PROJECT TITLE:

Distinguishing Infections on Different Graph Topologies

ABSTRACT:

The history of infections and epidemics holds famous examples where understanding, containing, and ultimately treating a virus began with understanding its mode of unfold. Influenza, HIV, and most laptop viruses unfold individual to individual, device to device, and through contact networks; Cholera, Cancer, and seasonal allergies, on the other hand, don't. In this paper, we tend to study two basic questions of detection. Initial, given a snapshot read of a (perhaps vanishingly small) fraction of those infected, under what conditions is a plague spreading via contact (e.g., Influenza), distinguishable from a random illness operating independently of any contact network (e.g., seasonal allergies)? Second, if we do have a deadly disease, below what conditions is it potential to see that network of interactions is the main cause of the unfold—the causative network—while not any knowledge of the epidemic, alternative than the identity of a minuscule subsample of infected nodes? The core, therefore, of this paper, is to obtain an understanding of the diagnostic power of network information. We tend to derive sufficient conditions that networks should satisfy for these issues to be identifiable, and turn out efficient, highly scalable algorithms that solve these issues. We tend to show that the identifiability condition we offer is fairly mild, and in particular, is happy by 2 common graph topologies: the $d$ -dimensional grid, and the Erdös-Renyi graphs.