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Diffusive Logistic Equations With Harvesting And Heterogeneity Under Strong Growth Rate, Saeed Shabani Rokn-E-Vafa, Hossein T. Tehrani
Diffusive Logistic Equations With Harvesting And Heterogeneity Under Strong Growth Rate, Saeed Shabani Rokn-E-Vafa, Hossein T. Tehrani
Mathematical Sciences Faculty Research
We consider the equation −Δu=au−b(x)u2−ch(x) in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in RN, b(x) and h(x) are nonnegative functions, and there exists Ω0⊂⊂Ω such that {x:b(x)=0}=Ω¯¯¯0. We investigate the existence of positive solutions of this equation for c large under the strong growth rate assumption a≥λ1(Ω0), where λ1(Ω0) is the first eigenvalue of the −Δ in Ω0 with Dirichlet boundary condition. We show that if h≡0 in Ω∖Ω¯¯¯0, then our equation has a unique positive solution for all c large, provided that a is in a right neighborhood of λ1(Ω0). For this purpose, we prove …
A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson
A Two-Species Stage-Structured Model For West Nile Virus Transmission, Taylor A. Beebe, Suzanne L. Robertson
Mathematics and Applied Mathematics Publications
We develop a host–vector model of West Nile virus (WNV) transmission that incorporates multiple avian host species as well as host stage-structure (juvenile and adult stages), allowing for both species-specific and stage-specific biting rates of vectors on hosts. We use this ordinary differential equation model to explore WNV transmission dynamics that occur between vectors and multiple structured host populations as a result of heterogeneous biting rates on species and/or life stages. Our analysis shows that increased exposure of juvenile hosts generally results in larger outbreaks of WNV infectious vectors when compared to differential host species exposure. We also find that …
Accounting For Locational, Temporal, And Physical Similarity Of Residential Sales In Mass Appraisal Modeling: The Development And Application Of Geographically, Temporally, And Characteristically Weighted Regression, Paul E. Bidanset, Michael Mccord, John R. Lombard, Peadar Davis, William J. Mccluskey
Accounting For Locational, Temporal, And Physical Similarity Of Residential Sales In Mass Appraisal Modeling: The Development And Application Of Geographically, Temporally, And Characteristically Weighted Regression, Paul E. Bidanset, Michael Mccord, John R. Lombard, Peadar Davis, William J. Mccluskey
School of Public Service Faculty Publications
Geographically weighted regression (GWR) has been recognized in the assessment community as a viable automated valuation model (AVM) to help overcome, at least in part, modeling hurdles associated with location, such as spatial heterogeneity and spatial autocorrelation of error terms. Although previous researchers have adjusted the GWR weights matrix to also weight by time of sale or by structural similarity of properties in AVMs, the research described in this paper is the first that has done so by all three dimensions (i.e., location, structural similarity, and time of sale) simultaneously. Using 24 years of single-family residential sales in Fairfax, Virginia, …