Multiscale models of Covid-19 with mutations and variants

Nicola Bellomo; Diletta Burini; Nisrine Outada

doi:10.3934/nhm.2022008

Article Contents

2022, Volume 17, Issue 3: 293-310. Doi: 10.3934/nhm.2022008

This issue Previous Article Advanced mathematical methodologies to contrast COVID-19 pandemic Next Article A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies

Multiscale models of Covid-19 with mutations and variants

1.
University of Granada, Departamento de Matemática Aplicada, 18071-Granada, Spain, Politecnico, Torino, Italy
2.
University of Perugia, Italy
3.
Faculty of Sciences Semlalia-UCA, LMDP, Morocco and UMMISCO (IRD-SU, France)

Received: May 31, 2021

Revised: July 31, 2021

Published: June 2022

Nicola Bellomo acknowledges the support of the University of Granada, Project Modeling in Nature, https://www.modelingnature.org.

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Abstract

This paper focuses on the multiscale modeling of the COVID-19 pandemic and presents further developments of the model [7] with the aim of showing how relaxations of the confinement rules can generate sequential waves. Subsequently, the dynamics of mutations into new variants can be modeled. Simulations are developed also to support the decision making of crisis managers.

Keywords:

Mathematics Subject Classification: Primary: 92C60, 92D30.

Citation:

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Figure 1. Transfer diagram of the model. Boxes represent functional subsystems and arrows indicate transition of individuals

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Figure 2. Infected population $ n_2 = n_2(t) $ : $ \varepsilon = 0.001 $, $ \kappa = 0.16 $, $ \alpha_\ell = 0.2 $ (red) and $ \alpha_\ell = 0.3 $ (black)

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Figure 3. Infected population $ n_2 = n_2(t) $ : $ \varepsilon = 0.001 $, $ \alpha_\ell = 0.3 $, $ \kappa = 0.1 $ (blue), $ \kappa = 0.2 $ (black)

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Figure 4. Infected population $ n_2 = n_2(t) $ for $ \varepsilon = 0.001 $, $ \kappa = 0.1 $, $ T_d = 1 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.40 $ (black), $ \alpha_d = 0.45 $ (red), and $ \alpha_d = 0.50 $ (blue)

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Figure 5. Infected population $ n_2 = n_2(t) $ for $ \varepsilon = 0.001 $, $ \kappa = 0.1 $, $ T_d = 1 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.20 $ (black), $ \alpha_d = 0.25 $ (red), and $ \alpha_d = 0.30 $ (blue)

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Figure 6. Infected population $ n_2 = n_2(t) $ and $ n_5 = n_5(t) $ for $ \varepsilon = 0.01 $, $ \varepsilon_v = 0.005 $, $ \kappa = 0.1 $, $ \lambda = 1.5 $, $ T_d = 0.5 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.50 $

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Figure 7. Infected population $ n_2 = n_2(t) $ and $ n_5 = n_5(t) $ for $ \varepsilon = 0.01 $, $ \varepsilon_v = 0.005 $, $ \kappa = 0.1 $, $ \lambda = 1.5 $, $ T_d = 1 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.50 $

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Figure 8. Infected population $ n_2 = n_2(t) $ and $ n_5 = n_5(t) $ for $ \varepsilon = 0.01 $, $ \varepsilon_v = 0.005 $, $ \kappa = 0.1 $, $ \lambda = 1.5 $, $ T_d = 0.75 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.50 $

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Figure 9. Death in the case of absence of mutations: $ n_4 = n_4(t) $ for $ \varepsilon = 0.001 $, $ \kappa = 0.1 $, $ T_d = 1 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.40 $ (black), $ \alpha_d = 0.50 $ (red) and $ \alpha_d = 0.60 $ (blue)

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Figure 10. Death in the case of mutations: $ n_4 = n_4(t) $ for $ \varepsilon = 0.01 $, $ \varepsilon_v = 0.005 $, $ \kappa = 0.1 $, $ T_d = 1 $, $ \alpha_\ell = 0.1 $, $ \alpha_d = 0.50 $ $ \lambda = 1.0 $ (red), $ \lambda = 1.5 $ (blue)

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