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SPATIAL HETEROGENEITY IN SIMPLE DETERMINISTIC SIR MODELS ASSESSED ECOLOGICALLY

Part of: Mathematical biology in general

Published online by Cambridge University Press:  09 April 2013

E. K. WATERS ,
H. S. SIDHU  and
G. N. MERCER
E. K. WATERS*
Affiliation:
School of Physical, Environmental and Mathematical Sciences, The University of New South Wales Canberra, Australian Defence Force Academy, PO Box 7916, Canberra BC 2610, Australia University of Notre Dame Australia, PO Box 944, Broadway, NSW 2007, Australia
H. S. SIDHU*
Affiliation:
School of Physical, Environmental and Mathematical Sciences, The University of New South Wales Canberra, Australian Defence Force Academy, PO Box 7916, Canberra BC 2610, Australia
G. N. MERCER*
Affiliation:
National Centre for Epidemiology and Population Health, The Australian National University, Canberra, ACT 0200, Australia
*
✉[email protected]
✉[email protected]
✉[email protected]
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Abstract

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Patchy or divided populations can be important to infectious disease transmission. We first show that Lloyd’s mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity.

Keywords

SIR modelecologyinfectious diseasesspatial dynamics

MSC classification

Secondary: 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 54 , Issue 1-2 , October 2012 , pp. 23 - 36
Copyright
Copyright ©2013 Australian Mathematical Society 

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