A Mathematical Model to Analyze Spread of Hemorrhagic Disease in White-Tailed Deer Population

Hemorrhagic disease (HD) is a fatal vector-borne disease that affects white-tailed deer and many other ruminants. They often suffer from one of two hemorrhagic diseases (HD): epizootic hemorrhagic disease (EHD) or bluetongue virus (BTV). The symptoms include hemorrhaging, swelling due to fluid accumulation, sores, ulcers, sloughing of hooves, high fever, and loss of fear of humans. And the vector that spreads HD is small biting midge (Culicoides Ceratopogondiae). These midges are tiny, blood-sucking flies that are merely pests to humans, but they are the vectors in the spread of the disease in deer and livestock.

In recent years, more realistic models have been constructed which take into account dispersion time and host movements of HD. However, few models have been constructed to analyze the dynamics of HD in white-tailed deer populations and dairy farms. In the present work, a vector-borne disease model was proposed in the present work, which took into account migrating effects of deer population using distributed delay terms. The model was employed to analyze the effects of deer migration on the HD spread. This was carried out in three steps. First, the conditions for existence and stability of the endemic and the disease free equilibria were established. Second, using the method of the Next Generation Matrix, the basic reproduction expression R₀ was derived from the model. Third, using the R₀ expression and its numerical simulations, it was illustrated that the severity of an HD outbreak was directly influenced by the migration rates of infected and susceptible deer (i.e., d_I and d_S, respectively).

The results showed that for small values of d_S, the value of R₀ was increased with d_I, whereas c decreased with d_I when d_S was large. And using the method of chain trick, the proposed model with distributed delay was reduced to a system of ordinary differential equations where the convergence of the system to endemic and diseases free equilibrium was numerically explored.

In conclusion, the present work is the first step towards inclusion of migration effects of deer population modeling of HD dynamics. The R₀ expression provides insights into the effects of deer movement on the spread of disease.

Article by Gerry Baygents and Majid Bani-Yaghoub, from University of Missouri Kansas City, Kansas City, MO, USA.

Full access: http://mrw.so/1yNXLb

Image by Angel Cher ♥, from Flickr-cc.