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

@article{Grave2020AdaptiveMR, 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={2020}, 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…

## 15 Citations

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

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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…

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

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- 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.

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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.

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- Computer ScienceDiscrete and Continuous Dynamical Systems - S
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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

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### Syndromic Surveillance Using Structured Telehealth Data: Case Study of the First Wave of COVID-19 in Brazil

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Whether a high-quality data set obtained from a state-based telehealth service could be used to forecast the geographical spread of new cases of COVID-19 and to feed computational models of disease spread is evaluated.

### 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…

### Metodologias para Índices de Vulnerabilidades Socioambientais, Dinâmicas de contágio da COVID 19 e Índice Brasileiro de Privação em Saúde

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