Qualitative Analysis Of The COVID-19 Model With Vaccination Effect

The COVID-19 pandemic is the global public health problems.The COVID-19 is an acute respiratory infectious disease caused by the novel coronavirus.The rapid spread and strong infectivity of the novel coronavirus are important causes of severe cases and death cases.Therefore,this paper analyses and discusses the dynamics model of the COVID-19 which caused by the novel coronavirs.The COVID-19 vaccine was licensed in December 2020.The vaccination provides the direction for the establishment and analysis of COVID-19 models,so we add vaccine recipients to the model.In this paper,the next generation matrix theory is used for obtaining the basic reproduction number of the two models,in addition,the Liapunov stability theorem and La Salle invariant principle are used for proving that results: the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than 1;the disease-free equilibrium of the model is unstable and the model exists the unique endemic equilibrium if the basic reproduction number is greater than 1.This paper is divided into five parts.The first section describes the prevention and control strategy and epidemic trend of the COVID-19,and introduces the research status of the COVID-19 and the research content of the paper.The second part gives the main tools used in the model analysis.In the third section,we assume that the infected people with symptoms are kept in quarantine and treated in the hospital,and the recovery from illness become susceptibles again,then we establish the epidemic model with vaccination,and carries out qualitative analysis,sensitivity analysis of parameters and optimal control strategy analysis.In the fourth section,we assume that symptomatic contacts infect susceptibles and vaccine recipients,then we discuss the epidemic model in which the susceptible persons are directly isolated,and carries out qualitative analysis,sensitivity analysis of parameters and optimal control strategy analysis.The fifth section is the summary of this paper.