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Article Contents

# Multiscale models of Covid-19 with mutations and variants

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.

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

 Citation:

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

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)

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

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)

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)

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

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

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

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)

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)

Figures(10)

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