Elsevier

Applied Mathematical Modelling

Volume 97, September 2021, Pages 281-307
Applied Mathematical Modelling

Review of fractional epidemic models

https://doi.org/10.1016/j.apm.2021.03.044Get rights and content

Abstract

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.

Keywords

Epidemic models
Fractional order differential equations
Multi-term epidemic models
Parameter estimation
Implicit numerical method
Hybrid simplex search and particle swarm optimisation

Classification

26A33
97M60
37M05
37N30

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