The Dynamics Of Two Stochastic Epidemic Models

In view of great threat of infectious disease to human health,the prevention and control of infectious diseases have always been the main concern in the word.In view of the random disturbance factors in the ecological environment,the environmental noise will affect the spread of infectious diseases,so it is more realistic to study the dynamic behavior of stochastic infectious disease model.In this paper,the dynamical behaviors of two kinds of stochastic models are studied by means of the ergodic theory given by Hasminskii,martingale inequality and the strong law of large numbers.Firstly,we stuided a stochastic tuberculosis model.We use Hasminskii's ergodic theory to obtain that if₀>1,the model has a unique stationary distribution.We use the strong law of large numbers to obtain that if₀⁰)<1,the disease will be in extinction.The numerical results show that taking protective measures is beneficial to the extinction of tuberculosis,and the noise is beneficial to the extinction of tuberculosis.Secondly,we considered a stochastic influenza virus model with disease resistance.If^₀>1,the model has a unique stationary distribution,which denotes that the disease is uniformly persistent.The sufficient conditions of disease extinction are obtained by using martingale inequality and law of large numbers.The results of numerical simulation experiments show that enhancing disease resistance can effectively control the spread of influenza virus.