Abstract
A large host population, living in a bounded and isolated habitat, is infected. Propagation of the disease is promoted by a time-periodic transmission rate between the organisms, which interact with one another, move within the habitat and possibly recover. Birth and death also affect the group. In this context, an epidemiological model is constructed to describe the dynamics of the population. In spite of its simplicity, such model necessarily depends on various parameters that regulate the organisms behavior. Hence, the analysis and numerical simulation of the population dynamics for many key scenarios, which is an important step to study and control the effects of the epidemic, may be somewhat computationally expensive. In order to decrease this effort, a high-order singular value decomposition is applied to data generated by the model for a limited number of parameter values, which provides few sets of modes accounting for the most relevant and uncorrelated features of the involved dynamics. Such modes are then used to approximate the population states for other, new values of the parameters in an efficient and reasonably accurate way.
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Acknowledgements
The author would like to thank the students of his group at the ECMI Modelling Week 2013, held at Universidad Carlos III of Madrid on July 2013, for their contribution to this work. The latter has been supported by the Ministerio de Economía y Competitividad grant MTM2014-56948-C2-2-P and by the FEDER / Ministerio de Ciencia, Innovación y Universidades-Agencia Estatal de Investigación grant MTM2017-84446-C2-2-R.
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Terragni, F. (2020). Efficient Parameter-Dependent Simulation of Infections in a Population Model. In: Lindner, E., Micheletti, A., Nunes, C. (eds) Mathematical Modelling in Real Life Problems. Mathematics in Industry(), vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-50388-8_10
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DOI: https://doi.org/10.1007/978-3-030-50388-8_10
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