It has been argued that epidemics have played a major role in human history. For example, the arrival of the British in Australia triggered a deadly wave of smallpox infections, with the estimated death of half of the indigenous Australians. The same virus wiped out the population of Easter Island, and measles eliminated a third of the inhabitants of Fiji. New threats have also emerged as human populations explode and pressure on ecosystems crosses sustainability thresholds. In order to understand how to deal with epidemics and eradicate them, there is a need to first understand how they spread. This chapter begins with a discussion of epidemic modeling, specifically the SIS model. It then covers the SIS model in space and graphs, modeling HIV-1 transmission, and halting viruses in scale-free networks.
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