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Stability of a stochastic SEIS model with saturation incidence and latent period |
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| Authors: | Xuehui Ji Sanling Yuan and Jiao Li |
| Institution: | School of Management, University of Shanghai for Science and Technology, No. 516 Jungong Road, Shanghai 200093, China;College of Science, University of Shanghai for Science and Technology, No. 516 Jungong Road, Shanghai 200093, China,College of Science, University of Shanghai for Science and Technology, No. 516 Jungong Road, Shanghai 200093, China and College of Science, University of Shanghai for Science and Technology, No. 516 Jungong Road, Shanghai 200093, China |
| Abstract: | In this paper, a stochastic SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. The model inherits the endemic steady state from its corresponding deterministic counterpart. We first show the existence and uniqueness of the global positive solution of the model. Then, by constructing Lyapunov functionals, we derive sufficient conditions ensuring the stochastic stability of the endemic steady state. Numerical simulations are carried out to confirm our analytical results. Furthermore, our simulation results shows that the existence of noise and delay may cause the endemic steady state to be unstable. |
| Keywords: | Stochastic SEIS model time delay Lyapunov functional It\^{o}''s formula stochastic stability |
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