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Impact of the infectious period on epidemics

Wilkinson, RR and Sharkey, KJ (2018) Impact of the infectious period on epidemics. Physical Review E, 97 (5). ISSN 2470-0045

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Open Access URL: https://dx.doi.org/10.1103/PhysRevE.97.052403 (Published version)

Abstract

The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time. For certain families of distributions, this result implies that epidemic severity is decreasing with respect to the variance of the infectious period. The striking importance of this relationship is demonstrated numerically. We then prove, with a fixed basic reproductive ratio (R0), a monotonic relationship between the variability of the posterior transmission probability (which is a function of the infectious period) and the probability that the infection will reach any given subset of the population by any given time. Thus again, even when R0 is fixed, variability of the infectious period tends to dampen the epidemic. Numerical results illustrate this but indicate the relationship is weaker. We then show how our results apply to message passing, pairwise, and Kermack-McKendrick epidemic models, even when they are not exactly consistent with the stochastic dynamics. For Poissonian contact processes, and arbitrarily distributed infectious periods, we demonstrate how systems of delay differential equations and ordinary differential equations can provide upper and lower bounds, respectively, for the probability that any given individual has been infected by any given time.

Item Type: Article
Uncontrolled Keywords: Science & Technology; Physical Sciences; Physics, Fluids & Plasmas; Physics, Mathematical; Physics; DYNAMICS; MODELS
Subjects: R Medicine > R Medicine (General)
R Medicine > RB Pathology
Divisions: Applied Mathematics
Publisher: American Physical Society
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Date Deposited: 03 Jul 2019 09:04
Last Modified: 03 Jul 2019 09:04
DOI or Identification number: 10.1103/PhysRevE.97.052403
URI: http://researchonline.ljmu.ac.uk/id/eprint/10962

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