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Systems of Populations with Multiple Structures: Modeling and Analysis

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Abstract

In this paper a class of functional–differential equations is considered, arising in modeling the dynamics of structured populations. This class includes model equations for diseases spreading by interactions of hosts, vectors and parasites considered in An (Drug Resistance in Infectious Diseases: Modeling, Analysis and Simulation, Doctoral thesis, University of Heidelberg, 2012) and An et al. (A structured population model for malaria including drug resistance. In preparation), where drug sensitive and drug resistant parasites and their effects on the infected host and vector populations are modeled via structural variables. In this paper, the evolution of n structured and m unstructured interacting populations is described by a coupled system of n functional–partial differential equations and m functional–ordinary differential equations. In general, besides initial conditions additional “boundary”  conditions are required in order to determine missing data for the structure dependent variables. As the main result of this paper, we are going to present the analysis for the existence of unique, positive solutions.

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Acknowledgments

The research of L.T.T. An was partially supported by BIOMS (Center for Modeling and Simulation in the Biosciences), University of Heidelberg, Germany.

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Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing (IWR), University of Heidelberg, Heidelberg, Germany

    Le Thi Thanh An & Willi Jäger

  2. Mathematics Department, University of Erlangen-Nuremberg, Erlangen, Germany

    Maria Neuss-Radu

Authors
  1. Le Thi Thanh An
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  2. Willi Jäger
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  3. Maria Neuss-Radu
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Correspondence to Maria Neuss-Radu.

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Dedicated to the memory of Prof. Klaus Kirchgässner.

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An, L.T.T., Jäger, W. & Neuss-Radu, M. Systems of Populations with Multiple Structures: Modeling and Analysis. J Dyn Diff Equat 27, 863–877 (2015). https://doi.org/10.1007/s10884-015-9469-3

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  • DOI: https://doi.org/10.1007/s10884-015-9469-3

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