MODELING SEASONALITY IN AVIAN INFLUENZA H5N1

The number of cases of H5N1 avian influenza in birds and humans exhibit seasonality which peaks during the winter months. What causes the seasonality in H5N1 cases is still being investigated. This article addresses the question of modeling the periodicity in cumulative number of human cases of H5N1. Three potential drivers of influenza seasonality are investigated: (1) seasonality in bird-to-bird transmission; (2) seasonality caused by wild bird migration or seasonal fluctuation of avian influenza in wild birds; (3) seasonality caused by environmental transmission. A framework of seven models is composed. The seven models involve these three mechanisms and combinations of the mechanisms. Each of the models in the framework is fitted to the cumulative number of humans cases of H5N1. The corrected akaike information criterion (AICc) is used to compare the models and it is found that the model with periodic bird-to-bird transmission rate best explains the data. The best fitted model with the best fitted parameters gives a reproduction number of highly pathogenic avian influenza . The best fitted model is a simple SI epidemic model with periodic transmission rate and disease-induced mortality, however, this model is capable of very complex dynamical behavior such as period doubling and chaos.

[1]  Pejman Rohani,et al.  The Role of Environmental Transmission in Recurrent Avian Influenza Epidemics , 2009, PLoS Comput. Biol..

[2]  T. P. van den Berg,et al.  H5N1 High Pathogenicity Avian Influenza Virus Survival in Different Types of Water , 2010 .

[3]  A. Osterhaus,et al.  Global Patterns of Influenza A Virus in Wild Birds , 2006, Science.

[4]  Angus Nicoll,et al.  Avian influenza A (H5N1) infection in humans. , 2005, The New England journal of medicine.

[5]  Amit Huppert,et al.  Seasonal dynamics and thresholds governing recurrent epidemics , 2008, Journal of mathematical biology.

[6]  Baoping Yan,et al.  Wild Bird Migration across the Qinghai-Tibetan Plateau: A Transmission Route for Highly Pathogenic H5N1 , 2011, PloS one.

[7]  D. Stallknecht,et al.  Persistence of avian influenza viruses in water. , 1990, Avian diseases.

[8]  Christopher M. Fuhrmann,et al.  The Effects of Weather and Climate on the Seasonality of Influenza: What We Know and What We Need to Know , 2010 .

[9]  M. Martcheva A non-autonomous multi-strain SIS epidemic model , 2009, Journal of biological dynamics.

[10]  Xianning Liu,et al.  Avian flu pandemic: Can we prevent it? , 2009, Journal of theoretical biology.

[11]  S. Morse,et al.  Seasonal Oscillation of Human Infection with Influenza A/H5N1 in Egypt and Indonesia , 2011, PloS one.

[12]  Y. Guan,et al.  Genesis of a highly pathogenic and potentially pandemic H5N1 influenza virus in eastern Asia , 2004, Nature.

[13]  E. Lofgren,et al.  Influenza Seasonality: Underlying Causes and Modeling Theories , 2006, Journal of Virology.

[14]  Xiao-Qiang Zhao,et al.  Threshold Dynamics for Compartmental Epidemic Models in Periodic Environments , 2008 .

[15]  J. Drake,et al.  A general multi-strain model with environmental transmission: invasion conditions for the disease-free and endemic states. , 2010, Journal of theoretical biology.

[16]  Junling Ma,et al.  Epidemic threshold conditions for seasonally forced seir models. , 2005, Mathematical biosciences and engineering : MBE.

[17]  M. Beer,et al.  Highly Pathogenic Avian Influenza Virus Infection of Mallards with Homo- and Heterosubtypic Immunity Induced by Low Pathogenic Avian Influenza Viruses , 2009, PloS one.

[18]  N. Stilianakis,et al.  Migratory birds, the H5N1 influenza virus and the scientific method , 2008, Virology Journal.

[19]  I B Schwartz,et al.  Seasonality and period-doubling bifurcations in an epidemic model. , 1984, Journal of theoretical biology.

