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.
Highlights
Hemorrhagic disease (HD) is a fatal disease of white-tailed deer (Odocoileus virginianus)
A vector-borne disease model is proposed in the present work, which takes into account migrating effects of deer population using distributed delay terms
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
Summary
Hemorrhagic disease (HD) is a fatal disease of white-tailed deer (Odocoileus virginianus) It is the collective term used for epizootic hemorrhagic disease and bluetongue disease (genus Orbivirus). Using a deterministic modeling approach, the main objective of the present study is to have a better understanding of the possible effects of deer-midge interactions and deer migrations on HD dynamics in a deer population. Few models have been constructed to analyze the dynamics of HD in white-tailed deer populations and dairy farms. The present work is the first step toward realistic modeling of HD dynamics with a focus on migrating effects of white-tailed deer population. This model takes into account the migration and immigration of deer from and into a single patch.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call