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

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.

Bishal Chhetri, D.K.K Vamsi, Carani Sanjeevi · 2021