toward optimal vaccination strategies for probabilistic models
Epidemic outbreaks such as the recent H1N1 influenza show how susceptible large communities are toward the spread of such outbreaks. The occurrence of a widespread disease transmission raises the question of vaccination strategies that are appropriate and close to optimal. The seemingly different problem of viruses disseminating through email networks, shares a common structure with disease epidemics. While it is not possible to vaccinate every individual during a virus outbreak, due to economic and logistical constraints, fortunately, we can leverage the structure and properties of face-to-face social networks to identify individuals whose vaccination would result in a lower number of infected people. The models that have been studied so far [3, 4] assume that once an individual is infected all its adjacent individuals would be infected with probability 1. However, this assumption is not realistic. In reality, if an individual is infected by a virus, the neighboring individuals would get infected with some probability (depending on the type of the disease and the contact). This modification to the model makes the problem more challenging as the simple version is already NP-complete [3]. Here we consider the following epidemiological model computationally: A number of individuals in the community get vaccinated which makes them immune to the disease. The disease then outbreaks and a number of nodes that are not vaccinated get infected at random. These nodes can transmit the infection to their friends with some probability. In this work we consider the optimization problem in which the number of nodes that get vaccinated is limited to k and our objective is to minimize the number of infected people overall. We design various algorithms that take into account the properties of social networks to select k nodes for vaccination in order to achieve the goal. We perform experiments on a real dataset of 34,546 vertices and 421,578 edges and assess their effectiveness and scalability.
vaccination probabilistic model social networks sir virus propagation