ALLEN, Linda; LANGLAIS, Michel; WESLEY, Curtis

doi:10.3934/mbe.2010.7.199

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ALLEN, Linda
Department of Mathematics and Statistics [Texas Tech]

LANGLAIS, Michel
Institut de Mathématiques de Bordeaux [IMB]
Tools of automatic control for scientific computing, Models and Methods in Biomathematics [ANUBIS]

WESLEY, Curtis
Department of Mathematics [Shreveport]

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Mathematical Biosciences and Engineering. 2010, vol. 7, n° 1, p. 199-215

AIMS Press

Résumé en anglais

Hantavirus, a zoonotic disease carried by wild rodents, is spread among rodents via direct contact and indirectly via infected rodent excreta in the soil. Spillover to humans is primarily via the indirect route through inhala- tion of aerosolized viral particles. Rodent-hantavirus models that include direct and indirect transmission and periodically varying demographic and epidemio- logical parameters are studied in this investigation. Two models are analyzed, a nonautonomous system of diﬀerential equations with time-periodic coeﬃ- cients and an autonomous system, where the coeﬃcients are taken to be the time-average. In the nonautonomous system, births, deaths, transmission rates and viral decay rates are assumed to be periodic. For both models, the basic reproduction numbers are calculated. The models are applied to two rodent populations, reservoirs for a New World and for an Old World hantavirus. The numerical examples show that periodically varying demographic and epidemi- ological parameters may substantially increase the basic reproduction number. Also, large variations in the viral decay rate in the environment coupled with an outbreak in rodent populations may lead to spillover infection in humans.< Réduire

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basic reproduction number

hantavirus

nonautonomous

periodic solutions

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Models for the spread and persistence of Hantavirus infection in rodents with direct and indirect transmission

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