A Nested Multi-Scale Model for COVID-19 Viral Infection

TL;DR

This paper presents a comprehensive multi-scale model for COVID-19 that links within-host viral dynamics with community spread, analyzing stability, sensitivity, and intervention strategies to inform effective containment measures.

Contribution

It introduces a novel nested multi-scale model for COVID-19, integrating within-host and between-host dynamics, and evaluates intervention strategies using the effective reproductive number.

Findings

The disease-free equilibrium is stable when R0<1.

A trans-critical bifurcation occurs at R0=1.

Combined interventions are most effective in controlling spread.

Abstract

In this study, we develop and analyze a nested multi-scale model for COVID -19 disease that integrates within-host scale and between-host scale sub-models. First, the well-posedness of the multi-scale model is discussed, followed by the stability analysis of the equilibrium points. The disease-free equilibrium point is shown to be globally asymptotically stable for $R_0 < 1$. When $R_0$ exceeds unity, a unique infected equilibrium exists, and the system is found to undergo a forward (trans-critical) bifurcation at $R_0=1$. Two parameter heat plots are also done to find the parameter combinations for which the equilibrium points are stable. The parameters $\beta, \pi$ and $\Lambda$ are found to be most sensitive to $R_0$. The influence of within-host sub-model parameter on the between-host sub-model variables is numerically illustrated. The spread of infection in a community is shown to be influenced by within-host level sub-model parameters, such as the production of viral particles by infected cells $(\alpha)$, the clearance rate of infected cells by the immune system $(x)$, and the clearance rate of viral particles by the immune system $(y)$. The comparative effectiveness of the three health interventions (antiviral drugs, immunomodulators, and generalized social distancing) for COVID-19 infection was examined using the effective reproductive number $R_E$ as an indicator of the effectiveness of the interventions. The results suggest that a combined strategy of antiviral drugs, immunomodulators and generalized social distancing would be the best strategy to implement to contain the spread of infection in the community.