  Even though transitivity is a central structural feature of social networks,
its influence on epidemic spread on coevolving networks has remained relatively
unexplored. Here we introduce and study an adaptive SIS epidemic model wherein
the infection and network coevolve with non-trivial probability to close
triangles during edge rewiring, leading to substantial reinforcement of network
transitivity. This new model provides a unique opportunity to study the role of
transitivity in altering the SIS dynamics on a coevolving network. Using
numerical simulations and Approximate Master Equations (AME), we identify and
examine a rich set of dynamical features in the new model. In many cases, the
AME including transitivity reinforcement provides accurate predictions of
stationary-state disease prevalences and network degree distributions.
Furthermore, for some parameter settings, the AME accurately trace the temporal
evolution of the system. We show that higher transitivity reinforcement in the
model leads to lower levels of infective individuals in the population, when
closing a triangle is the dominant rewiring mechanism. These methods and
results may be useful in developing ideas and modeling strategies for
controlling SIS type epidemics.
