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a r t i c l e i n f o a b s t r a c t Keywords: Radially projected finite elements Reaction–diffusion systems Pattern formation Surface geometry Surface partial differential equations In this paper we present a robust, efficient and accurate finite element method for solving reaction–diffusion systems on stationary spheroidal surfaces (these are surfaces(More)
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)
In this paper, we use a two-host one pathogen immuno-epidemiological model to argue that the principle for host evolution, when the host is subjected to a fatal disease, is minimization of the case fatality proportion [Formula: see text]. This principle is valid whether the disease is chronic or leads to recovery. In the case of continuum of hosts,(More)
In this article, we discuss the structural and practical identifiability of a nested immuno-epidemiological model of arbovirus diseases, where host-vector transmission rate, host recovery, and disease-induced death rates are governed by the within-host immune system. We incorporate the newest ideas and the most up-to-date features of numerical methods to(More)
The focus of this article is to present the projected finite element method for solving systems of reaction-diffusion equations on evolving closed spheroidal surfaces with applications to pattern formation. The advantages of the projected finite element method are that it is easy to implement and that it provides a conforming finite element discretization(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)
This paper introduces a time-since-recovery structured, multi-strain, multi-population model of avian influenza. Influenza A viruses infect many species of wild and domestic birds and are classified into two groups based on their ability to cause disease: low pathogenic avian influenza (LPAI) and high pathogenic avian influenza (HPAI). Prior infection with(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)