| Author | Grave, Malú | |
| Author | Viguerie, Alex | |
| Author | Barros, Gabriel F. | |
| Author | Reali, Alessandro | |
| Author | Andrade, Roberto F. S. | |
| Author | Coutinho, Álvaro L. G. A. | |
| Access date | 2024-09-25T15:06:16Z | |
| Available date | 2024-09-25T15:06:16Z | |
| Document date | 2022 | |
| Citation | GRAVE, Malu et al. Modeling nonlocal behavior in epidemics via a reaction–diffusion system incorporating population movement along a network. Computer Methods in Applied Mechanics and Engineering, v. 401, part. A, p. 1-18, 2022. | en_US |
| ISSN | 1879-2138 | en_US |
| URI | https://www.arca.fiocruz.br/handle/icict/66091 | |
| Sponsorship | Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).
Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ).
Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). | en_US |
| Language | eng | en_US |
| Publisher | Elsevier | en_US |
| Rights | open access | en_US |
| Subject in Portuguese | COVID-19 | en_US |
| Subject in Portuguese | Modelos compartimentais | en_US |
| Subject in Portuguese | Difusão-reação | en_US |
| Subject in Portuguese | Equações diferenciais parciais | en_US |
| Subject in Portuguese | Movimento populacional | en_US |
| Title | Modeling nonlocal behavior in epidemics via a reaction–diffusion system incorporating population movement along a network | en_US |
| Type | Article | en_US |
| DOI | 10.1016/j.cma.2022.115541 | |
| Abstract | The outbreak of COVID-19, beginning in 2019 and continuing through the time of writing, has led to renewed interest in the mathematical modeling of infectious disease. Recent works have focused on partial differential equation (PDE) models, particularly reaction–diffusion models, able to describe the progression of an epidemic in both space and time. These studies have shown generally promising results in describing and predicting COVID-19 progression. However, people often travel long distances in short periods of time, leading to nonlocal transmission of the disease. Such contagion dynamics are not well-represented by diffusion alone. In contrast, ordinary differential equation (ODE) models may easily account for this behavior by considering disparate regions as nodes in a network, with the edges defining nonlocal transmission. In this work, we attempt to combine these modeling paradigms via the introduction of a network structure within a reaction–diffusion PDE system. This is achieved through the definition of a population-transfer operator, which couples disjoint and potentially distant geographic regions, facilitating nonlocal population movement between them. We provide analytical results demonstrating that this operator does not disrupt the physical consistency or mathematical well-posedness of the system, and verify these results through numerical experiments. We then use this technique to simulate the COVID-19 epidemic in the Brazilian region of Rio de Janeiro, showcasing its ability to capture important nonlocal behaviors, while maintaining the advantages of a reaction–diffusion model for describing local dynamics. | en_US |
| Affilliation | Universidade Federal do Rio de Janeiro. Departamento de Engenharia Civil. Rio de Janeiro, RJ, Brasil / Fundação Oswaldo Cruz. Rio de Janeiro, RJ, Brasil. | en_US |
| Affilliation | Department of Mathematics. Gran Sasso Science Institute. Italy. | en_US |
| Affilliation | Universidade Federal do Rio de Janeiro. Departamento de Engenharia Civil. Rio de Janeiro, RJ, Brasil. | en_US |
| Affilliation | Dipartimento di Ingegneria Civile e Architettura. Universita di Pavia. Italy. | en_US |
| Affilliation | Universidade Federal da Bahia. Instituto de Física. Salvador, BA, Brasil / Fundação Oswaldo Cruz. Instituto Gonçalo Moniz. Centro de Integração de Dados e Conhecimento para Saúde. Salvador, BA, Brasil. | en_US |
| Affilliation | Universidade Federal do Rio de Janeiro. Departamento de Engenharia Civil. Rio de Janeiro, RJ, Brasil. | en_US |
| Subject | COVID-19 | en_US |
| Subject | Compartmental models | en_US |
| Subject | Diffusion–reaction | en_US |
| Subject | Partial differential equations | en_US |
| Subject | Population movement | en_US |
| DeCS | COVID-19 | en_US |
| DeCS | Modelos epidemiológicos | en_US |
| DeCS | Difusão | en_US |
