Modeling And Research Of Coronaviruses

Coronavirus,with a very high infectivity and lethality,is a single stranded RNA virus causing the disease of respiratory system,such as influenza,viral pneumonia and dengue fever,etc.This type of virue has brought great losses to human society.Therefore,it is of great practical significance to establish a mathematical model to study the treatment of coronavirus.In this paper,based on the classical model of viral infectious disease in vivo,we considered two treatment schemes which are the dynamic model of antiviral active drug therapy and the dynamic model artificial ACE2 receptor therapy to establish the model.In this paper,the second chapter and the third chapter focused on antiviral active drug treatment model.In the second chapter,we established a treatment model with a constant injection rate of antiviral active drug and proved that the model's solution is positive and bounded,then gave the expression of basic reproductive number R₀and proved that the disease-free equilibrium is locally asymptotically stable when R₀<1.Next,we obtained the su cient conditions for global stability of the disease-free equilibrium point by constructing Lyapunov function combined with Russell's Invariance Principle.In addition,we obtained the su cient conditions for locally asymptotic stability of positive equilibrium point by Rouths-Hurwitz's Criterion.Finally,we gave a numerical simulation.Our results showed that when the constant injection rate of the drug is greater than the critical value,it can e?ectively eliminate all the viruses in the body.In the third chapter,we studied the model of antiviral active drug therapy based on viral load.First,we gave the theorems of the positive invariance and boundedness of the solution,then the su cient conditions for locally asymptotic stability and globally asymptotic stability of the disease-free equilibrium point were given respectively.Finally,the correctness of the obtained conclusions was verified by numerical simulation.Our results showed that the antiviral active drugs injected according to the viral load,i.e.when the condition is light,we inject a small amount of drug,but when the condition is serious,even though the injection volume is increased,the e?ect on the overall elimination of the virus in the body is not obvious.In the fourth chapter,we developed the dynamic model for artificial ACE2 receptor therapy regimens.First,we gave the theorems of the positive invariance and boundedness of the solution.Then the su cient conditions for locally asymptotic stability and globally asymptotic stability of the disease-free equilibrium point were given respectively.In addi-tion,we obtained the su cient conditions for the stability of the positive equilibrium point.Finally,the correctness of the obtained conclusions was verified by numerical simulation.Our results showed that when the injection of artificial ACE2 receptors reaches the critical value,it can e?ectively remove the virus in vivo.