  Understanding the interplay between human behavioral phenomena and infectious
disease dynamics has been one of the central challenges of mathematical
epidemiology. However, socio-cognitive processes critical for the initiation of
desired behavioral responses during an outbreak have often been neglected or
oversimplified in earlier models. Combining the microscopic Markov chain
approach with the law of total probability, we herein institute a mathematical
model describing the dynamic interplay between stage-based progression of
awareness diffusion and endemic disease transmission in multiplex networks. We
analytically derived the epidemic thresholds for both discrete-time and
continuous-time versions of our model, and we numerically demonstrated the
accuracy of our analytic arguments in capturing the time course and the
steady-state of the coupled disease-awareness dynamics. We found that our model
is exact for arbitrary unclustered multiplex networks, outperforming a widely
adopted probability-tree-based method, both in the prediction of the
time-evolution of a contagion and in the final epidemic size. Our findings show
that informing the unaware individuals about the circulating disease will not
be sufficient for the prevention of an outbreak unless the distributed
information triggers strong awareness of infection risks with adequate
protective measures, and that the immunity of highly-aware individuals can
elevate the epidemic threshold, but only if the rate of transition from weak to
strong awareness is sufficiently high. Our study thus reveals that awareness
diffusion and other behavioral parameters can nontrivially interact when
producing their effects on epidemiological dynamics of an infectious disease,
suggesting that future public health measures should not ignore this complex
behavioral interplay and its influence on contagion transmission in
multilayered networked systems.
