tetano
Editor, Senior Moderator
Math Biosci Eng
. 2022 Jan;19(2):1213-1238.
doi: 10.3934/mbe.2022056. Epub 2021 Dec 1.
A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics
Sarah Treibert[SUP] 1 [/SUP], Helmut Brunner[SUP] 2 [/SUP], Matthias Ehrhardt[SUP] 1 [/SUP]
Affiliations
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.
Keywords: COVID-19; SARS-CoV-2; compartment models; epidemiology; nonstandard finite difference scheme.
. 2022 Jan;19(2):1213-1238.
doi: 10.3934/mbe.2022056. Epub 2021 Dec 1.
A nonstandard finite difference scheme for the SVICDR model to predict COVID-19 dynamics
Sarah Treibert[SUP] 1 [/SUP], Helmut Brunner[SUP] 2 [/SUP], Matthias Ehrhardt[SUP] 1 [/SUP]
Affiliations
- PMID: 35135201
- DOI: 10.3934/mbe.2022056
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.
Keywords: COVID-19; SARS-CoV-2; compartment models; epidemiology; nonstandard finite difference scheme.