  The spread of one disease, in some cases, can stimulate the spreading of
another infectious disease. Here, we treat analytically a symmetric coinfection
model for spreading of two diseases on a two-layer multiplex network. We allow
layer overlapping, but we assume that each layer is random and locally
loopless. Infection with one of the diseases increases the probability of
getting infected with the other. Using the generating function method, we
calculate exactly the fraction of individuals infected with both diseases
(so-called coinfected clusters) in the stationary state, as well as the
epidemic spreading thresholds and the phase diagram of the model.With
increasing cooperation, we observe a tricritical point and the type of
transition changes from continuous to hybrid. Finally, we compare the
coinfected clusters in the case of cooperating diseases with the so-called
"viable" clusters in networks with dependencies.
