Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown
Abstract
:1. Introduction and Preliminaries
- 1.
- .
- 2.
- 3.
- .
- 4.
- .
- 5.
- , for .
- 6.
- , for .
2. Model Formulation
3. Equilibrium Points and Basic Reproduction Number
4. Local and Global Asymptotic Stability of the Disease-Free and Endemic Equilibrium Points
5. Approximate Solution
6. Numerical Simulations and Examples
6.1. Exact and Approximated Solutions of System (8) When
6.2. Exact and Approximated Solutions of System (8) When
7. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameters | Description of the Parameters |
---|---|
Recruitment rate | |
Infection contact rate | |
Imposition of lockdown on susceptible group | |
Imposition of lockdown on infected group | |
Recovery rate of the infected group | |
Recovery rate of the infected group under lockdown | |
Death rate of the infected group | |
Death rate of the infected group under lockdown | |
d | Natural death rates |
Rate of transfer of susceptible lockdown individuals to susceptible class | |
Rate of transfer of susceptible lockdown individuals to infected class | |
rate of implementation of the lockdown program | |
rate of depletion of the lockdown program |
Parameters | Description of the Parameters | Data Set 1 | Data Set 2 | Reference |
---|---|---|---|---|
Recruitment rate | 400 | 400 | [38,43] | |
Infection contact rate | [44] | |||
Imposition of lockdown on susceptible group | [38,43] | |||
Imposition of lockdown on infected group | 0.002 | 0.002 | [38,43] | |
Recovery rate of the infected group | 0.16979 | 0.16979 | [38,43] | |
Recovery rate of the infected group under lockdown | 0.16979 | 0.16979 | [38,43] | |
Death rate of the infected group | 0.03275 | 0.03275 | [44] | |
Death rate of the infected group under lockdown | 0.03275 | 0.03275 | [44] | |
d | Natural death rates | 0.096 | 0.06 | [38,43] |
Rate of transfer of susceptible lockdown individuals to susceptible class | 0.2 | 0.52 | [38,43] | |
Rate of transfer of susceptible lockdown individuals to infected class | 0.2 | [38,43] | ||
rate of implementation of the lockdown program | [38,43] | |||
rate of depletion of the lockdown program | 0.06 | 0.06 | [38,43] |
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Denu, D.; Kermausuor, S. Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown. Vaccines 2022, 10, 1773. https://doi.org/10.3390/vaccines10111773
Denu D, Kermausuor S. Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown. Vaccines. 2022; 10(11):1773. https://doi.org/10.3390/vaccines10111773
Chicago/Turabian StyleDenu, Dawit, and Seth Kermausuor. 2022. "Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown" Vaccines 10, no. 11: 1773. https://doi.org/10.3390/vaccines10111773
APA StyleDenu, D., & Kermausuor, S. (2022). Analysis of a Fractional-Order COVID-19 Epidemic Model with Lockdown. Vaccines, 10(11), 1773. https://doi.org/10.3390/vaccines10111773