Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics

Karen R. Ríos-Soto; Baojun Song; Carlos Castillo-Chavez

doi:10.3934/mbe.2011.8.199

Article Contents

2011, Volume 8, Issue 1: 199-222. Doi: 10.3934/mbe.2011.8.199 open access

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Epidemic spread of influenza viruses: The impact of transient populations on disease dynamics

1.
Department of Mathematical Sciences, University of Puerto Rico-Mayagüez, Mayagüez, PR 00686
2.
Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043
3.
Mathematical, Computational and Modeling Science Center, School of Mathematics and Statistic, Arizona State University, Tempe, AZ 85287

Received: June 2010

Revised: September 2010

Published: January 2011

Abstract / Introduction Related Papers Cited by

Abstract

The recent H1N1 ("swine flu") pandemic and recent H5N1 ("avian flu") outbreaks have brought increased attention to the study of the role of animal populations as reservoirs for pathogens that could invade human populations. It is believed that pigs acquired flu strains from birds and humans, acting as a mixing vessel in generating new influenza viruses. Assessing the role of animal reservoirs, particularly reservoirs involving highly mobile populations (like migratory birds), on disease dispersal and persistence is of interests to a wide range of researchers including public health experts and evolutionary biologists. This paper studies the interactions between transient and resident bird populations and their role on dispersal and persistence. A metapopulation framework based on a system of nonlinear ordinary differential equations is used to study the transmission dynamics and control of avian diseases. Simplified versions of mathematical models involving a limited number of migratory and resident bird populations are analyzed. Epidemiological time scales and singular perturbation methods are used to reduce the dimensionality of the model. Our results show that mixing of bird populations (involving residents and migratory birds) play an important role on the patterns of disease spread.

Keywords:

Epidemic Models; Epidemiological Time Scales; Singular Perturbation Theory; Avian Influenza; Mixing Probabilities.

Mathematics Subject Classification: 92D30, 92D25, 37N25.

Citation:

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