Global dynamics of an nonautonomous SEIRS epidemic model with vaccination and nonlinear incidence
• Long Zhang,
• Xiaolin Fan,
• Zhidong Teng
Long Zhang
Xinjiang University
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Xiaolin Fan
Xinjiang Institute of Engineering
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Zhidong Teng
Xinjiang University
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## Abstract

In this paper, a class of nonautonomous SEIRS epidemic models with vaccination and nonlinear incidence is investigated. Under some quite weak assumptions, a couple of new threshold values in the form of integral, i.e., $R_1$, $R^*_1$, $R_2$ and $R^*_2$ on the extinction and permanence of disease for the model are established. As special cases of our model, the autonomous, periodic and almost periodic circumstances are discussed respectively. The nearly necessary and sufficient criteria of threshold on the extinction and permanence of disease for above cases are obtained as well. Numerical examples and simulations are presented to illustrate the analytic results.

#### Peer review status:ACCEPTED

25 Feb 2020Submitted to Mathematical Methods in the Applied Sciences
01 Mar 2020Submission Checks Completed
01 Mar 2020Assigned to Editor
01 Mar 2020Reviewer(s) Assigned
07 Feb 2021Review(s) Completed, Editorial Evaluation Pending
08 Feb 2021Editorial Decision: Revise Minor