Clustering for epidemics on networks: A geometric approach

Infectious diseases typically spread over a contact network with millions of individuals, whose sheer size is tremendous challenge to analyzing and controlling an epidemic outbreak. For some networks, it possible group individuals into clusters. A high-level description the between few clusters considerably simpler than on individual level. However, cluster most studies rely equitable partitions, rather restrictive structural property network. In this work, we focus Susceptible–Infected–Susceptible (SIS) epidemics, our contribution threefold. First, propose geometric approach specify all networks for which outbreak simplifies interaction only Second, complete graph any initial viral state vectors, derive closed-form solution nonlinear differential equations N-intertwined mean-field approximation SIS process. Third, by relaxing notion low-complexity approximations bounds epidemics arbitrary networks. Our results are important step toward understanding large