  There is a rich history of models for the interaction of a biological
contagion like influenza with the spread of related information such as an
influenza vaccination campaign. Recent work on the spread of interacting
contagions on networks has highlighted that these interacting contagions can
have counter-intuitive interplay with network structure. Here we generalize one
of these frameworks to tackle three important features of the spread of
awareness and disease: one, we model the dynamics on highly clustered,
cliquish, networks to mimic the role of workplaces and households; two, the
awareness contagion affects the spread of the biological contagion by reducing
its transmission rate where an aware or vaccinated individual is less likely to
be infected; and three, the biological contagion also affects the spread of the
awareness contagion but by increasing its transmission rate where an infected
individual is more receptive and more likely to share information related to
the disease. Under these conditions, we find that increasing network
clustering, which is known to hinder disease spread, can actually allow them to
sustain larger epidemics of the disease in models with awareness. This
counter-intuitive result goes against the conventional wisdom suggesting that
random networks are justifiable as they provide worst-case scenario forecasts.
To further investigate this result, we provide a closed-form criterion based on
a two-step branching process (i.e., the numbers of expected tertiary
infections) to identify different regions in parameter space where the net
effect of clustering and co-infection varies. Altogether, our results highlight
once again the need to go beyond random networks in disease modeling and
illustrate the type of analysis that is possible even in complex models of
interacting contagions.
