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Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic

Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in hydrology available for modelling in e...

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Autores principales: Moussa, Roger, Majdalani, Samer
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Cambridge University Press 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8207560/
https://www.ncbi.nlm.nih.gov/pubmed/33910670
http://dx.doi.org/10.1017/S0950268821001011
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author Moussa, Roger
Majdalani, Samer
author_facet Moussa, Roger
Majdalani, Samer
author_sort Moussa, Roger
collection PubMed
description Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in hydrology available for modelling in epidemiology. We adapt the Hayami model solution of the diffusive wave equation generally used in hydrological modelling to compartmental I–R–D models in epidemiology by simulating the relationships between the number of infectious I(t), the number of recoveries R(t) and the number of deaths D(t). The Hayami model is easy-to-use, robust and parsimonious. We compare the empirical one-parameter exponential model usually used in SIRD models to the two-parameter Hayami model. Applications were implemented on the recent Covid-19 pandemic. The application on data from 24 countries shows that both models give comparable performances for modelling the I–D relationship. However, for modelling the I–R relationship and the active cases, the exponential model gives fair performances whereas the Hayami model substantially improves the model performances. The Hayami model also presents the advantage that its parameters can be easily estimated from the analysis of the data distributions of I(t), R(t) and D(t). The Hayami model is parsimonious with only two parameters which are useful to compare the temporal evolution of recoveries and deaths in different countries based on different contamination rates and recoveries strategies. This study highlights the interest of knowledge transfer between different scientific disciplines in order to model different processes.
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spelling pubmed-82075602021-06-16 Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic Moussa, Roger Majdalani, Samer Epidemiol Infect Original Paper Susceptible S-Infected I-Recovered R-Death D (SIRD) compartmental models are often used for modelling of infectious diseases. On the basis of the analogy between SIRD and compartmental models in hydrology, this study makes mathematical formulations developed in hydrology available for modelling in epidemiology. We adapt the Hayami model solution of the diffusive wave equation generally used in hydrological modelling to compartmental I–R–D models in epidemiology by simulating the relationships between the number of infectious I(t), the number of recoveries R(t) and the number of deaths D(t). The Hayami model is easy-to-use, robust and parsimonious. We compare the empirical one-parameter exponential model usually used in SIRD models to the two-parameter Hayami model. Applications were implemented on the recent Covid-19 pandemic. The application on data from 24 countries shows that both models give comparable performances for modelling the I–D relationship. However, for modelling the I–R relationship and the active cases, the exponential model gives fair performances whereas the Hayami model substantially improves the model performances. The Hayami model also presents the advantage that its parameters can be easily estimated from the analysis of the data distributions of I(t), R(t) and D(t). The Hayami model is parsimonious with only two parameters which are useful to compare the temporal evolution of recoveries and deaths in different countries based on different contamination rates and recoveries strategies. This study highlights the interest of knowledge transfer between different scientific disciplines in order to model different processes. Cambridge University Press 2021-04-29 /pmc/articles/PMC8207560/ /pubmed/33910670 http://dx.doi.org/10.1017/S0950268821001011 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Original Paper
Moussa, Roger
Majdalani, Samer
Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title_full Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title_fullStr Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title_full_unstemmed Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title_short Use of the Hayami diffusive wave equation to model the relationship infected–recoveries–deaths of Covid-19 pandemic
title_sort use of the hayami diffusive wave equation to model the relationship infected–recoveries–deaths of covid-19 pandemic
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8207560/
https://www.ncbi.nlm.nih.gov/pubmed/33910670
http://dx.doi.org/10.1017/S0950268821001011
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