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Unformatted text preview: 11/2/2009 1 Spreading Processes Modeling Infectious Disease Dynamics with Networks What is epidemiology? • Terms – Susceptible – Infected – Epidemic • Questions asked: • will an epidemic occur? • what is the typical size of an outbreak? • what determines the probability of an epidemic? • How do we control the spread? I dt dR I I IS dt dI IS dt dS γ α γ β β = = = S I R susceptible infectious recovered Compartmental models S I R susceptible infectious recovered Compartmental models R = Infection rate Mortality + Recovery rate Reproductive Ratio/Number: average number of secondary cases per infected individual 11/2/2009 2 Generation time ≈ 10 days SARS and its Reproductive Ratio (R0) Initial estimates for SARS: R 0 = 2.2  3.7 SARS spread unchecked in China for 120 days. 30,00010,000,000 782 Days 10 20 30 40 120 R = reproductive ratio b number of secondary infections caused by a single infected person Ref: Meyers et al (2005) J Theor Biol. 2005 Jan 7;232(1):7181 What’s missing in this model? nurse poet teacher infant S I R susceptible infectious removed Review: Compartmental Models Advantages : SimpleExtendable Amenable to mathematical analysis Disadvantage : Assume everyone in the population is equally vulnerable to infection and to spreading infection. S I R susceptible infectious removed What can we do to fix this? 11/2/2009 3 Terminology Node (vertex): These represent people or places that can become infected Edge: contacts between nodes (people) that can lead to disease transmission Degree: The number of edges coming out of a node 1 3 2 6 CONTACT NETWORK (graph) What makes up a contact network?What makes up a contact network?...
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 Fall '09
 Epidemiology, Infectious Disease, Work, cluster size distribution, randomly chosen edge

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