Abstract / Summary
This study proposes a multiscale system with bidirectional coupling between disease transmission and viral dynamics. By incorporating treatment adherence that varies with the epidemic situation, the model creates a population-to-individual feedback mechanism. By integrating fast–slow and non-smooth system theory, we demonstrate that the dynamics of the coupled system are fully characterized by the non-smooth slow subsystem, in conjunction with the behavior of the fast subsystem. Specifically, the model’s solutions may reach equilibria with disease eradicated at both levels, only at the population level, or persisting at both levels. Our analysis reveals significant differences in the dynamical behavior between the bidirectionally and unidirectionally coupled systems. In particular, the feedback mechanism from between-host to within-host scales leads to the occurrence of a subcritical Hopf bifurcation, resulting in the emergence of large-amplitude periodic solutions. Furthermore, merely increasing treatment efficacy is insufficient for disease elimination, potentially resulting instead in a stabilized nonzero infection level, a continued rise, or large-amplitude oscillatory dynamics. These outcomes highlight the necessity of combining treatment with broader non-pharmaceutical interventions for effective control.