doi: 10.3390/e20050376.
Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size
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- PMID:33265467
- PMCID: PMC7512895
- DOI: 10.3390/e20050376
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Dynamics Analysis of a Nonlinear Stochastic SEIR Epidemic System with Varying Population Size
Xiaofeng Han et al. Entropy (Basel)..
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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.
Keywords: Stochastic SEIR model; permanence in mean; stationary distribution; vaccination; varying population size.
Conflict of interest statement
The authors declare no conflict of interest.
Figures
Time sequence diagram of system (6) for extinctions of the exposed and infective individuals.
Time sequence diagram of system (6) for permanence in mean of the infective individuals.
(a–c) represent the solutions of system (6); (d–e) stand for the density functions of, and, respectively.
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