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Coupled Systems of Renewal Equations for Forces of Infection through a Contact Network

Part of: Mathematical biology in general

Published online by Cambridge University Press:  04 December 2019

Mahnaz Alavinejad  and
Jianhong Wu
Mahnaz Alavinejad
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada Email: mahnazal@yorku.cawujh@mathstat.yorku.ca
Jianhong Wu
Affiliation:
Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada Email: mahnazal@yorku.cawujh@mathstat.yorku.ca
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Abstract

We formulate a coupled system of renewal equations for the forces of infections in interacting subgroups through a contact network. We use the theory of order-preserving and sub-homogeneous discrete dynamical systems to show the existence and uniqueness of the disease outbreak final sizes in the sub-populations. We illustrate the general theory through a simple SIR model with exponentially and non-exponentially distributed infectious period.

Keywords

force of infectionrenewal equationepidemic final size

MSC classification

Primary: 92B05: General biology and biomathematics
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 3 , September 2020 , pp. 624 - 632
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

This research has been partially supported by NSERC, the Canada Research Chair Program, and the NSERC-Sanofi Industrial Research Chair Program in Vaccine Mathematics, Modeling, and Manufacturing.

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