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Modeling nonlocal behavior in epidemics via a reaction-diffusion system incorporating population movement along a network.
Grave, Malú; Viguerie, Alex; Barros, Gabriel F; Reali, Alessandro; Andrade, Roberto F S; Coutinho, Alvaro L G A.
  • Grave M; Dept. of Civil Engineering, COPPE/Federal University of Rio de Janeiro, Fundação Oswaldo Cruz, Fiocruz, Brazil.
  • Viguerie A; Department of Mathematics, Gran Sasso Science Institute, Italy.
  • Barros GF; Dept. of Civil Engineering, COPPE/Federal University of Rio de Janeiro, Brazil.
  • Reali A; Dipartimento di Ingegneria Civile e Architettura, Università di Pavia, Italy.
  • Andrade RFS; Instituto de Física, Universidade Federal da Bahia (UFBA), Center of Data and Knowledge Integration for Health (CIDACS), Instituto Gonçalo Moniz, Fiocruz-Ba, Brazil.
  • Coutinho ALGA; Dept. of Civil Engineering, COPPE/Federal University of Rio de Janeiro, Brazil.
Comput Methods Appl Mech Eng ; 401: 115541, 2022 Nov 01.
Article in English | MEDLINE | ID: covidwho-2031208
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.
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Full text: Available Collection: International databases Database: MEDLINE Type of study: Prognostic study Language: English Journal: Comput Methods Appl Mech Eng Year: 2022 Document Type: Article Affiliation country: J.cma.2022.115541

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Full text: Available Collection: International databases Database: MEDLINE Type of study: Prognostic study Language: English Journal: Comput Methods Appl Mech Eng Year: 2022 Document Type: Article Affiliation country: J.cma.2022.115541