Analysis of an age-dependent SI epidemic model with disease-induced mortality and proportionate mixing assumption: the case of vertically transmitted diseases.
El-Doma, M. (2004)
Journal of Applied Mathematics
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El-Doma, M. (2004)
Journal of Applied Mathematics
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Joshua A. Enszer, Mark A. Stadtherr (2009)
International Journal of Applied Mathematics and Computer Science
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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain...
J. Li, X. Zou (2009)
Mathematical Modelling of Natural Phenomena
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In this paper, with the assumptions that an infectious disease has a fixed latent period in a population and the latent individuals of the population may disperse, we reformulate an SIR model for the population living in two patches (cities, towns, or countries etc.), which is a generalization of the classic Kermack-McKendrick SIR model. The model is given by a system of delay differential equations with a fixed delay accounting for the latency and non-local terms caused by the mobility...
Alison M. Etheridge (2008)
Banach Center Publications
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Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to...
A.S. Novozhilov (2012)
Mathematical Modelling of Natural Phenomena
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We present a unified mathematical approach to epidemiological models with parametric heterogeneity, i.e., to the models that describe individuals in the population as having specific parameter (trait) values that vary from one individuals to another. This is a natural framework to model, e.g., heterogeneity in susceptibility or infectivity of individuals. We review, along with the necessary theory, the results obtained using the discussed...
W. E. Fitzgibbon, M. Langlais, J. J. Morgan, D. Pontier, C. Wolf (2003)
Banach Center Publications
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Global existence results and long time behavior are provided for a mathematical model describing the propagation of Feline Panleucopenia Virus (FPLV) within a domestic cat population; two transmission modes are involved: a direct one from infective cats to susceptible ones, and an indirect one from the contaminated environment to susceptible cats. A more severe impact of the virus on young cats requires an age-structured model.