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Periodicity in an Epidemiological Model of Measles Infection and Immunity

In: Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells

Author

Listed:
  • Hossein Zivari Piran

    (Evidera Inc)

  • Jane Heffernan

    (York University, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Hossein Zivari Piran & Jane Heffernan, 2025. "Periodicity in an Epidemiological Model of Measles Infection and Immunity," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling Health Across Ecology, Social Interactions, and Cells, pages 1-24, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-97461-8_1
    DOI: 10.1007/978-3-031-97461-8_1
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