Next Article in Journal
Fractal Simulation of Flocculation Processes Using a Diffusion-Limited Aggregation Model
Next Article in Special Issue
The Kernel of the Distributed Order Fractional Derivatives with an Application to Complex Materials
Previous Article in Journal
The Fractal Nature of an Approximate Prime Counting Function
Previous Article in Special Issue
From Circular to Bessel Functions: A Transition through the Umbral Method
Open AccessArticle

A Fractional-Order Infectivity and Recovery SIR Model

School of Mathematics and Statistics, UNSW, Sydney, NSW 2052, Australia
*
Author to whom correspondence should be addressed.
Fractal Fract 2017, 1(1), 11; https://doi.org/10.3390/fractalfract1010011
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)
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
MDPI and ACS Style

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

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop