System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions
Abstract
:1. Introduction
2. Preliminaries
3. Model Formulation
4. Analysis of the Time-Fractional COVID-19 Model
4.1. Results on the Existence and Uniqueness Of Solutions
- (a)
- the function u is non-decreasing if , .
- (b)
- the function u is non-increasing if , .
4.2. Existence, Stability, and Equilibrium Results for COVID-19 Model of Fractional Type
4.2.1. Computation of
4.2.2. Stability Results
4.2.3. Computation of an Endemic Equilibrium
4.2.4. Sensitivity Analysis
- Quarantining infected people may be an essential prevention measure to reduce the spread of COVID-19 infection.
- Reducing the transmission parameter is essential in reducing the transmission of the infection. To reduce the transmission parameter, compliance with protocols such as social distancing, wearing a face mask, and washing hands are necessary.
5. Numerical Analysis and Simulation
5.1. Adams–Bashforth–Moulton Method for Fractional-Order
5.2. Numerical Simulation and Analysis
5.2.1. Impact of Time-Fractional-Order on the Solution Profiles for the COVID-19 Model
5.2.2. Impact of the Effective Contact Rate on the Solution Profiles for the Coivd-19 Model
5.2.3. Impact of Quarantining Exposed Individuals on the Solution Profiles for the Coivd-19 Model
5.2.4. The Impact of the Loss of Immunity
5.2.5. The Impact of Quarantine Infected Individuals on the Solution Profiles for the Coivd-19 Model
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Likely Range (Sources) | Default Value |
---|---|---|
b (Recruitment rate of the population) | 78,680 | |
(Effective contact rate) | [5,43] | day |
(Transition rate from exposed quarantined to susceptible individuals) | 1/14 [43] | 1/14 |
(Transition rate from recovered to susceptible individuals) | Assumed | 5/100 |
(Quarantine rate of exposed individuals) | 1/10 [5] | 1/10 day |
(Transition rate from exposed to infected class ) | 1/14–1/3 [43,44,45] | 1/7 day |
(Transition from exposed quarantined to infected quarantined) | 0.1259 [43] | 0.1259 |
(Quarantining rate of individuals in the class) | 0.2– 1 [43,46] | 0.3654 day |
(Disease-induced death rate) | [5,43] | |
(Natural death rate) | 7.1/1000 | 7.1/1000 |
(Natural recovery rate) | 1/30–1/3 day [43,47] | 1/20 day |
(Recovery rate of quarantine infected) | 0.11624 [43,48] | 0.11624 day |
(Initial value of the susceptible) | [5] | 11,081,000 |
(Initial value of the expose) | [5] | 399 |
(Initial value of the expose, quarantined) | [5] | 159 |
(Initial value of the infected) | [5] | 54 |
(Initial value of the infected, quarantined) | [5] | 28 |
(Initial value of the recovered) | [5] | 12 |
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Iyiola, O.; Oduro, B.; Zabilowicz, T.; Iyiola, B.; Kenes, D. System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions. Symmetry 2021, 13, 787. https://doi.org/10.3390/sym13050787
Iyiola O, Oduro B, Zabilowicz T, Iyiola B, Kenes D. System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions. Symmetry. 2021; 13(5):787. https://doi.org/10.3390/sym13050787
Chicago/Turabian StyleIyiola, Olaniyi, Bismark Oduro, Trevor Zabilowicz, Bose Iyiola, and Daniel Kenes. 2021. "System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions" Symmetry 13, no. 5: 787. https://doi.org/10.3390/sym13050787
APA StyleIyiola, O., Oduro, B., Zabilowicz, T., Iyiola, B., & Kenes, D. (2021). System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions. Symmetry, 13(5), 787. https://doi.org/10.3390/sym13050787