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Entropy 2018, 20(5), 376; https://doi.org/10.3390/e20050376

Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size

1
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
2
State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China
*
Author to whom correspondence should be addressed.
Received: 16 April 2018 / Revised: 14 May 2018 / Accepted: 16 May 2018 / Published: 17 May 2018
(This article belongs to the Special Issue Information Theory and Stochastics for Multiscale Nonlinear Systems)
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Abstract

This paper considers a stochastic susceptible exposed infectious recovered (SEIR) epidemic model with varying population size and vaccination. We aim to study the global dynamics of the reduced nonlinear stochastic proportional differential system. We first investigate the existence and uniqueness of global positive solution of the stochastic system. Then the sufficient conditions for the extinction and permanence in mean of the infectious disease are obtained. Furthermore, we prove that the solution of the stochastic system has a unique ergodic stationary distribution under appropriate conditions. Finally, the discussion and numerical simulation are given to demonstrate the obtained results. View Full-Text
Keywords: Stochastic SEIR model; varying population size; vaccination; permanence in mean; stationary distribution Stochastic SEIR model; varying population size; vaccination; permanence in mean; stationary distribution
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Han, X.; Li, F.; Meng, X. Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size. Entropy 2018, 20, 376.

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