期刊
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
卷 -, 期 -, 页码 -出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793524523500444
关键词
SIRS epidemic model; fear effect; Mittag-Leffler function; Hopf bifurcation; parameter estimation
In this paper, an SIRS epidemic model using Grunwald-Letnikov fractional-order derivative is formulated 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 validity of the analytic results is confirmed through numerical simulations using the Grunwald-Letnikov approximation. The fractional-order model shows closer forecast of the disease compared to the classical one using real data of COVID-19 in India.
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.
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