further,the optimal control strategy of epidemic disease is found by using the relevant theory of optimal control,and the effectiveness of the prevention and control measures is verified by numerical simulation.The paper is summarized and the further prospects are given in chapter four.