Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 138757, 12 pages
http://dx.doi.org/10.1155/2012/138757
Research Article
An Epidemiological Model of Rift Valley Fever with Spatial Dynamics
1Division of Integrated Biodefense, ISIS Center, Georgetown University Medical Center, Washington, DC 20007, USA
2Fogarty International Center, National Institutes of Health, Bethesda, MD 20892-2220, USA
3Department of Biological Sciences, Old Dominion University, Norfolk, VA 23529, USA
4Virginia Modeling Analysis & Simulation Center, Old Dominion University, Suffolk, VA 23435, USA
5Department of Microbiology and Immunology, Georgetown University Medical Center, Washington, DC 20007, USA
Received 26 January 2012; Revised 30 May 2012; Accepted 5 June 2012
Academic Editor: Gary C. An
Copyright © 2012 Tianchan Niu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of Rift Valley fever virus (RVFV) between two mosquito and one livestock species, and mother-to-offspring transmission of virus in one of the mosquito species. Space effects are introduced by dividing geographic space into smaller patches and considering the patch-to-patch movement of species. For each patch, a system of ordinary differential equations models fractions of populations susceptible to, incubating, infectious with, or immune to RVFV. The main contribution of this work is a methodology for analyzing the likelihood of pathogen establishment should an introduction occur into an area devoid of RVF. Examples are provided for general and specific cases to illustrate the methodology.