Mathematical Modeling of Epidemiology on Scale Free Networks

To understand the outbreak of epidemics, our research models the spread of infectious disease on scale-free networks. In such networks, certain nodes called “hubs” have many connections, while most other nodes have a... [ view full abstract ]

To understand the outbreak of epidemics, our research models the spread of infectious disease on scale-free networks. In such networks, certain nodes called “hubs” have many connections, while most other nodes have a significantly smaller degree. A scale-free network is one in which the degree follows a power distribution law. That is, the number of nodes with k connections is proportional to x^k, where x is a constant. This gives rise to a long-tail distribution, in which few nodes have many connections and many nodes have few connections. We choose this type of model because contact networks between people are typically scale-free. For instance, the football star on Adrian’s campus would have many connections, while the nerds in the physics lab may have few. Epidemics have been shown to be inevitable on a conventional scale-free network, so we choose to examine subnetworks which change from day to day. Perhaps, the popular student does not have class on Thursdays, and chooses to stay in bed for most of the day. Being a hub one day does not necessarily mean that the node will continue to be a hub in the future. This concept of dynamic centrality, that the most connected node changes over time, may be significant to the spread of disease. If a hub on a certain day is infected, he may infect many other humans, or perhaps he is not a hub and the rest of the population will remain safe.