What is the in-host dynamics of the SARS-CoV-2 virus? A challenge within a multiscale vision of living systems

Nicola Bellomo; Raluca Eftimie; Guido Forni; Nicola Bellomo; Raluca Eftimie; Guido Forni

doi:10.3934/nhm.2024029

Networks and Heterogeneous Media

2024, Volume 19, Issue 2: 655-681. doi: 10.3934/nhm.2024029

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What is the in-host dynamics of the SARS-CoV-2 virus? A challenge within a multiscale vision of living systems

1.
Departamento de Matematica Aplicada and Modeling Nature (MNat) Research Unit, Facultad de Ciencia, Universidad de Granada, Spain
2.
Laboratoire de Mathématiques de Besançon, CNRS-UMR 6623, Université de Franche-Comté, France
3.
Accademia Nazionale Lincei, Italy

Received: 28 December 2023 Revised: 24 May 2024 Accepted: 25 June 2024 Published: 27 June 2024

This paper deals with the modeling and simulation of the in-host dynamics of a virus. The modeling approach was developed according to the idea that mathematical models should go beyond deterministic single-scale population dynamics by taking into account the multiscale, heterogeneous features of the complex system under consideration. Here, we considered modeling the competition between the virus, the epithelial cells it infects, and the heterogeneous immune system with evolving activation states that induce a range of different effects on virus particles and infected cells. The subsequent numerical simulations showed different types of model outcomes: from virus elimination, to virus persistence and periodic relapse, to virus uncontrolled growth that triggers a blow-up in the fully activated immune response. The simulations also showed the existence of a threshold in the immune response that separates the regimes of higher re-infections from lower re-infections (compared to the magnitude of the first viral infection).
- complexity,
- active particles model,
- multiscale vision,
- virus contagion,
- mutations
Citation: Nicola Bellomo, Raluca Eftimie, Guido Forni. What is the in-host dynamics of the SARS-CoV-2 virus? A challenge within a multiscale vision of living systems[J]. Networks and Heterogeneous Media, 2024, 19(2): 655-681. doi: 10.3934/nhm.2024029

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Abstract

This paper deals with the modeling and simulation of the in-host dynamics of a virus. The modeling approach was developed according to the idea that mathematical models should go beyond deterministic single-scale population dynamics by taking into account the multiscale, heterogeneous features of the complex system under consideration. Here, we considered modeling the competition between the virus, the epithelial cells it infects, and the heterogeneous immune system with evolving activation states that induce a range of different effects on virus particles and infected cells. The subsequent numerical simulations showed different types of model outcomes: from virus elimination, to virus persistence and periodic relapse, to virus uncontrolled growth that triggers a blow-up in the fully activated immune response. The simulations also showed the existence of a threshold in the immune response that separates the regimes of higher re-infections from lower re-infections (compared to the magnitude of the first viral infection).

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