Periodicity in an Epidemiological Model of Measles Infection and Immunity

Hossein Zivari Piran and Jane Heffernan ()
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Hossein Zivari Piran: Evidera Inc
Jane Heffernan: York University, Department of Mathematics and Statistics

A chapter in Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, 2025, pp 1-24 from Springer

Abstract: Abstract Interest lies in understanding the mechanisms that underlie temporal oscillations of diseases and their associated mathematical models. Here, we study the oscillations reported in Heffernan and Keeling (Proc. Biol Sci R Soc 276:2071–80, 2009) that use a model of > 500 $${>}500$$ ordinary differential equations to model measles infection and immunity. While very large, the system is sparse and lends itself to numerical bifurcation analysis. Bifurcation analysis uncovers a Hopf bifurcation with small amplitude. Medium- and large-amplitude cycles are also found to exist. The existence of all three generators of cyclic dynamics and the changes of cycles related to global bifurcations are described using a corresponding Poincaré return map.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-97461-8_1

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DOI: 10.1007/978-3-031-97461-8_1

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