2010/01/04 by Michael Shapiro, Shapiro, Michael, Edgar Delgado‐Eckert +1 · 1 citation
Computer Science · Physics and Astronomy · #Anomaly Detection Techniques and Applications #Complex Network Analysis Techniques #Computational Complexity (cs.CC) #FOS: Biological sciences #FOS: Computer and information sciences #Network Security and Intrusion Detection #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1001.0595
openalex publication_date 2010/01/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The celebrated Kermack-McKendric model of epidemics studies the transmission of a disease in a population where each individual is initially susceptible (S), may become infective (I) and then removed or recovered (R) and plays no further epidemiological role. This ODE model arises as the limiting case of a network model where each individual has an equal chance of infecting every other. More recent work gives explicit consideration to the network of social interaction and attendant probability of transmission for each interacting pair. The state of such a network is an assignment of the values S,I,R to its members. Given such a network, an initial state and a particular susceptible individual, we would like to compute their probability of becoming infected in the course of an epidemic. It turns out that this problem is NP-hard. In particular, it belongs in a class of problems all of whose known solutions require an exponential amount of computation and for which it is unlikely that there will be more efficient solutions.