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The number of cases of avian influenza in birds and humans exhibits seasonality 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 Bnf 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 Bnf → f if and only if f is linear. The iterates of Bnf are(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)
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)
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)
Vector-borne disease transmission is a common dissemination mode used by many pathogens to spread in a host population. Similar to directly transmitted diseases, the within-host interaction of a vector-borne pathogen and a host's immune system influences the pathogen's transmission potential between hosts via vectors. Yet there are few theoretical studies(More)
In this paper, we introduce a malaria model with an asymptomatic class in human population and exposed classes in both human and vector populations. The model assumes that asymptomatic individuals can get re-infected and move to the symptomatic class. In the case of an incomplete treatment, symptomatic individuals move to the asymptomatic class. If(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)