dorsal/arxiv
View SchemaPredicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility
| Authors | Joel C. Miller |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0702007 |
| URL | https://arxiv.org/abs/q-bio/0702007 |
| DOI | 10.1103/PhysRevE.76.010101 |
Abstract
We analytically address disease outbreaks in large, random networks with heterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$ (the probability that infection of $u$ causes infection of $v$) depends on the infectivity of $u$ and the susceptibility of $v$. Initially a single node is infected, following which a large-scale epidemic may or may not occur. We use a generating function approach to study how heterogeneity affects the probability that an epidemic occurs and, if one occurs, its attack rate (the fraction infected). For fixed average transmissibility, we find upper and lower bounds on these. An epidemic is most likely if infectivity is homogeneous and least likely if the variance of infectivity is maximized. Similarly, the attack rate is largest if susceptibility is homogeneous and smallest if the variance is maximized. We further show that heterogeneity in infectious period is important, contrary to assumptions of previous studies. We confirm our theoretical predictions by simulation. Our results have implications for control strategy design and identification of populations at higher risk from an epidemic.
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"abstract": "We analytically address disease outbreaks in large, random networks with\nheterogeneous infectivity and susceptibility. The transmissibility $T_{uv}$\n(the probability that infection of $u$ causes infection of $v$) depends on the\ninfectivity of $u$ and the susceptibility of $v$. Initially a single node is\ninfected, following which a large-scale epidemic may or may not occur. We use a\ngenerating function approach to study how heterogeneity affects the probability\nthat an epidemic occurs and, if one occurs, its attack rate (the fraction\ninfected). For fixed average transmissibility, we find upper and lower bounds\non these. An epidemic is most likely if infectivity is homogeneous and least\nlikely if the variance of infectivity is maximized. Similarly, the attack rate\nis largest if susceptibility is homogeneous and smallest if the variance is\nmaximized. We further show that heterogeneity in infectious period is\nimportant, contrary to assumptions of previous studies. We confirm our\ntheoretical predictions by simulation. Our results have implications for\ncontrol strategy design and identification of populations at higher risk from\nan epidemic.",
"arxiv_id": "q-bio/0702007",
"authors": [
"Joel C. Miller"
],
"categories": [
"q-bio.QM",
"q-bio.PE"
],
"doi": "10.1103/PhysRevE.76.010101",
"title": "Predicting the size and probability of epidemics in a population with heterogeneous infectiousness and susceptibility",
"url": "https://arxiv.org/abs/q-bio/0702007"
},
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