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Understanding the interplay between human behavioral phenomena and infectiousdisease dynamics has been one of the central challenges of mathematicalepidemiology. However, socio-cognitive processes critical for the initiation ofdesired behavioral responses during an outbreak have often been neglected oroversimplified in earlier models. Combining the microscopic Markov chainapproach with the law of total probability, we herein institute a mathematicalmodel describing the dynamic interplay between stage-based progression ofawareness diffusion and endemic disease transmission in multiplex networks. Weanalytically derived the epidemic thresholds for both discrete-time andcontinuous-time versions of our model, and we numerically demonstrated theaccuracy of our analytic arguments in capturing the time course and thesteady-state of the coupled disease-awareness dynamics. We found that our modelis exact for arbitrary unclustered multiplex networks, outperforming a widelyadopted probability-tree-based method, both in the prediction of thetime-evolution of a contagion and in the final epidemic size. Our findings showthat informing the unaware individuals about the circulating disease will notbe sufficient for the prevention of an outbreak unless the distributedinformation triggers strong awareness of infection risks with adequateprotective measures, and that the immunity of highly-aware individuals canelevate the epidemic threshold, but only if the rate of transition from weak tostrong awareness is sufficiently high. Our study thus reveals that awarenessdiffusion and other behavioral parameters can nontrivially interact whenproducing their effects on epidemiological dynamics of an infectious disease,suggesting that future public health measures should not ignore this complexbehavioral interplay and its influence on contagion transmission inmultilayered networked systems.

Coupled dynamics of endemic disease transmission and gradual awareness diffusion in multiplex networks