Traveling waves of infection in the hantavirus epidemics

Traveling waves are analyzed in a model of the hantavirus infection in deer mice. The existence of two kinds of wave phenomena is predicted. An environmental parameter governs a transition between two regimes of propagation. In one of them the front of infection lags behind at a constant rate. In the other, fronts of susceptible and infected mice travel at the same speed, separated by a constant delay. The dependence of the delay on system parameters is analyzed numerically and through a piecewise linearization.

[1]  J. Childs,et al.  SMALL MAMMAL SURVIVAL AND TRAPABILITY IN MARK-RECAPTURE MONITORING PROGRAMS FOR HANTAVIRUS , 1998, Journal of wildlife diseases.

[2]  James E. Childs,et al.  Long-term studies of hantavirus reservoir populations in the southwestern United States: rationale, potential, and methods. , 1999, Emerging infectious diseases.

[3]  N. Rashevsky,et al.  Mathematical biology , 1961, Connecticut medicine.

[4]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[5]  S. Ernest,et al.  Rodents, plants, and precipitation: spatial and temporal dynamics of consumers and resources , 2000 .

[6]  Biology of Peromyscus (Rodentia) , 1970 .

[7]  S. Vessey.  Long-term Population Trends in White-Footed Mice and the Impact of Supplemental Food and Shelter , 1987 .

[8]  J. Franklin,et al.  The long‐term ecological research program , 1988 .

[9]  J. Childs,et al.  Long-term studies of hantavirus reservoir populations in the southwestern United States: a synthesis. , 1999, Emerging infectious diseases.

[10]  R. Parmenter,et al.  Statistical sensitivity for detection of spatial and temporal patterns in rodent population densities. , 1999, Emerging infectious diseases.

[11]  V M Kenkre,et al.  Effects of transport memory and nonlinear damping in a generalized Fisher's equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  V. M. Kenkre,et al.  Spatiotemporal patterns in the Hantavirus infection. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  M. Morrison,et al.  The Ecology and Evolutionary History of an Emergent Disease: Hantavirus Pulmonary Syndrome , 2002 .

[14]  J J Gestal Otero,et al.  [Emerging infectious diseases]. , 1997, Medicina clinica.

[15]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[16]  J. L. Montagne,et al.  Emerging infectious diseases. , 1994, The Journal of infectious diseases.

[17]  J. Childs,et al.  Genetic identification of a hantavirus associated with an outbreak of acute respiratory illness. , 1993, Science.

[18]  J. Childs,et al.  Serologic and genetic identification of Peromyscus maniculatus as the primary rodent reservoir for a new hantavirus in the southwestern United States. , 1994, The Journal of infectious diseases.

[19]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.