Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases
Abstract
:1. Introduction
- As a first attempt, in this paper, a fuzzy fractional Caputo derivatives approach subject to a SIR dynamic is developed for childhood dieases.
- The fixed point theorem of Schauder and Banach is used to demonstrate the existence and uniqueness of the solution to the addressed model.
- Perform the numerical simulations by using fuzzy Laplace and inverse Laplace transform based on the Adomian decomposition method.
- Numerical results shows the validity and effectiveness of the tracking performance of the proposed fuzzy fractional SIR dynamic.
2. Preliminaries
- should be bounded, increasing function, right continuous at 0 and left continuous over .
- should be bounded, decreasing over , right continuous at 0.
- should be less than or equal to .
- 1.
- for all ;
- 2.
- for all ;
- 3.
- for all ;
- 4.
- is a complete metric space.
3. Formulation of Fuzzy Fractional SIR Model
4. Existence and Uniqueness Results
- There exists a constant and
- There exists constant such that for each we have
5. Method Description
6. Numerical Simulation Results and Discussions
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SIR | Susceptible-Infectious-Removed |
WHO | World Health Organization |
DEs | Differential Equations |
FODEs | Fractional Order Differential Equations |
ML | Mittag–Leffler |
LT | Laplace Transform. |
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Parameters | Representation | Values |
---|---|---|
Natural death rate | 0.4 | |
Birth rate | 0.4 | |
p | Fraction of the vaccinated population at birth | 0.9 |
Contact rate of susceptible individual | 0.8 | |
Infected individuals recover at a rate | 0.03 |
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Subramanian, S.; Kumaran, A.; Ravichandran, S.; Venugopal, P.; Dhahri, S.; Ramasamy, K. Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases. Mathematics 2024, 12, 466. https://doi.org/10.3390/math12030466
Subramanian S, Kumaran A, Ravichandran S, Venugopal P, Dhahri S, Ramasamy K. Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases. Mathematics. 2024; 12(3):466. https://doi.org/10.3390/math12030466
Chicago/Turabian StyleSubramanian, Suganya, Agilan Kumaran, Srilekha Ravichandran, Parthiban Venugopal, Slim Dhahri, and Kavikumar Ramasamy. 2024. "Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases" Mathematics 12, no. 3: 466. https://doi.org/10.3390/math12030466
APA StyleSubramanian, S., Kumaran, A., Ravichandran, S., Venugopal, P., Dhahri, S., & Ramasamy, K. (2024). Fuzzy Fractional Caputo Derivative of Susceptible-Infectious- Removed Epidemic Model for Childhood Diseases. Mathematics, 12(3), 466. https://doi.org/10.3390/math12030466