{"responseHeader":{"status":0,"QTime":4,"params":{"q":"{!q.op=AND}id:\"418044\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"modified_tdt":"2013-11-19T00:00:00Z","thumb_s":"/ce/cb/cecbfa52ae756d0919eee37f226e7c46ff827f8b.jpg","oldid_t":"UROP 3575","setname_s":"uu_urop","file_s":"/64/59/6459473b6c9ef2e6204abf1280d6385fbde7e722.pdf","title_t":"076_072","ocr_t":"COLLEGE OF SCIENCE UNDERGRADUATE RESEARCH ABSTRACTS MATHEMATICAL MODELING OF EPIDEMICS USING A PROBABILISTIC GRAPH Skip Fowler (Frederick R. Adler) Department of Mathematics University of Utah In order to predict the number of survivors, w e study a stochastic model of an epidemic that inÂcludes with transitions infection and recovery. This approach can be represented as a graph with probabilities on the edges between states. The distribution of the number of survivors can be found from the set of probabilities associated with states where the number of infected people equals 0. W e find that this probability distribution breaks into two distinct components. W e compute the probability of rapid epidemic extinction with many survivors, Q, using methods from stochastic process theory. If the epidemic takes hold, w e use an SIR model without vital dynamics, a deterÂministic set of differential equations describing the spread of an epidemic, which approaches zero only when the epidemic begins and ends. W e compare the mean of the probabilities for states after Q to determine if the mean matches the end point of the epidemic in the deterministic SIR model, and check whether their distribution is approximately normal. W e developed computer simulations to calculate and plot the probabilities and compare with the mathematical analysis of Q and the SIR model. Our discoveries during the course of this project include finding the Catalan numbers and Catalan's triangle within the graph structure and finding a knights move based on the number of steps to any state within the graph structure. The probabilities after Q are not normal due to increasing kurtosis as population size and infection rate are increased, although the mean is well-approximated by the differential equation. W e are searching for a higher dimensional system that captures this deviation from normality. Skip Fowler Frederick R. Alder","restricted_i":0,"id":418044,"created_tdt":"2013-11-19T00:00:00Z","format_t":"application/pdf","parent_i":418234,"_version_":1642982625033322496}]},"highlighting":{"418044":{"ocr_t":[]}}}