Analysis Of Two COVID-19 Models Based On Asymptomatic Infection

COVID-19 is a highly contagious acute respiratory disease transmitted,causing persistent and major public health problems worldwide.COVID-19 is mainly transmitted by droplet and close contact,and people can be infected by contact with objects carrying the virus.Once infected with COVID-19,the patient initially has no obvious clinical symptoms,which is called asymptomatic infection,after a certain period of time,an asymptomatic infection can develop into a symptomatic infection.In order to analyze the stability of the models and to explore the impact of asymptomatic infection and non-pharmaceutical intervention on the spread of the disease,two types of COVID-19 models are established.First,a COVID-19 model including asymptomatic and symptomatic infections is studied,and the influence of non-pharmaceutical interventions on the spread of infectious diseases are considered.The basic reproduction number is calculated by the next generation matrix method and the existence of endemic equilibrium is discussed.By using of Routh-Hurwitz criterion and La Salle invariance principle,it is proved that the disease-free equilibrium is locally asymptotically stable and globally asymptotically stable when₀R<1.Using the center manifold theory,it is proved that the endemic equilibrium is locally asymptotically stable when₀R>1.Finally,the accuracy of the conclusion is verified by numerical simulation.Secondly,considering the complexity of disease transmission,SEALIQHR model was established by introducing a sealed and isolated warehouse.The positive and boundedness of solutions and the existence and uniqueness of solutions are analyzed.The basic regeneration number is calculated,the stability of disease-free equilibrium and endemic equilibrium is proved.Finally,the sensitivity of the key parameters of basic regeneration number is analyzed,and the results are verified by numerical simulation.