  Rift Valley fever is a vector-borne zoonotic disease which causes high
morbidity and mortality in livestock. In the event Rift Valley fever virus is
introduced to the United States or other non-endemic areas, understanding the
potential patterns of spread and the areas at risk based on disease vectors and
hosts will be vital for developing mitigation strategies. Presented here is a
general network-based mathematical model of Rift Valley fever. Given a lack of
empirical data on disease vector species and their vector competence, this
discrete time epidemic model uses stochastic parameters following several PERT
distributions to model the dynamic interactions between hosts and likely North
American mosquito vectors in dispersed geographic areas. Spatial effects and
climate factors are also addressed in the model. The model is applied to a
large directed asymmetric network of 3,621 nodes based on actual farms to
examine a hypothetical introduction to some counties of Texas, an important
ranching area in the United States of America (U.S.A.). The nodes of the
networks represent livestock farms, livestock markets, and feedlots, and the
links represent cattle movements and mosquito diffusion between different
nodes. Cattle and mosquito (Aedes and Culex) populations are treated with
different contact networks to assess virus propagation. Rift Valley fever virus
spread is assessed under various initial infection conditions (infected
mosquito eggs, adults or cattle). A surprising trend is fewer initial
infectious organisms result in a longer delay before a larger and more
prolonged outbreak. The delay is likely caused by a lack of herd immunity while
the infections expands geographically before becoming an epidemic involving
many dispersed farms and animals almost simultaneously.
