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A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics.

Authors
  • Treibert, Sarah1
  • Brunner, Helmut2
  • Ehrhardt, Matthias1
  • 1 Chair of Applied Mathematics and Numerical Analysis, School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal 42119, Germany. , (Germany)
  • 2 Chair of Health Economics, Faculty of Management and Economics, University of Wuppertal, Wuppertal 42119, Germany. , (Germany)
Type
Published Article
Journal
Mathematical biosciences and engineering : MBE
Publication Date
Jan 01, 2022
Volume
19
Issue
2
Pages
1213–1238
Identifiers
DOI: 10.3934/mbe.2022056
PMID: 35135201
Source
Medline
Keywords
Language
English
License
Unknown

Abstract

In the context of 2019 coronavirus disease (COVID-19), considerable attention has been paid to mathematical models for predicting country- or region-specific future pandemic developments. In this work, we developed an SVICDR model that includes a susceptible, an all-or-nothing vaccinated, an infected, an intensive care, a deceased, and a recovered compartment. It is based on the susceptible-infectious-recovered (SIR) model of Kermack and McKendrick, which is based on ordinary differential equations (ODEs). The main objective is to show the impact of parameter boundary modifications on the predicted incidence rate, taking into account recent data on Germany in the pandemic, an exponential increasing vaccination rate in the considered time window and trigonometric contact and quarantine rate functions. For the numerical solution of the ODE systems a model-specific non-standard finite difference (NSFD) scheme is designed, that preserves the positivity of solutions and yields the correct asymptotic behaviour.

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