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

Stephen A. Gourley | Zendy; Rongsong Liu | Zendy; Jian Wu | Zendy

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

Author(s) -

Stephen A. Gourley,

Rongsong Liu,

Jian Wu

Publication year - 2007

Publication title -

siam journal on applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.954

H-Index - 99

eISSN - 1095-712X

pISSN - 0036-1399

DOI - 10.1137/050648717

Subject(s) - monotone polygon , mathematics , extinction (optical mineralogy) , population , diffusion , vector field , mathematical analysis , statistical physics , physics , geometry , demography , optics , thermodynamics , sociology

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 reaction diffusion systems with nonlocal delayed terms. Specific conditions for the disease eradication and sharp conditions for the local stability of the disease-free equilibrium are obtained using comparison techniques coupled with the spectral theory of monotone linear semi flows. A formal calculation of the minimal wave speed for the traveling waves is given and compared with field observation data.

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