On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19
Abstract
:1. Introduction
2. Background
2.1. SEIR Epidemic Model
2.2. Contextualization of the New Epidemic Model
2.3. Preliminaries on Fractional Differential Equations
3. Mathematical Analysis
3.1. Basic Reproduction Number
3.2. Equilibrium Points
3.3. Feasibility Region Analysis
- (i)
- The initial populations.
- (ii)
- All possible disease-free equilibrium points.
- (iii)
- The disease-dependent equilibrium points.
4. Positivity in Solutions and Sensitivity Analysis
4.1. Existence of Positivity in Solutions
- (i)
- The solution of the SEIR model is positive for any non-negative initial conditions and for all t.
- (ii)
- The total population remains unvaried even for a long time, which holds for any given arbitrary non-negative initial conditions.
- (iii)
- All the solutions are positively bounded.
4.2. Sensitivity Analysis
5. Numerical Results
5.1. Graphical Representation of , , , and
5.2. Laplace Adomian Decomposition Method
6. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Notations/Symbols | Definition |
---|---|
t | Time instant |
Susceptible population at t | |
Exposed population at t | |
Infected population at t | |
Recovered population at t | |
Total population at t | |
Initial susceptible population, (fixed) | |
Initial exposed population, (fixed) | |
Initial infected population, (fixed) | |
Initial recovered population, (fixed) | |
Initial total population | |
Basic reproduction number | |
a | Rate at which susceptible become exposed, (fixed) |
b | Rate at which exposed become infected, (fixed) |
c | Rate at which exposed become recovered, (fixed) |
r | Rate at which infected become recovered, (fixed) |
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Rangasamy, M.; Chesneau, C.; Martin-Barreiro, C.; Leiva, V. On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19. Symmetry 2022, 14, 1436. https://doi.org/10.3390/sym14071436
Rangasamy M, Chesneau C, Martin-Barreiro C, Leiva V. On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19. Symmetry. 2022; 14(7):1436. https://doi.org/10.3390/sym14071436
Chicago/Turabian StyleRangasamy, Maheswari, Christophe Chesneau, Carlos Martin-Barreiro, and Víctor Leiva. 2022. "On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19" Symmetry 14, no. 7: 1436. https://doi.org/10.3390/sym14071436
APA StyleRangasamy, M., Chesneau, C., Martin-Barreiro, C., & Leiva, V. (2022). On a Novel Dynamics of SEIR Epidemic Models with a Potential Application to COVID-19. Symmetry, 14(7), 1436. https://doi.org/10.3390/sym14071436