Fig. 4.

First-order phase transition and epidemic latent heat. (A) Emergence of an endemic steady state for a scenario where equivalent diseases are either noninteracting ($\alpha =1$) or interacting ($\alpha =4)$ on the community structure (again, cliques of size 10) and its equivalent random network. Their transmission rates ${\beta }_1={\beta }_2$ are given as a fraction of the recovery rate $r_1=r_2$. The shaded region highlights a parameter region where interacting diseases on CS networks can spread explosively, whereas they cannot on the ERN. (B) Time evolution of the interacting diseases at the value ${\beta }_1={\beta }_2=0.056$ (indicated with an arrow in A). The markers give the median state of the Monte Carlo simulations with error bars corresponding to the 75% interval, whereas the curves give the prediction of our mean-field formalism. Note that the epidemics die out on the ERN and not on the CS, despite the heavy stochasticity caused by the nearby discontinuity (as seen in A).