Journal of Mathematical Biology
, Volume 67, Issue 4, pp 963987
First online:
The effect of population heterogeneities upon spread of infection
 Damian ClancyAffiliated withDepartment of Mathematical Sciences, University of Liverpool Email author
 , Christopher J. PearceAffiliated withDepartment of Mathematical Sciences, University of Liverpool
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It has often been observed that population heterogeneities can lead to outbreaks of infection being less frequent and less severe than homogeneous population models would suggest. We address this issue by comparing a model incorporating various forms of heterogeneity with a homogenised model matched according to the value of the basic reproduction number \(R_0\). We mainly focus upon heterogeneity in individuals’ infectivity and susceptibility, though with some allowance also for heterogeneous patterns of mixing. The measures of infectious spread we consider are (i) the probability of a major outbreak; (ii) the mean outbreak size; (iii) the mean endemic prevalence level; and (iv) the persistence time. For each measure, we establish conditions under which heterogeneity leads to a reduction in infectious spread. We also demonstrate that if such conditions are not satisfied, the reverse may occur. As well as comparison with a homogeneous population, we investigate comparisons between two heterogeneous populations of differing degrees of heterogeneity. All of our results are derived under the assumption that the susceptible population is sufficiently large.
Keywords
Basic reproduction number SIR epidemic SIS epidemic Outbreak size Endemic prevalence Fadeout of infectionMathematics Subject Classification (2000)
92D30 60J85 60J28 Title
 The effect of population heterogeneities upon spread of infection
 Journal

Journal of Mathematical Biology
Volume 67, Issue 4 , pp 963987
 Cover Date
 201310
 DOI
 10.1007/s002850120578x
 Print ISSN
 03036812
 Online ISSN
 14321416
 Publisher
 Springer Berlin Heidelberg
 Additional Links
 Topics
 Keywords

 Basic reproduction number
 SIR epidemic
 SIS epidemic
 Outbreak size
 Endemic prevalence
 Fadeout of infection
 92D30
 60J85
 60J28
 Industry Sectors
 Authors

 Damian Clancy ^{(1)}
 Christopher J. Pearce ^{(1)}
 Author Affiliations

 1. Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK