### Mathematical Biosciences and Engineering

2022, Issue 2: 1213-1238. doi: 10.3934/mbe.2022056
Research article Special Issues

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

• Received: 15 September 2021 Accepted: 27 October 2021 Published: 01 December 2021
• 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.

Citation: Sarah Treibert, Helmut Brunner, Matthias Ehrhardt. A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1213-1238. doi: 10.3934/mbe.2022056

### Related Papers:

• 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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• © 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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沈阳化工大学材料科学与工程学院 沈阳 110142

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