A Stochastic SEI1I2RQ Epidemic Model with Infectious Latent Period
In order to study the influence of random factors in the environment on infectious diseases,a random infectious disease model with infectious latent period is considered.By constructing Lyapunov function and combining with the Ito formula,the exis-tence and uniqueness of the global positive solutions of the stochastic model is proved;Then,the fluctuation behavior of the solu-tions of the deterministic model and the stochastic model near the disease-free equilibrium point and the endemic equilibrium point are analyzed,and we obtained the solutions of the deterministic model and the stochastic model fluctuate near the disease-free equi-librium point when the basic reproduction number is less than 1,and the solution of the deterministic model and the stochastic model fluctuate near the endemic equilibrium point when the basic regeneration number is greater than 1.The fluctuation amplitude of the stochastic model solution is positively correlated with the interference intensity.The sufficient conditions for the average persistence and extinction of the stochastic model solution are also given.Finally,the corresponding numerical simulation of the model shows that the disease will become extinct when the disturbance is strong enough.
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