6 research outputs found
Adapting the Standard SIR Disease Model in Order to Track and Predict the Spreading of the EBOLA Virus Using Twitter Data
Get PDFA method has been developed to track infectious diseases by using data mining of active Twitter accounts and its efficacy was demonstrated during the West African Ebola outbreak of 2014. Using a meme based n-gram semantic usage model to search the Twitter database for indications of illness, flight and death from the spread of Ebola in Africa, principally from Guinea, Sierra Leone and Liberia. Memes of interest relate disease to location and severity and are coupled to the density of Tweets and re-Tweets. The meme spreads through the community of social users in a fashion similar to nonlinear wave propagation- like a shock wave, visualized as a spike in Tweet activity. The spreading was modeled as a system isomorphic to a modified SIR (Susceptible, Infected, Removed disease model) system of three coupled nonlinear differential equations using Twitter variables. The nonlinear terms in this model lead to feedback mechanisms that result in unusual behavior that does not always reduce the spread of the disease. The resulting geographic Tweet densities are coupled to geographic maps of the region. These maps have specific threat levels that are ported to a mobile application (app) and can be used by travelers to assess the relative safety of the region they will be in
Fluid aggregations for Markovian process algebra
Get PDFQuantitative analysis by means of discrete-state stochastic processes is hindered by the well-known phenomenon of state-space explosion, whereby the size of the state space may have an exponential growth with the number of objects in the model. When the stochastic process underlies a Markovian process algebra model, this problem may be alleviated by suitable notions of behavioural equivalence that induce lumping at the underlying continuous-time Markov chain, establishing an exact relation between a potentially much smaller aggregated chain and the original one. However, in the modelling of massively distributed computer systems, even aggregated chains may be still too large for efficient numerical analysis. Recently this problem has been addressed by fluid techniques, where the Markov chain is approximated by a system of ordinary differential equations (ODEs) whose size does not depend on the number of the objects in the model. The technique has been primarily applied in the case of massively replicated sequential processes with small local state space sizes. This thesis devises two different approaches that broaden the scope of applicability of efficient fluid approximations. Fluid lumpability applies in the case where objects are composites of simple objects, and aggregates the potentially massive, naively constructed ODE system into one whose size is independent from the number of composites in the model. Similarly to quasi and near lumpability, we introduce approximate fluid lumpability that covers ODE systems which can be aggregated after a small perturbation in the parameters. The technique of spatial aggregation, instead, applies to models whose objects perform a random walk on a two-dimensional lattice. Specifically, it is shown that the underlying ODE system, whose size is proportional to the number of the regions, converges to a system of partial differential equations of constant size as the number of regions goes to infinity. This allows for an efficient analysis of large-scale mobile models in continuous space like ad hoc networks and multi-agent systems
