Mathematical Biosciences and Engineering (MBE)

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

Pages: 199 - 222, Volume 8, Issue 1, January 2011      doi:10.3934/mbe.2011.8.199

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Karen R. Ríos-Soto - Department of Mathematical Sciences, University of Puerto Rico-Mayagüez, Mayagüez, PR 00686, United States (email)
Baojun Song - Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043, United States (email)
Carlos Castillo-Chavez - Mathematical, Computational and Modeling Science Center, School of Mathematics and Statistic, Arizona State University, Tempe, AZ 85287, United States (email)

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.

Received: June 2010;      Accepted: September 2010;      Available Online: January 2011.