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Advanced mathematical methodologies to contrast COVID-19 pandemic
June  2022, 17(3): 293-310. doi: 10.3934/nhm.2022008

## 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  June 2021 Revised  August 2021 Published  June 2022 Early access  March 2022

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

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.

Citation: Nicola Bellomo, Diletta Burini, Nisrine Outada. Multiscale models of Covid-19 with mutations and variants. Networks and Heterogeneous Media, 2022, 17 (3) : 293-310. doi: 10.3934/nhm.2022008
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##### References:
Transfer diagram of the model. Boxes represent functional subsystems and arrows indicate transition of individuals
Infected population $n_2 = n_2(t)$ : $\varepsilon = 0.001$, $\kappa = 0.16$, $\alpha_\ell = 0.2$ (red) and $\alpha_\ell = 0.3$ (black)
Infected population $n_2 = n_2(t)$ : $\varepsilon = 0.001$, $\alpha_\ell = 0.3$, $\kappa = 0.1$ (blue), $\kappa = 0.2$ (black)
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)
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)
Infected population $n_2 = n_2(t)$ and $n_5 = n_5(t)$ for $\varepsilon = 0.01$, $\varepsilon_v = 0.005$, $\kappa = 0.1$, $\lambda = 1.5$, $T_d = 0.5$, $\alpha_\ell = 0.1$, $\alpha_d = 0.50$
Infected population $n_2 = n_2(t)$ and $n_5 = n_5(t)$ for $\varepsilon = 0.01$, $\varepsilon_v = 0.005$, $\kappa = 0.1$, $\lambda = 1.5$, $T_d = 1$, $\alpha_\ell = 0.1$, $\alpha_d = 0.50$
Infected population $n_2 = n_2(t)$ and $n_5 = n_5(t)$ for $\varepsilon = 0.01$, $\varepsilon_v = 0.005$, $\kappa = 0.1$, $\lambda = 1.5$, $T_d = 0.75$, $\alpha_\ell = 0.1$, $\alpha_d = 0.50$
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)
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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