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High order discretization methods for spatial-dependent epidemic models

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  • Takács, Bálint
  • Hadjimichael, Yiannis

Abstract

In this paper, an epidemic 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 partial-differential equations with integral terms. The uniqueness and qualitative properties of the continuous model are analyzed. Furthermore, different spatial and temporal discretizations are employed, and step-size restrictions for the discrete model’s positivity, monotonicity preservation, and population conservation are investigated. We provide sufficient conditions under which high-order numerical schemes preserve the stability of the computational process and provide sufficiently accurate numerical approximations. Computational experiments verify the convergence and accuracy of the numerical methods.

Suggested Citation

  • Takács, Bálint & Hadjimichael, Yiannis, 2022. "High order discretization methods for spatial-dependent epidemic models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 211-236.
    • Handle: RePEc:eee:matcom:v:198:y:2022:i:c:p:211-236
    DOI: 10.1016/j.matcom.2022.02.021
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