Author(s)

Gerry Baygents^*, Majid Bani-Yaghoub

Department of Mathematics and Statistics, University of Missouri Kansas City, Kansas City, MO, USA.

Hemorrhagic disease (HD) is a fatal vector-borne disease that affects white-tailed deer and many other ruminants. A vector-borne disease model is proposed in the present work, which takes into account migrating effects of deer population using distributed delay terms. The model is employed to analyze the effects of deer migration on the HD spread. This is carried out in three steps. First, the conditions for existence and stability of the endemic and the disease free equilibria are established. Second, using the method of the Next Generation Matrix, the basic reproduction expression R₀ is derived from the model. Third, using the R₀ expression and its numerical simulations, it is illustrated that the severity of an HD outbreak is directly influenced by the migration rates of infected and susceptible deer (i.e., d_I and d_S, respectively). For small values of d_S, the value of R₀ is increased with d_I, whereas R₀ decreases with d_I when d_S is large. Using the method of chain trick, the proposed model with distributed delay is reduced to a system of ordinary differential equations where the convergence of the system to endemic and diseases free equilibrium is numerically explored.

Hemorrhagic Disease, Distributed Delay, Migration, Basic Reproduction Number

Baygents, G. and Bani-Yaghoub, M. (2017) A Mathematical Model to Analyze Spread of Hemorrhagic Disease in White-Tailed Deer Population. Journal of Applied Mathematics and Physics, 5, 2262-2282. doi: 10.4236/jamp.2017.511184.