Review of fractional epidemic models

The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fr...

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Bibliographic Details
Published in:Applied Mathematical Modelling Vol. 97; p. 281
Main Authors: Chen, Yuli, Liu, Fawang, Yu, Qiang, Li, Tianzeng
Format: Journal Article
Language:English
Published: England Elsevier BV 01.09.2021
Subjects:
Coronaviruses
COVID-19
Differential equations
Epidemics
Infectious diseases
Parameter estimation
Parameter modification
Particle swarm optimization
Predictive control
Public health
Viruses
Parameter estimation
Fractional order differential equations
Implicit numerical method
97M60
Epidemic models
Multi-term epidemic models
37M05
Hybrid simplex search and particle swarm optimisation
26A33
37N30
ISSN:0307-904X, 1088-8691, 0307-904X
Online Access:Get full text
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Summary:The global impact of corona virus (COVID-19) has been profound, and the public health threat it represents is the most serious seen in a respiratory virus since the 1918 influenza A(H1N1) pandemic. In this paper, we have focused on reviewing the results of epidemiological modelling especially the fractional epidemic model and summarized different types of fractional epidemic models including fractional Susceptible-Infective-Recovered (SIR), Susceptible-Exposed-Infective-Recovered (SEIR), Susceptible-Exposed-Infective-Asymptomatic-Recovered (SEIAR) models and so on. Furthermore, we propose a general fractional SEIAR model in the case of single-term and multi-term fractional differential equations. A feasible and reliable parameter estimation method based on modified hybrid Nelder-Mead simplex search and particle swarm optimisation is also presented to fit the real data using fractional SEIAR model. The effective methods to solve the fractional epidemic models we introduced construct a simple and effective analytical technique that can be easily extended and applied to other fractional models, and can help guide the concerned bodies in preventing or controlling, even predicting the infectious disease outbreaks.
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ISSN:0307-904X
1088-8691
0307-904X
DOI:10.1016/j.apm.2021.03.044