TITLE:
A Mathematical Model to Analyze Spread of Hemorrhagic Disease in White-Tailed Deer Population
AUTHORS:
Gerry Baygents, Majid Bani-Yaghoub
KEYWORDS:
Hemorrhagic Disease, Distributed Delay, Migration, Basic Reproduction Number
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.11,
November
29,
2017
ABSTRACT: 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., dI and dS, respectively). For small values of dS, the value of R0 is increased with dI, whereas R0 decreases with dI when dS 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.