اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدContact process on a graph with communities
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تأليف
David Sivakoff
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We are interested in the spread of an epidemic between two communities that have higher connectivity within than between them. We model the two communities as independent Erdos-Renyi random graphs, each with n vertices and edge probability p = n^{a-1} (0<a<1), then add a small set of bridge edges, B, between the communities. We model the epidemic on this network as a contact process (Susceptible-Infected-Susceptible infection) with infection rate lambda and recovery rate 1. If nplambda = b > 1 then the contact process on the Erdos-Renyi random graph is supercritical, and we show that it survives for exponentially long. Further, let tau be the time to infect a positive fraction of vertices in the second community when the infection starts from a single vertex in the first community. We show that on the event that the contact process survives exponentially long, tau |B|/(np) converges in distribution to an exponential random variable with a specified rate. These results generalize to a graph with N communities.
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