Stability Analysis Of Infectious Disease Models Guided By Isolation Information

The mathematical model of infectious disease transmission mechanism is established by using differential equations,and the dynamic behavior of infectious disease system is analyzed,which has attracted close attention from scholars.Researchers have established a large number of mathematical models by considering the relationship between susceptible,infected,and recoverers.From the perspective of mathematical modeling,based on the transmission mechanism of infectious diseases,based on the work of previous scholars,the isolation and vaccine immunization are considered,and the immune status of the vaccine is guided by the isolation information to reveal the different forms of infectious diseases.The model is simplified and its basic characteristics are studied,including the positive definiteness and boundedness of the system solution given the initial values.The basic reproduction number0 R is obtained by the method of the next generation matrix.The equilibrium point of the dynamic system,that is,the disease-free equilibrium point and the endemic disease balance point,is obtained,and the conditions for their respective existence are analyzed.Using the Cartesian symbolic criterion,different forms of existence of multiple endemic equilibrium points are given.The characteristic equations at the disease-free equilibrium point and the endemic disease balance point are calculated.The local asymptotic stability conditions of the disease-free equilibrium point and the endemic disease equilibrium point are obtained by using the Routh-Hurtwiz criterion.The Lyapunov function is constructed to verify the global asymptotic stability of the disease-free equilibrium.The geometric approximation method is used to prove the condition of global asymptotic stability when the dynamic system has only one endemic equilibrium point.The above is an analysis of the stability of the balance point of the power system.Then we prove the condition that the system solution is periodically oscillated.The Hopf branch occurs when the parametercrit?=?,the equilibrium point3 E is stable whencrit?(27)?,and the equilibrium point3 E is unstable whencrit?(29)?.According to the model we have established,the number of isolations is proportional to the number of infections.From the macroscopic analysis of the trend of the number of isolations,we have used real data,the changes in the number of hepatitis B virus infections in the country and the models we established earlier.The simulations of the number of isolations under certain conditions are compared and found to be in the form of periodic oscillations.It is further verified that our model is biologically significant.We simulated the ARIMA model of the data,and compared the fitting effect with the real data.The ARIMA model was used to predict the data after May 2017,and the actual number of hepatitis B patients was compared.From the micro-analysis of the effect of isolation therapy on individuals,due to the drug resistance of the drug,the effect of isolation drug therapy will be worse or even negative.In order to observe the optimal stopping time of individual isolation treatment,we analyzed the changes of HIV virus in AIDS patients after isolation treatment,and established a least squares model to give the best stopping time for AIDS patients.