[20]  Jonathan Z Kaye,et al.  Environmental persistence of a highly pathogenic avian influenza (H5N1) virus. , 2010, Environmental science & technology.

[21]  A. Hampson Epidemiological data on influenza in Asian countries. , 1999, Vaccine.

[22]  J. du Prel,et al.  Are meteorological parameters associated with acute respiratory tract infections? , 2009, Clinical infectious diseases : an official publication of the Infectious Diseases Society of America.

[23]  Xianning Liu,et al.  Avian-human influenza epidemic model. , 2007, Mathematical biosciences.

[24]  David R. Anderson,et al.  Model selection and multimodel inference : a practical information-theoretic approach , 2003 .

[25]  Theo M Bestebroer,et al.  Airborne Transmission of Influenza A/H5N1 Virus Between Ferrets , 2012, Science.

[26]  D. Stallknecht,et al.  Effects of pH, temperature, and salinity on persistence of avian influenza viruses in water. , 1990, Avian diseases.

[27]  Marcos A. Capistrán,et al.  First Principles Modeling of Nonlinear Incidence Rates in Seasonal Epidemics , 2011, PLoS Comput. Biol..

[28]  Xianning Liu,et al.  Prevention of avian influenza epidemic: what policy should we choose? , 2008, Journal of theoretical biology.

[29]  Horst R. Thieme,et al.  Mathematics in Population Biology , 2003 .

[30]  John M Drake,et al.  Environmental transmission of low pathogenicity avian influenza viruses and its implications for pathogen invasion , 2009, Proceedings of the National Academy of Sciences.

[31]  L. Fang,et al.  Environmental Factors Contributing to the Spread of H5N1 Avian Influenza in Mainland China , 2008, PloS one.

[32]  J. Guégan,et al.  Water-borne transmission drives avian influenza dynamics in wild birds: the case of the 2005-2006 epidemics in the Camargue area. , 2009, Infection, genetics and evolution : journal of molecular epidemiology and evolutionary genetics in infectious diseases.

[33]  Suzanne M. O’Regan Impact of seasonality upon the dynamics of a novel pathogen in a seabird colony , 2008 .

[34]  A. Ike,et al.  Long-Term Study on Tenacity of Avian Influenza Viruses in Water (Distilled Water, Normal Saline, and Surface Water) at Different Temperatures , 2010, Avian diseases.

[35]  I. A. Moneim,et al.  Seasonally varying epidemics with and without latent period: a comparative simulation study. , 2007, Mathematical medicine and biology : a journal of the IMA.

[36]  Takafumi Suzuki,et al.  Paradox of Vaccination: Is Vaccination Really Effective against Avian Flu Epidemics? , 2009, PloS one.

[37]  Yi Guan,et al.  Avian Influenza Virus (H5N1): a Threat to Human Health , 2007, Clinical Microbiology Reviews.

[38]  Andrew W Park,et al.  Dynamic patterns of avian and human influenza in east and southeast Asia. , 2007, The Lancet. Infectious diseases.

[39]  M. Ward,et al.  Estimation of the basic reproductive number (R0) for epidemic, highly pathogenic avian influenza subtype H5N1 spread , 2008, Epidemiology and Infection.

[40]  H. Heesterbeek,et al.  Wild Birds and Increased Transmission of Highly Pathogenic Avian Influenza (H5N1) among Poultry, Thailand , 2011, Emerging Infectious Diseases.

[41]  Rudolf T Hoogenveen,et al.  Chronic disease projections in heterogeneous ageing populations: approximating multi-state models of joint distributions by modelling marginal distributions. , 2010, Mathematical medicine and biology : a journal of the IMA.

[42]  W. J. Bean,et al.  Intestinal influenza: Replication and characterization of influenza viruses in ducks , 1978, Virology.

[43]  Christl A. Donnelly,et al.  Estimation of Transmission Parameters of H5N1 Avian Influenza Virus in Chickens , 2009, PLoS pathogens.