On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect
Abstract
:1. Introduction
2. An SEIRS Model with NPI Depending on the Number of Infected People
2.1. Disease-Free Equilibria
2.2. Endemic Equilibria
2.3. Stability Analysis
2.3.1. Local Stability of the DFE
2.3.2. Local Stability for an Endemic Equilibrium
2.4. Numerical Simulations
2.5. Sensitivity Analysis
3. Application to the COVID-19 Epidemic
3.1. Background of the COVID-19 Pandemic
3.2. Dynamics without Protection Measures: Parameters Estimation Based on COVID-19
4. Possible Strategies against an Epidemic with Reinfection
4.1. Strategy 1: Constant Control
4.2. Strategy 2: NPI Intensity Increasing with the Number of Cases
4.3. Strategy 3: Seek to Extinguish the Epidemic
5. Case of the COVID-19 Pandemic: Estimation of NPI Intensities and Identification of the Strategies Chosen by Several Countries
6. Comparison and Discussion of the Effects of Various NPI Strategies on the Dynamics of the Epidemic
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
NPIs | Non-Pharmaceutical Interventions |
Appendix A. Mathematical Properties of the Model
Appendix B. More Details on the Infection Rate Formula
Appendix B.1. Detailed Calculation of the Infection Rate Formula
Appendix B.2. Simulation of Infectious Contacts
Appendix C. Illustration for Several Other Countries
References
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Parameter | Interpretation |
---|---|
infection rate | |
k | transfer rate from exposed to infected. is the average incubation duration. |
is the average time spent in the infectious state. | |
transfer rate from recovered to susceptible. is the average time before | |
losing immunity. | |
v | intensity of NPI, measured as the equivalent proportion of the population |
in isolation. |
Strategy 1 | Strategy 2 | Strategy 3 | |
---|---|---|---|
Effectiveness | high | low | high |
Intensity | highest | medium | high |
Duration | short | very long | short |
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Nguyen-Huu, T.; Auger, P.; Moussaoui, A. On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect. Mathematics 2023, 11, 2822. https://doi.org/10.3390/math11132822
Nguyen-Huu T, Auger P, Moussaoui A. On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect. Mathematics. 2023; 11(13):2822. https://doi.org/10.3390/math11132822
Chicago/Turabian StyleNguyen-Huu, Tri, Pierre Auger, and Ali Moussaoui. 2023. "On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect" Mathematics 11, no. 13: 2822. https://doi.org/10.3390/math11132822
APA StyleNguyen-Huu, T., Auger, P., & Moussaoui, A. (2023). On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect. Mathematics, 11(13), 2822. https://doi.org/10.3390/math11132822