WIAS Preprint No. 2805, (2021)

High order discretization methods for spatial-dependent SIR models



Authors

  • Takács, Bálint
  • Hadjimichael, Yiannis

2020 Mathematics Subject Classification

  • 5M12 65L07 65L06 91D25

Keywords

  • Epidemic models, SIR model, integro-differential equations, strong stability preservation

DOI

10.20347/WIAS.PREPRINT.2805

Abstract

In this paper, an SIR model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size of the populations differs in space. The use of local spatial dependence yields a system of integro-differential equations. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different choices of spatial and temporal discretizations are employed, and step-size restrictions for population conservation, positivity, and monotonicity preservation of the discrete model are investigated. We provide sufficient conditions under which high order numerical schemes preserve the discrete properties of the model. Computational experiments verify the convergence and accuracy of the numerical methods.

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