In recent years, epidemics caused by HIV, SARS, and swine flu have worried health experts across the globe. While public health officials and epidemiologists have been tasked with combating these outbreaks, physicists have also lent support by modeling disease outbreaks. Researchers at Boston University have delved into how our increasingly interconnected networks contribute to the spread of disease.

*A generic influenza virus. Image credit: CDC*

Mark Dickison and his colleagues at BU ran computer simulations on the spread of disease between two networks, which could represent two cities, states or countries. The simulations started with one infected virtual person, or node. For each simulation, researchers assigned a probability of spreading the disease to adjacent nodes.

After crunching the numbers, the researchers found that two different types of epidemics can arise. First, systems with strong ties tend to develop outbreaks at the same time. For example, if Springfield has close social and economic ties to Shelbyville, then an outbreak in one city will quickly spill over into the next city. If, on the other hand, both cities are only weakly-connected, then the epidemic can be contained to one city. Even if the two cities are connected, the degree of closeness will determine whether or not the disease can be contained.

The work may seem straightforward, but the researchers now have established key mathematical cut-off points between the weakly-connected and strongly-connected networks.

In particular, the number of neighboring people in contact with an infected person determines whether or not the disease can be contained. The researchers calculated three variables that measure this level of contact: contact only within the first system (e.g. Springfield); contact only within the second system (e.g. Shelbyville); and finally, contact solely between these two systems.

If the number of "infectable" neighbors within either of the individual cities exceeds the number between the two cities, then the epidemic can be contained. But if the inter-city number is higher, then a full-blow pandemic can be underway.

Now that researchers have better modeled epidemics between quasi-independent systems, they hope to apply the mathematical representations to real-life scenarios. If the variables used could be accurately measured in a real world scenario, officials would have a better idea of where the disease would spread. The researchers note that if two systems were going to become infected, then they may be able to more quickly appeal to a higher authority to help address the situation.

You can find this new research posted on the arXiv preprint server.

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