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Unformatted text preview: AN AVIAN INFLUENZA MODEL AND ITS FIT TO HUMAN AVIAN INFLUENZA CASES JOSEPH LUCCHETTI, MANOJIT ROY, AND MAIA MARTCHEVA * Abstract. Low Pathogenic Avian Influenza (LPAI) virus, which circulates in wild bird populations in mostly benign form, is suspected to have mutated into a highly pathogenic (HPAI) strain after transmission to the domestic birds. HPAI has recently garnered worldwide attention because of the spillover infection of this strain from do- mestic birds to humans - primarily those in poultry industry - causing significant human fatality and thus creating potentially favorable conditions for another flu pandemic. We use an ordinary differential equation model to describe this complex dynamics of the HPAI virus, which epidemiologically links a number of species in a multi-species com- munity. We include the wild bird population as a periodic source feeding infection to the coupled domestic bird-human system. We also account for mutation between the low and high pathogenic strains. Finally, we fit our model to the actual number of human avian influenza cases obtained from WHO, and estimate the relevant repro- duction numbers. We discuss open questions and problems in modeling the complex epidemiology of avian influenza. Keywords: avian influenza, low-pathogenic avian influenza, high-pathogenic avian influenza, strains, competitive coexistence exclusion, human cases, data fitting. AMS Subject Classification: 92D30, 92D40 1. The Ecology and Epidemiology of Avian Influenza Influenza viruses belong to the family Orthomyxoviridae (Greek orthos means straight, and myxo means mucus, implying a disease with respiratory symptoms), and are made up of segmented, negative sense, single stranded RNA genomes . Orthomyxoviridae family currently consists of five distinct genera: Influenzavirus A , Influenzavirus B , Influenzavirus C (also known as Influenza virus types A, B and C those that cause influenza in vertebrate animals including birds), Thogotovirus (tickborne viruses that can also infect mammals) and Isavirus (a viral disease of Atlantic salmon). Among them, only the viruses of Influenza A genus are known to cause Avian Influenza (AI) infection in birds. The RNA genome of these viruses is made up of eight sections corresponding to the proteins they encode, and is encapsulated by a lipid bilayer obtained from host cells. Studding this outer shell are hemagglutinin (HA) and neuraminidase (NA) proteins, which play key roles in fusion of the viral envelope to host cells. Sixteen sufficiently distinct HA molecules (H1H16) and nine NA molecules (N1N9) have been observed in influenza A viruses that allow their further classification into subtypes. For example, the most recent AI outbreaks are due to the H5N1 subtype, whereas the previous three major outbreaks that led to pandemics were attributed to H1N1 (Spanish Influenza, during Date : November 26, 2008....
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