An Epidemiological Model of Rift Valley Fever with Spatial Dynamics

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.

A dynamic, climate-driven model of Rift Valley fever

“…For further information regarding the derivation of this transmission term see the Appendix. The incubation parameter, si, is defined as the inverse of a 3.5-day latent period (Turell et al, 1985;Gaff et al, 2007;Niu et al, 2012) and the recovery rate is based on a 6.5-day infectious period (Bird et al, 2009;Nfon et al, 2012). The infection-induced mortality probability, i.e., the probability of dying due to RVF infection before recovering, is based on case fatality rates (Bird et al, 2009 …”

“…Previous RVF modelling efforts using dynamic mathematical models have largely focused on the epidemic stability of susceptible host populations when the virus is introduced (Gaff et al, 2007;Mpeshe et al, 2011;Niu et al, 2012). These studies comprise theoretical exercises concentrating purely on transmission during different epidemiological states independent of climate.…”

Modelling Vaccination Strategies against Rift Valley Fever in Livestock in Kenya

“…al [17] reported that an outbreak size was sensitive to vector-to-host ratio, mosquito biting rate and the infectivity of hosts. Other models [15][16][35] reported adequate contact rates between vectors and hosts and the rate of recovery livestock as sensitive to the basic reproduction number. However, their definition of adequate contact rates between vectors and hosts considered a composite term whereas in our model, we disaggregated the term into its individual components including the vector biting rate, host infectivity, blood meal index and vector host ratio.…”

A Flexible Spatial Framework for Modeling Spread of Pathogens in Animals with Biosurveillance and Disease Control Applications

“…The framework we outline here builds upon and extends existing work to model spatial spread of animal disease [14][15][16][17][18][19][20]. Our work highlights the important and interacting roles of geography, and the spatial aspects of host diversity, host distribution, long and short distance movement, human-livestock interactions, and possible interventions.…”