A fractional-order infectivity SIR model

C.N. Angstmann, B.I. Henry and A.V. McGann

Physica A: Statistical Mechanics and its Applications, 2016, vol. 452, issue C, 86-93

Abstract: Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order infectivity SIR model from a stochastic process that incorporates a time-since-infection dependence on the infectivity of individuals. The fractional derivative appears in the generalised master equations of a continuous time random walk through SIR compartments, with a power-law function in the infectivity. We show that this model can also be formulated as an infection-age structured Kermack–McKendrick integro-differential SIR model. Under the appropriate limit the fractional infectivity model reduces to the standard ordinary differential equation SIR model.

Keywords: Epidemiological models; SIR models; Fractional order differential equations; Continuous time random walk (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:452:y:2016:i:c:p:86-93

DOI: 10.1016/j.physa.2016.02.029

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