Multiscale feedback drives viral evolution and epidemic dynamics

We introduce a minimal multiscale framework that links within-host virus dynamics to population-level SIRS epidemiology through explicit, bidirectional coupling.

At the microscopic layer, a two variant quasispecies (master and mutant genomes with packaged virions) evolves on a fast timescale.

At the macroscopic layer, two infectious classes (master- and mutant-infected), susceptible, recovered, and deceased individuals evolve slowly.

The two scales are connected through transmission rates that depend on instantaneous virion abundance and through prevalence-weighted effective replication rates.

Exploiting the timescale separation, we formalize a coarse-grained slow-fast closure: the genome-virion subsystem rapidly relaxes to quasi-steady states that parameterize time-varying transmission in the slow epidemiological system.

This yields an integrated expression for the basic reproduction number and sharp inequalities that delineate coexistence versus exclusion.

A key prediction is a context-dependent error threshold that shifts with the prevalence ratio, enabling transient pseudo-error catastrophes driven by epidemic composition rather than intrinsic fidelity.

Linearization reveals parameter regions with damped oscillations arising solely from the microscopic-macroscopic feedback.

Two illustrative extremes bracket the model's behavior: an avirulent strongly immunizing strain that benignly replaces the master, and a hypervirulent weakly immunizing that self-limits via host depletion and collapses transmission.

This framework yields testable signatures linking viral load, incidence, and within-host composition.