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- Title
SIRS epidemic modeling using fractional-ordered differential equations: Role of fear effect.
- Authors
Mangal, Shiv; Misra, O. P.; Dhar, Joydip
- Abstract
In this paper, an SIRS epidemic model using Grunwald–Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious diseases. The criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction number. The condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation parameter. Additionally, using the Grunwald–Letnikov approximation, the simulation is carried out to confirm the validity of analytic results graphically. Using the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021, we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical one. Both the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.
- Subjects
INDIA; DIFFERENTIAL equations; FRACTIONAL differential equations; EPIDEMICS; HOPF bifurcations; COMMUNICABLE diseases; BASIC reproduction number; CLASSICAL swine fever
- Publication
International Journal of Biomathematics, 2024, Vol 17, Issue 5, p1
- ISSN
1793-5245
- Publication type
Article
- DOI
10.1142/S1793524523500444