Impact of the infectious period on epidemics

Wilkinson, R and sharkey, KJ ORCID: 0000-0002-7210-9246 (2018) Impact of the infectious period on epidemics. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 97 (5). 052403-.

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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:	diseases, epidemic, spreading
Depositing User:	Symplectic Admin
Date Deposited:	24 May 2018 10:30
Last Modified:	19 Jan 2023 01:33
DOI:	10.1103/PhysRevE.97.052403
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3021701

Available Versions of this Item

• The impact of the infectious period on epidemics. (deposited 22 Nov 2017 10:04)
  • Impact of the infectious period on epidemics. (deposited 24 May 2018 10:30) [Currently Displayed]