  Pandemic distribution of COVID-19 in the world has motivated us to discuss
combined effects of network clustering and adaptivity on epidemic spreading. We
address the question concerning the choice of optimal mechanism for most
effective prohibiting disease propagation in a connected network: adaptive
clustering, which mimics self-isolation (SI) in local communities, or sharp
instant clustering, which looks like frontiers closing (FC) between cities and
countries. SI-networks are "adaptively grown" under condition of maximization
of small cliques in the entire network, while FC-networks are "instantly
created". Running the standard SIR model on clustered SI- and FC-networks, we
demonstrate that the adaptive network clustering prohibits the epidemic
spreading better than the instant clustering in the network with similar
parameters. We found that SI model has scale-free property for degree
distribution $P(k)\sim k^{\eta}$ with small critical exponent $-2<\eta<-1$ and
argue that scale-free behavior emerges due to the randomness in the initial
degree distributions and is absent for random regular graphs.
