Abstract
This paper investigates numerical properties of a flux-based finite element method for the discretization of a SEIQRD (susceptible-exposed-infected-quarantined-recovered-deceased) model for the spread of COVID-19. The model is largely based on the SEIRD (susceptible-exposed-infected-recovered-deceased) models developed in recent works, with additional extension by a quarantined compartment of the living population and the resulting first-order system of coupled PDEs is solved by a Least-Squares meso-scale method. We incorporate several data on political measures for the containment of the spread gathered during the course of the year 2020 and develop an indicator that influences the predictions calculated by the method. The numerical experiments conducted show a promising accuracy of predictions of the space-time behavior of the virus compared to the real disease spreading data.
Highlights
The outbreak of the global pandemic caused by the novel virus responsible for COVID19 had, and still has, a great impact on the life of the global human population
We aimed at presenting a solution technique to the system of PDEs constructed by the SEIQRD model using a Least-Squares Method to predict the regional spread of COVID-19 in the country of Germany
The class of Least-Squares Finite Element Methods is based on the idea of the residual minimization of a variational problem and as these methods rely on inner-product projections, they tend to be robust and stable
Summary
The outbreak of the global pandemic caused by the novel virus responsible for COVID19 had, and still has, a great impact on the life of the global human population. We aimed at presenting a solution technique to the system of PDEs constructed by the SEIQRD (susceptible-exposed-infected-quarantined-recovered-deceased) model using a Least-Squares Method to predict the regional spread of COVID-19 in the country of Germany. We want to consider the additional effect of the quarantine and choose a quarantine scheme connected to the infected, exposed and recovered, as a natural way to symbolize that quarantined people can be both in a state of yet non-discovered infection, being asymptomatic, healthy, or symptomatic (which means visibly showing symptoms that a possible infection with the virus might be accounted for) This quarantine rate should change with time and based on political decisions, as it has been mandatory for returnees from highly affected areas to undergo self-quarantine for several days while waiting for the result of the test that indicates the infection status.
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