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Fractal Fract 2017, 1(1), 11; doi:10.3390/fractalfract1010011

A Fractional-Order Infectivity and Recovery SIR Model

School of Mathematics and Statistics, UNSW, Sydney, NSW 2052, Australia
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Received: 31 October 2017 / Revised: 14 November 2017 / Accepted: 15 November 2017 / Published: 17 November 2017
(This article belongs to the Special Issue Fractional Dynamics)
View Full-Text   |   Download PDF [238 KB, uploaded 19 November 2017]

Abstract

The introduction of fractional-order derivatives to epidemiological compartment models, such as SIR models, has attracted much attention. When this introduction is done in an ad hoc manner, it is difficult to reconcile parameters in the resulting fractional-order equations with the dynamics of individuals. This issue is circumvented by deriving fractional-order models from an underlying stochastic process. Here, we derive a fractional-order infectivity and recovery Susceptible Infectious Recovered (SIR) model from the stochastic process of a continuous-time random walk (CTRW) that incorporates a time-since-infection dependence on both the infectivity and the recovery of the population. By considering a power-law dependence in the infectivity and recovery, fractional-order derivatives appear in the generalised master equations that govern the evolution of the SIR populations. Under the appropriate limits, this fractional-order infectivity and recovery model reduces to both the standard SIR model and the fractional recovery SIR model. View Full-Text
Keywords: epidemiological models; SIR models; fractional-order differential equations; continuous-time random walk epidemiological models; SIR models; fractional-order differential equations; continuous-time random walk
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Angstmann, C.N.; Henry, B.I.; McGann, A.V. A Fractional-Order Infectivity and Recovery SIR Model. Fractal Fract 2017, 1, 11.

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