Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function
Abstract
:1. Introduction
2. Model Formulation
Equilibria of the Model
3. Stability Analysis of the Endemic Equilibria
3.1. Notations
3.2. Global Stability of the Endemic Equilibrium
- (i)
- First, utilizing Proposition 1, they showed that is a Volterra-Lyapunov stable matrix.
- (ii)
- The second step was to evaluate the Volterra-Lyapunov stability of matrix They must specify the matrices and , such that
- (iii)
- Finally, they considered
4. Numerical Simulations and Discussions
- and
- and
- and
- and
- and
- and
- and
- and
- and
- and
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Appendix B
References
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Parameter | Description |
---|---|
Rate of conversion of exposed population to infectious | |
Rate of conversion of infectious to recovered | |
Rate of conversion of immunity to recovered | |
The birth (and death) rate | |
The nonlinear transmission rate |
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Shao, P.; Shateyi, S. Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function. Mathematics 2021, 9, 2644. https://doi.org/10.3390/math9212644
Shao P, Shateyi S. Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function. Mathematics. 2021; 9(21):2644. https://doi.org/10.3390/math9212644
Chicago/Turabian StyleShao, Pengcheng, and Stanford Shateyi. 2021. "Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function" Mathematics 9, no. 21: 2644. https://doi.org/10.3390/math9212644
APA StyleShao, P., & Shateyi, S. (2021). Stability Analysis of SEIRS Epidemic Model with Nonlinear Incidence Rate Function. Mathematics, 9(21), 2644. https://doi.org/10.3390/math9212644