# Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models

@article{Grave2021AdaptiveMR, title={Adaptive mesh refinement and coarsening for diffusion–reaction epidemiological models}, author={Mal'u Grave and Alvaro L.G.A. Coutinho}, journal={Computational Mechanics}, year={2021}, volume={67}, pages={1177 - 1199} }

The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into compartments and has assumptions about the nature and time rate of transfer from one compartment to another. Usually, they are composed of a system of ordinary differential equations in time. A class of such models considers the Susceptible, Exposed, Infected…

## 14 Citations

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

- MathematicsArchives of computational methods in engineering : state of the art reviews
- 2021

The robustness of this modeling framework for COVID-19 contagion dynamics is assessed by considering different geometries over more extended periods than in other similar studies, suggesting that the modeling approach is both valid and robust.

### Well-posedness for a diffusion-reaction compartmental model simulating the spread of COVID-19

- Mathematics
- 2022

This paper is concerned with the well-posedness of a diffusion-reaction system for a Susceptible-Exposed-Infected-Recovered (SEIR) mathematical model. This model is written in terms of four nonlinear…

### Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID‐19

- Mathematics, Computer ScienceMathematical methods in the applied sciences
- 2022

This work introduces a DDE epidemic model in both an ordinary and partial differential equation framework, and presents a series of mathematical results assessing the stability of the formulation and validating both the mathematical results and the model's ability to reproduce measured data on realistic problems.

### Modeling nonlocal behavior in epidemics via a reaction–diffusion system incorporating population movement along a network

- MathematicsComputer Methods in Applied Mechanics and Engineering
- 2022

### Qualitative and quantitative analysis of a nonlinear second-order anisotropic reaction-diffusion model of an epidemic infection spread

- Computer ScienceDiscrete and Continuous Dynamical Systems - S
- 2022

It is proved the well-posedness (the existence, a priori estimates, regularity and uniqueness) of a classical solution in the Sobolev space of a second-order system of coupled PDEs equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction.

### Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

- Computer ScienceEngineering with Computers
- 2021

This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations, and evaluates DMD’s ability to extrapolate in time (short-time future estimates).

### Identification of Time Delays in COVID-19 Data

- Computer Science
- 2021

This work introduces a novel optimization technique for the identification of time delays in COVID-19 data, making use of a delay-differential equation model, which may be applied not only to CO VID-19, but for generic dynamical systems in which time delays may be present.

### On a nonlocal and nonlinear second-order anisotropic reaction-diffusion system with in-homogeneous Cauchy-Neumann boundary conditions. Applications on epidemic infection spread

- Computer ScienceDiscrete and Continuous Dynamical Systems - S
- 2022

The implicit-explicit (IMEX) numerical approximation scheme which allows to compute the solution of the system of coupled PDEs is constructed and the well-posedness of a classical solution is proved.

### Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems

- Computer ScienceComputer Methods in Applied Mechanics and Engineering
- 2022

### Efficient stochastic finite element analysis of irregular wall structures with inelastic random field properties over manifold

- EngineeringComputational Mechanics
- 2021

In the stochastic finite element analysis of irregular wall structures considering material uncertainties, the random fields simulation and deterministic finite element analysis (FEA) are the two…

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