High order discretization methods for spatial-dependent epidemic models

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...

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Bibliographic Details
Published in:arXiv.org 2022-04
Main Authors: Takács, Bálint, Hadjimichael, Yiannis
Format: Article
Language:English
Subjects:
Dependence
Differential equations
Epidemics
Mathematical models
Numerical methods
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.01330