# American Institute of Mathematical Sciences

2010, 7(1): 195-211. doi: 10.3934/mbe.2010.7.195

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

 1 Louisiana State University in Shreveport, Department of Mathematics, Shreveport, LA 71115, United States 2 Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, United States 3 Université Victor Segalen Bordeaux 2, IMB UMR CNRS 5251 & INRIA Bordeaux Sud Ouest projet Anubis, case 36, UFR Sciences et Modelisation, 3 ter place de la Victoire, 33076 Bordeaux Cedex, France

Received  March 2009 Revised  July 2009 Published  January 2010

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 inhalation of aerosolized viral particles. Rodent-hantavirus models that include direct and indirect transmission and periodically varying demographic and epidemiological parameters are studied in this investigation. Two models are analyzed, a nonautonomous system of differential equations with time-periodic coefficients 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 epidemiological 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.
Citation: Curtis L. Wesley, Linda J. S. Allen, Michel Langlais. Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 195-211. doi: 10.3934/mbe.2010.7.195
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