A Multi-Scale SEIR Model with Within-Host Viral Dynamics and Fractional Memory

Abstract

We develop a multi-scale SEIR framework coupling representative within-host profiles to age- and strain-structured transmission through infectious stages. Occupancy-weighted coefficients preserve expected cumulative infectiousness along a sequential infectious path. The population model incorporates vaccination, breakthrough infections, strain switching and waning immunity. We prove global well-posedness and population conservation, and derive invasion thresholds for autonomous reference configurations. A reanalysis of the Atangana strength number shows that its minimal exposed-infectious subsystem has real characteristic roots and admits no damped oscillatory regime under nonnegative transmission. A separate Caputo surrogate is locally well posed in a continuous Volterra formulation. The interpretation of epidemic trajectories distinguishes compartment stocks, transition flows, cumulative events and peak regularity. The results clarify which conclusions follow from the stage model, its reduced subsystems and the fractional surrogate.