Stability Analysis of a Class of SEIR Infectious Disease Models with Standard Incidence
According to the transmission mechanism of tuberculosis(TB),a SEIR model of TB infec-tious disease with standard incidence was established,and the stability of the model was discussed.Through constant variation method and the reduction to absurdity,the prove the positive invariant sets of the model is proved;The basic regeneration number R0 of the model is calculated by the next generation matrix method,and it is proved that the disease-free equilibrium point D0 is globally asymptotically stable by constructing Lyapunov function method when R0≤1.It is proved by Hurwitz criterion that the endemic equilibrium point D* is locally asymptotically stable when R0>1,and based on the Li-Mulowney geometric approach to determine the global stability,we obtain the conditions for global stability of the endemic equilibrium.Finally,the validity of the results is verified by numerical simulation.