SIRS epidemic modeling using fractional-ordered differential equations:Role of fear effect  

作　　者：Shiv Mangal O.P.Misra Joydip Dhar 

机构地区：[1]School of Mathematics and Allied Sciences,Jiwaji University Gwalior,Madhya Pradesh,India [2]Department of Mathematics,Post Graduate College Bina,Madhya Pradesh,India [3]Department of Applied Sciences,Atal Bihari Vajpayee-Indian Institute of Information Technology and Management Gwalior,Madhya Pradesh,India

出　　处：《International Journal of Biomathematics》2024年第5期79-100,共22页生物数学学报（英文版）

摘　　要：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.

关 键 词：SIRS epidemic model fear effect Mittag-Leffler function Hopf bifurcation parameter estimation 

分 类 号：O17[理学—数学]