Complex dynamics of a multiscale model with bidirectional coupling of the transmission and viral dynamics.

Abstract

The dynamic model that couples micro- and macro-level factors holds significant importance for studying diseases with long incubation periods, which also presents a major challenge in multiscale modeling. Based on the nested models, we propose a multiscale model with bidirectional coupling between population-level transmission and within-host viral progression, by including the feedback from the population scale to the individual scale mediated by perceived disease-induced mortality and its effect on treatment adherence. Suppose a saturating incidence and a linear mortality law, we rigorously analyze the dynamics of the proposed system and reveal multiple endemic equilibria and local bifurcations (backward, fold, and Hopf). Numerical continuation further identifies codimension-two organizing centers (Bogdanov-Takens points) and global bifurcations, including homoclinic bifurcations and fold bifurcations of limit cycles. These give rise to parameter regions exhibiting two distinct forms of bistability: the coexistence of two equilibria and the coexistence of an equilibrium with a stable periodic orbit. By contrast, a corresponding unidirectional model exhibits comparatively simple dynamics and predicts that sufficiently high drug efficacy alone will achieve elimination. The bidirectional model, however, yields richer asymptotical and transient behavior and indicates that population-level eradication generally requires simultaneous, substantial improvements in both drug efficacy and medication adherence. These findings show that the multiscale model with bidirectional coupling can change epidemic outcomes and produce more realistic predictions for control of chronic infections.