How to distribute antidote to control epidemics

Abstract

We give a rigorous analysis of variations of the contact process on a finite graph in which the cure rate is allowed to vary from one vertex to the next, and even to depend on the current state of the system. In particular, we study the epidemic threshold in the models where the cure rate is proportional to the degree of the node or when it is proportional to the number of its infected neighbors. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 2010

Distributing Antidote Using PageRank Vectors

“…If such an H does not exist, then the algorithm will terminate with the entire graph inoculated. For example, in the case of expander graphs, the algorithm will soon terminate and is reduced to same scenario as in [4]. Nevertheless, it is likely for a general contact graph to contain small h-clusters.…”

“…the Cheeger ratio h is small), then we can effectively combat the infection by only attacking the epidemic within that h-cluster. 4 An outline of the analysis of the inoculation scheme and several useful facts…”

“…Many analytical models have been used to address numerous crucial problems, such as the conditions for disease spreading, the critical threshold for the infection rate, the duration of persistent epidemics, and the effective distribution of limited amounts of antidote. We will examine a well-studied contact process model [4,14], coupled with an inoculation scheme using PageRank vectors. In this paper, we give a complete analysis of our scheme, showing the improved efficiency of the inoculation scheme without affecting the performance guarantee as in previous results in [4].…”

“…We will examine a well-studied contact process model [4,14], coupled with an inoculation scheme using PageRank vectors. In this paper, we give a complete analysis of our scheme, showing the improved efficiency of the inoculation scheme without affecting the performance guarantee as in previous results in [4].…”

“…In [4], Borgs et al show that for the contact process on a contact graph G, inoculating every node with antidote equal to its degree will result in any infection dying out in O(log n) time with high probability, where n is the number of nodes in G. This scheme uses a total amount of antidote equal to the sum of the degrees in G. For special graphs such as the expanders, it was shown [4] that such a large amount of antidote is necessary (up to a constant factor) when a constant proportion of the nodes are initially infected. Our proposed model will not improve this result on expander graphs, but for many classes of graphs, we will require antidote only on smaller portions of the network.…”