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The number of cases of avian influenza in birds and humans exhibits sea-sonality which peaks during the winter months. What causes the seasonality in H5N1 cases is still being investigated. This article addresses the question of modeling the periodicity in cumulative number of human cases of H5N1. Three potential drivers of influenza seasonality are… (More)

The convergence properties of q-Bernstein polynomials are investigated. When q 1 is fixed the generalized Bernstein polynomials B n f of f , a one parameter family of Bernstein polynomials, converge to f as n → ∞ if f is a polynomial. It is proved that, if the parameter 0 < q < 1 is fixed, then B n f → f if and only if f is linear. The iterates of B n f are… (More)

- Necibe Tuncer, Juan Torres, Maia Martcheva
- 2012

This chapter introduces an avian influenza model which includes the dynamics of low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). The model structures the LPAI-recovered individuals by time-since-recovery and involves the cross-immunity that LPAI infection generates toward the HPAI. Reproduction numbers (R Lw 0 , R Hw 0) and… (More)

This article introduces a two-strain spatially explicit SIS epidemic model with space-dependent transmission parameters. We define reproduction numbers of the two strains, and show that the disease-free equilibrium will be globally stable if both reproduction numbers are below one. We also introduce the invasion numbers of the two strains which determine… (More)

The authors developed and analyzed a new method for an exact discretization of the spheroidal domains and for a construction of finite element spaces on such domains. Such method is based on a radial projection mapping defined on the ball into the cube in any space dimensions. The new method is applied on the Laplace–Beltrami equation and an eigenvalue… (More)

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