Thresholds and control in a multiscale epidemic model

We formulated a multiscale epidemic model linking within-host viral dynamics to population transmission under resistance-mediated loss of treatment efficacy. The within-host subsystem tracked target cells, infected cells, viral load, and immune effectors, while an SEIR model represents population spread, vaccination, and recovery. We established positivity and invariance, derived a quasi-steady population model through singular perturbation, and provided a finite-horizon reduction error estimate that included the effects of initial conditions and changes in control. For constant controls and frozen efficacy, a next-generation matrix yielded a control reproduction number and local and global disease-free stability thresholds. A finite-horizon control problem compared vaccination and treatment schedules under progressive efficacy decay, using numerically optimized open-loop policies and explicitly defined baseline controls. In 180-day full-model simulations at baseline resistance, the computed policy had a composite cost of 8623.88, compared with 9638.97 for constant maximal control, while cumulative incidence was 0.240 versus 0.221. A cost-component analysis and a comparison without the explicit viral-load penalty revealed how the objective weights affect these rankings. Under active treatment, resistance influences cumulative incidence, and a synthetic negative-binomial fit reproduces weekly exposure means.

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