Dynamics Analysis Of Tuberculosis And COVID-19 Co-infection Models

Both tuberculosis and COVID-19 are respiratory infections caused by pathogens infecting the lungs and presenting with similar symptoms such as cough,fever or difficulty breathing.Therefore,based on the transmission mechanism of tuberculosis and COVID-19,this paper establishes several types of models of tuberculosis and COVID-19 co-infection,and studies the possible impact of COVID-19 on tuberculosis control.The specific research work of this paper is as follows:Considering the similarities of tuberculosis and COVID-19,based on the classic SEIR chamber model,a type of dissemination dynamic model of a class of tuberculosis and COVID-19 is established.First of all,we verify the properness of the model and introduce the conditions of the existence of each equilibrium.Secondly,by analyzing the corresponding characteristic equations and eigenvalue,the local asymptotic stability of each equilibrium is studied.Next,we use the Lyapunov function to prove the corresponding stability.Finally,we verifies the correctness of the theoretical analysis through numerical simulation,showing the stable regions of each equilibrium.As a result,the possibility of continuous transmission of COVID-19 in the crowd is greater than tuberculosis.In view of the dynamic model of tuberculosis and co-infection of recurrent COVID-19 considering relapse,the interaction between tuberculosis and COVID19 at the same time is further studied.Firstly,the dynamic behavior of the model is analyzed,and the existence of the equilibrium of the model is discussed.It also defines the threshold for whether only tuberculosis or COVID-19 can spread in the population,and whether the two diseases spread in the population at the same time.The local asymptotic stability of each equilibrium,the disease-free equilibrium and the boundary equilibrium of only tuberculosis are proved.Finally,numerical simulation verifies the stability of the four equilibria,and shows the stable regions of each equilibrium.The results show that after considering the recurrent infection of COVID-19,compared with the model in Chapter 2,the area where COVID-19 formed endemic disease in the population is greater than that of tuberculosis in the population.For the model of co-infection of tuberculosis and COVID-19 with agestructure,we consider the time-lag effect of transforming from susceptible individuals to infected individuals.Firstly,the suitability of the model is proved,the existence of each equilibrium is calculated,and the conditions for the existence of each equilibrium are given.Secondly,by analyzing the corresponding characteristic equations,the Routh-Hurwitz criterion is used to give the local asymptotic stability conditions of each equilibrium.Next,we use the method of constructing the Lyapunov function to prove the global asymptotic stability of the disease-free equilibrium and the equilibrium of tuberculosis-only,and give the corresponding stability conditions.Finally,through numerical simulation,the stability of the four equilibria is verified.We find that the infection rate of COVID19 in the population is higher than that of tuberculosis,that is,the COVID-19 will continue to spread in the population.As the risk of transmission of COVID-19 within a population increases,so does the risk of transmission of tuberculosis within a population.