ArticleComputational mechanics2021
Adaptive mesh refinement and coarsening for diffusion-reaction epidemiological models.
Article in Computational mechanics, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers, 1 of them a synthesis that pooled it.
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8 citing papers in PubMed, 1 synthesis or guideline pooled it.
- A systematic review of spatial epidemiological modeling approaches applied during the COVID-19 pandemic.BMC public health · 2026Pooled it
- A Systematic Review of Spatial Epidemiological Modeling Approaches Applied During the COVID-19 Pandemic.medRxiv : the preprint server for health sciences · 2025Article
- Syndromic Surveillance Using Structured Telehealth Data: Case Study of the First Wave of COVID-19 in Brazil.JMIR public health and surveillance · 2023Article
- Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.Computer methods in applied mechanics and engineering · 2022Article
- Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19.Mathematical methods in the applied sciences · 2022Article
- An Explicit Adaptive Finite Difference Method for the Cahn-Hilliard Equation.Journal of nonlinear science · 2022Article
- Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations.Engineering with computers · 2022Article
- Assessing the Spatio-temporal Spread of COVID-19 via Compartmental Models with Diffusion in Italy, USA, and Brazil.Archives of computational methods in engineering : state of the art reviews · 2021Article
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2 authors.
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No grant is acknowledged in the PubMed record.
Abstract
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, Recovered, and Deceased populations, the SEIRD model. However, these models do not always account for the movement of individuals from one region to another. In this work, we extend the formulation of SEIRD compartmental models to diffusion-reaction systems of partial differential equations to capture the continuous spatio-temporal dynamics of COVID-19. Since the virus spread is not only through diffusion, we introduce a source term to the equation system, representing exposed people who return from travel. We also add the possibility of anisotropic non-homogeneous diffusion. We implement the whole model in libMesh, an open finite element library that provides a framework for multiphysics, considering adaptive mesh refinement and coarsening. Therefore, the model can represent several spatial scales, adapting the resolution to the disease dynamics. We verify our model with standard SEIRD models and show several examples highlighting the present model's new capabilities.
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