Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission

Pierre Magal; Ousmane Seydi; Glenn Webb

doi:10.1016/j.mbs.2018.03.020

Final size of a multi-group SIR epidemic model: Irreducible and non-irreducible modes of transmission

Math Biosci. 2018 Jul:301:59-67. doi: 10.1016/j.mbs.2018.03.020. Epub 2018 Mar 29.

Authors

Pierre Magal¹, Ousmane Seydi², Glenn Webb³

Affiliations

¹ Université Bordeaux, CNRS, IMB, UMR 5251, Talence F-33400, France. Electronic address: pierre.magal@u-bordeaux.fr.
² Département Tronc Commun, École Polytechnique de Thiès, Sénégal.
³ Mathematics Department, Vanderbilt University, Nashville, TN 37240, USA.

PMID: 29604303
DOI: 10.1016/j.mbs.2018.03.020

Abstract

A model of an epidemic outbreak incorporating multiple subgroups of susceptible and infected individuals is investigated. The asymptotic behavior of the model is analyzed and it is proved that the infected classes all converge to 0. A computational algorithm is developed for the cumulative final size of infected individuals over the course of the epidemic. The results are applied to the SARS epidemic in Singapore in 2003, where it is shown that the two-peak evolution of the infected population can be attributed to a two-group formulation of transmission.

Keywords: Epidemic models; Final size; Irreducible and non-irreducible transmission; Multi-group.

MeSH terms

Algorithms
Communicable Diseases / epidemiology*
Communicable Diseases / transmission*
Disease Susceptibility
Epidemics*
Humans
Mathematical Concepts
Models, Biological*
Severe Acute Respiratory Syndrome / epidemiology
Severe Acute Respiratory Syndrome / transmission
Singapore / epidemiology