Mapping the spread of disease is essential to preventing epidemics. The fascinating mathematics of infection is explained here: http://www.gresham.ac.uk/lectures-and-events/modelling-the-spread-of-infectious-diseases
Mathematics has proved to be of considerable benefit in modelling the population biology of infectious diseases by examining the rate of change of the proportion of the population susceptible to, infected with and recovered from a particular infectious disease. In particular, if a vaccine is available, mathematics helps in understanding the impact of different vaccination strategies.
The transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/lectures-and-events/modelling-the-spread-of-infectious-diseases
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