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

Chhetri, Bishal; Vamsi, D.K.K; Sanjeevi, Carani

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.