title: A mathematical model of avian influenza with half-saturated incidence.
abstract: The widespread impact of avian influenza viruses not only poses risks to birds, but also to humans. The viruses spread from birds to humans and from human to human In addition, mutation in the primary strain will increase the infectiousness of avian influenza. We developed a mathematical model of avian influenza for both bird and human populations. The effect of half-saturated incidence on transmission dynamics of the disease is investigated. The half-saturation constants determine the levels at which birds and humans contract avian influenza. To prevent the spread of avian influenza, the associated half-saturation constants must be increased, especially the half-saturation constant H m for humans with mutant strain. The quantity H m plays an essential role in determining the basic reproduction number of this model. Furthermore, by decreasing the rate β m at which human-to-human mutant influenza is contracted, an outbreak can be controlled more effectively. To combat the outbreak, we propose both pharmaceutical (vaccination) and non-pharmaceutical (personal protection and isolation) control methods to reduce the transmission of avian influenza. Vaccination and personal protection will decrease β m, while isolation will increase H m. Numerical simulations demonstrate that all proposed control strategies will lead to disease eradication; however, if we only employ vaccination, it will require slightly longer to eradicate the disease than only applying non-pharmaceutical or a combination of pharmaceutical and non-pharmaceutical control methods. In conclusion, it is important to adopt a combination of control methods to fight an avian influenza outbreak.
authors.affiliation: Department of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada.
authors.forename: Nyuk Sian
authors.initials: NS
authors.lastname: Chong
authors.forename: Jean Michel
authors.initials: JM
authors.lastname: Tchuenche
authors.forename: Robert J
authors.initials: RJ
authors.lastname: Smith
mesh_terms: D000818:Animals; D001717:Birds; D003198:Computer Simulation; D004196:Disease Outbreaks / Q000517:prevention & control; D006801:Humans; D015994:Incidence; D007252:Influenza Vaccines; D005585:Influenza in Birds / Q000453:epidemiology* / Q000635:transmission; D007251:Influenza, Human / Q000453:epidemiology* / Q000517:prevention & control / Q000635:transmission; D008962:Models, Theoretical; D009154:Mutation; D013997:Time Factors
chemical_list: D007252:Influenza Vaccines