2010/04/01 by B. Aditya Prakash, Prakash, B. Aditya, Deepayan Chakrabarti +7
Mathematics · Physics and Astronomy · #COVID-19 epidemiological studies #Complex Network Analysis Techniques #FOS: Biological sciences #FOS: Physical sciences #Opinion Dynamics and Social Influence #Physics and Society (physics.soc-ph) #Populations and Evolution (q-bio.PE) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1004.0060
openalex publication_date 2010/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
For a given, arbitrary graph, what is the epidemic threshold? That is, under what conditions will a virus result in an epidemic? We provide the super-model theorem, which generalizes older results in two important, orthogonal dimensions. The theorem shows that (a) for a wide range of virus propagation models (VPM) that include all virus propagation models in standard literature (say, [8][5]), and (b) for any contact graph, the answer always depends on the first eigenvalue of the connectivity matrix. We give the proof of the theorem, arithmetic examples for popular VPMs, like flu (SIS), mumps (SIR), SIRS and more. We also show the implications of our discovery: easy (although sometimes counter-intuitive) answers to `what-if' questions; easier design and evaluation of immunization policies, and significantly faster agent-based simulations.