The Final Size of an Epidemic and Its Relation to the Basic Reproduction Number.
Summary of "The Final Size of an Epidemic and Its Relation to the Basic Reproduction Number."
We study the final size equation for an epidemic in a subdivided population with general mixing patterns among subgroups. The equation is determined by a matrix with the same spectrum as the next generation matrix and it exhibits a threshold controlled by the common dominant eigenvalue, the basic reproduction number [Formula: see text]: There is a unique positive solution giving the size of the epidemic if and only if [Formula: see text] exceeds unity. When mixing heterogeneities arise only from variation in contact rates and proportionate mixing, the final size of the epidemic in a heterogeneously mixing population is always smaller than that in a homogeneously mixing population with the same basic reproduction number [Formula: see text]. For other mixing patterns, the relation may be reversed.
Affiliation
Department of Science, Roskilde University, 4000, Roskilde, Denmark, viggo@ruc.dk.
Journal Details
This article was published in the following journal.
Name: Bulletin of mathematical biology
ISSN: 1522-9602
Pages:
Links
- PubMed Source: http://www.ncbi.nlm.nih.gov/pubmed/21210241
- DOI: http://dx.doi.org/10.1007/s11538-010-9623-3
Medical and Biotech [MESH] Definitions
Basic Reproduction Number
The expected number of new cases of an infection caused by an infected individual, in a population consisting of susceptible contacts only.
Reproductive Rights
Reproductive rights rest on the recognition of the basic right of all couples and individuals to decide freely and responsibly the number, spacing and timing of their children and to have the information and means to do so, and the right to attain the highest standard of sexual and reproductive health. They also include the right of all to make decisions concerning reproduction free of discrimination, coercion and violence.
Sample Size
The number of units (persons, animals, patients, specified circumstances, etc.) in a population to be studied. The sample size should be big enough to have a high likelihood of detecting a true difference between two groups. (From Wassertheil-Smoller, Biostatistics and Epidemiology, 1990, p95)
Rickettsia Prowazekii
A species of gram-negative, aerobic bacteria that is the etiologic agent of epidemic typhus fever acquired through contact with lice (TYPHUS, EPIDEMIC LOUSE-BORNE) as well as Brill's disease.
Crowding
Behavior with respect to an excessive number of individuals, human or animal, in relation to available space.
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