Processes on Complex Networks
Mathematically describing and modeling complex networks, such as the people-to-people spreading of the flu, helps us understand and analyze their behavior.Copyright US Department of Health and Human Services http://www.hhs.gov/ash/oah/resources-and-publications/learning/coll-tk/index.html#chapter-2/section-2-3/subsection-2-3-1/ http://openi.nlm.nih.gov/detailedresult.php?img=2715422_1741-7015-7-30-1&query=the&fields=all&favor=none&it=none&sub=none&uniq=0&sp=none&req=4&simCollection=1557856_1471-2180-6-70-5&npos=17&prt=3 http://www.nih.gov/researchmatters/august2008/08042008network.htm
Building on their understanding of graphs, students are introduced to random processes on networks. They walk through an illustrative example to see how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students. This demonstrates how scientists and engineers use mathematics to model and simulate random processes on complex networks. Topics covered include random processes and modeling disease spread, specifically the SIR (susceptible, infectious, resistant) model.
Scientists and engineers use the mathematics of random processes on networks to study and understand a wide range of network science problems. For example, bioengineers and public health researchers study how infectious diseases spread on social networks. By building an extensive computer network of molecular relationships, researchers have been able to uncover links to diseases they never before suspected. Biomolecular engineers investigate how life is maintained by the ebb and flow of biochemical species on reaction networks in cells. Neural engineers and neuroscientists examine how human thoughts arise in the brain due to complex firing patterns over neural networks. Financial engineers analyze how money flows through economic systems to create global wealth and stability.
After this lesson, students should be able to:
- Identify processes as being non-random and random.
- Model the spread of an infectious disease, such as the flu, on a given social network by flipping a coin.
- Generally explain how scientists and engineers use mathematics to model and simulate random processes on complex networks.