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SEIRS epidemics with disease fatalities in growing populations
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 2
2018 (English)In: Mathematical Biosciences, ISSN 0025-5564, E-ISSN 1879-3134, Vol. 296, p. 45-59Article, review/survey (Refereed) Published
Abstract [en]

An SEIRS epidemic with disease fatalities is introduced in a growing population (modelled as a super-critical linear birth and death process). The study of the initial phase of the epidemic is stochastic, while the analysis of the major outbreaks is deterministic. Depending on the values of the parameters, the following scenarios are possible. i) The disease dies out quickly, only infecting few; ii) the epidemic takes off, the number of infected individuals grows exponentially, but the fraction of infected individuals remains negligible; iii) the epidemic takes off, the number of infected grows initially quicker than the population, the disease fatalities diminish the growth rate of the population, but it remains super critical, and the fraction of infected go to an endemic equilibrium; iv) the epidemic takes off, the number of infected individuals grows initially quicker than the population, the diseases fatalities turn the exponential growth of the population to an exponential decay.

Place, publisher, year, edition, pages
2018. Vol. 296, p. 45-59
Keyword [en]
SEIRS epidemic, Threshold quantities, Initial growth, Endemic level
National Category
Biological Sciences
Identifiers
URN: urn:nbn:se:su:diva-153628DOI: 10.1016/j.mbs.2017.11.006ISI: 000425071700005PubMedID: 29155133OAI: oai:DiVA.org:su-153628DiVA, id: diva2:1189853
Available from: 2018-03-13 Created: 2018-03-13 Last updated: 2018-03-13Bibliographically approved

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