Coupling multiscale within-host dynamics and between-host transmission with recovery (SIR) dynamics

Multiscale models that link within-host infection to between-host transmission are valuable tools to progress understanding of viral infectious diseases. In this paper, we present two multiscale models that couple within-host infection to a susceptible-infected-recovered (SIR) model. A disease-induced transmission rate bridges the scales from within to between-host. Our stability analysis on the first model (influenza infection) reveals two equilibrium points for the SIR model that describe endemic scenarios where both susceptible and infected cases maintain nonzero population sizes. Consequently, the between-host system has two bifurcations determined by the corresponding basic reproduction number of the within-host and the size of the infected population at the interior equilibrium point. Analysis on the second model (Ebola infection) reveals the limited transient inhibitory effect of antibodies on viral replication, which influences the time window from infection to a potential outbreak. Simulations numerically illustrate our results.