title: Environmentally driven epizootics.
abstract: Environmental conditions can be the driving force behind an epizootic. Environmental changes may favor growth of a particular species, which results in increased contact rates and spread of a disease. We examine this particular phenomenon in SI and SIS models and use it to explain the possible disease outbreaks in nature. Either infected individuals recover from the disease (SIS model) or suffer disease fatalities (SI model). Epizootic models for a single population are examined where contact rate depends on population size. A reproductive number R is defined that depends on environmental carrying capacity. The single-population models are coupled to form three different two-species models with intra- and interspecies contact rates that depend on the population sizes of both populations. The stability results show that it is possible for the disease to drive one of the populations to extinction, the one with disease fatalities. The surviving species serves as a reservoir for the disease. Single- and two-species epizootic models are examined in a particular case where the contact rates are assumed to be constant. This leads to a new definition for the contact rate. A complete global analysis is possible in these latter cases. The results are compared and contrasted with the models with variable contact rates. The prototype for the models is the spread of disease in wildlife populations, which includes such diseases as plague or Lyme disease.
authors.affiliation: Department of Mathematics, Texas Tech University, Lubbock 79409, USA.
authors.forename: L J
authors.initials: LJ
authors.lastname: Allen
authors.forename: P J
authors.initials: PJ
authors.lastname: Cormier
mesh_terms: D000818:Animals; D003141:Communicable Diseases / Q000635:transmission / Q000662:veterinary; D004196:Disease Outbreaks / Q000662:veterinary*; D004777:Environment; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D011157:Population Dynamics