Least-Squares Finite Element Method for a Meso-Scale Model of the Spread of COVID-19

Bertrand, Fleurianne; Pirch, Emilie

doi:10.3390/computation9020018

Cited by 17 publications

(33 citation statements)

References 38 publications

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“…Examples of past applications include Dengue [14], Zika [10], HIV [31], SARS [13], Malaria [30], Ebola [28], and many others. However, the urgency of the COVID-19 pandemic has motivated the need for more research in this area, with several models for this pandemic outbreak being presented in recent months [2,5,8,17,20,26,33,[41][42][43].…”

Section: Introductionmentioning

confidence: 99%

“…For the specific case of COVID-19, PDE models were applied in [19,20,41,42], in which a compartmental SEIRD model (susceptible, exposed, infected, recovered, deceased) was used. A modified version of this model, with the addition of a quarantined compartment, was applied in [5]. Such modeling framework has shown promising results, being able to recreate observed data and make predictions with reasonable accuracy, but these successful applications have been so far obtained on a limited scale, with results restricted to single, specific regions.…”

Section: Introductionmentioning

confidence: 99%

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Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

Grave

Viguerie

Barros

et al. 2021

Arch Computat Methods Eng

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The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments based on qualitative characteristics, with different assumptions about the nature and rate of transfer across compartments. Though most commonly formulated as ordinary differential equation models, in which the compartments depend only on time, recent works have also focused on partial differential equation (PDE) models, incorporating the variation of an epidemic in space. Such research on PDE models within a Susceptible, Infected, Exposed, Recovered, and Deceased framework has led to promising results in reproducing COVID-19 contagion dynamics. In this paper, we assess the robustness of this modeling framework by considering different geometries over more extended periods than in other similar studies. We first validate our code by reproducing previously shown results for Lombardy, Italy. We then focus on the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of the most impacted areas in the world. Our results show good agreement with real-world epidemiological data in both time and space for all regions across major areas and across three different continents, suggesting that the modeling approach is both valid and robust.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

Grave

Viguerie

Barros

et al. 2021

Arch Computat Methods Eng

View full text Add to dashboard Cite

show abstract

“…There is an ongoing interest in SIR-type models. Bertrand and Pirch [8] presented a least-squares finite element method for the SEIQRD model. Cherniha and Davydovych [9] studied a nonlinear model based on logistic equations, while Keller et al [10] simulated the spread of an infectious disease across a heterogeneous and continuous landscape.…”

Section: Introductionmentioning

confidence: 99%

Real-Time Estimation of R0 for COVID-19 Spread

et al. 2021

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We propose a real-time approximation of R0 in an SIR-type model that applies to the COVID-19 epidemic outbreak. A very useful direct formula expressing R0 is found. Then, various type of models are considered, namely, finite differences, cubic splines, Piecewise Cubic Hermite interpolation and linear least squares approximation. Preserving the monotonicity of the formula under consideration proves to be of crucial importance. This latter property is preferred over accuracy, since it maintains positive R0. Only the Linear Least Squares technique guarantees this, and is finally proposed here. Tests on real COVID-19 data confirm the usefulness of our approach.

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“…For instance, Fig. 8 in Bertrand ( 2021 ) shows the initial spread of Covid-19 in Germany, which is naturally related to the geographic locations. The authors change there the SEIRD model (susceptible- exposed- infected- recovered- deceased) to SEIQRD by adding the quarantined compartment.…”

Section: Prior Approachesmentioning

confidence: 99%

Modeling the Waves of Covid-19

Cherednik

2021

Acta Biotheor

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The challenges with modeling the spread of Covid-19 are its power-type growth during the middle stages of the waves with the exponents depending on time, and that the saturation of the waves is mainly due to the protective measures and other restriction mechanisms working in the same direction. The two-phase solution we propose for modeling the total number of detected cases of Covid-19 describes the actual curves for many its waves and in many countries almost with the accuracy of physics laws. Bessel functions play the key role in our approach. The differential equations we obtain are of universal type and can be used in behavioral psychology, invasion ecology (transient processes), etc. The initial transmission rate and the intensity of the restriction mechanisms are the key parameters. This theory provides a convincing explanation of the surprising uniformity of the Covid-19 waves in many places, and can be used for forecasting the epidemic spread. For instance, the early projections for the 3rd wave in the USA appeared sufficiently exact. The Delta-waves (2021) in India, South Africa, UK, and the Netherlands are discussed at the end.

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Least-Squares Finite Element Method for a Meso-Scale Model of the Spread of COVID-19

Cited by 17 publications

References 38 publications

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil

Real-Time Estimation of R0 for COVID-19 Spread

Modeling the Waves of Covid-19

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