Some Vector Borne Diseases with Structured Host Populations: Extinction and Spatial Spread

Stephen A. Gourley, Rongsong Liu, Jianhong Wu
2007 SIAM Journal on Applied Mathematics  
We derive from a structured population model a system of delay differential equations describing the interaction of five subpopulations, namely susceptible and infected adult and juvenile reservoirs and infected adult vectors, for a vector borne disease with particular reference to West Nile virus, and we also incorporate spatial movements by considering the analogue reactiondiffusion systems with nonlocal delayed terms. Specific conditions for the disease eradication and sharp conditions for
more » ... e local stability of the disease-free equilibrium are obtained using comparison techniques coupled with the spectral theory of monotone linear semiflows. A formal calculation of the minimal wave speed for the traveling waves is given and compared with field observation data.
doi:10.1137/050648717 fatcat:lc66ujbzgjgbbcrfayx2dlxqzq