Epidemiology Epidemiology studies the causes, distribution, and control of disease in populations.
What is an SIR Model? An SIR model is an epidemiological model that computes the theoretical number of people infected with a contagious illness in a closed population over time. The name of this class of models derives from the fact that they involve coupled equations relating the number of susceptible people S(t), number of people infected I(t), and number of people who have recovered R(t). One of the simplest SIR models is the Kermack-McKendrick Model. 1
Discrete vs. Continuous Discrete Distinct separate values. Having consecutive values that are not infinitesimally close, so that its analysis requires summation rather than integration. 2 Continuous Objects that vary smoothly. uninterrupted connection or union
Kermack-McKendrick model t = time (days) S(t) = Susceptible I(t) = Infected R(t) = Recovered* a = Infection rate b = Recovery rate
Results The modified SIR model indicates a much higher maximum number of infecteds but also a much faster recovery for the student body as a whole. Yes it does.
S-I-R Model is so cool Good Intro to calculus Art of Math Modeling Learn how to analyze numerically a system of ODE’s See connection between discrete and continuous dynamical systems Tie sophisticated math to spread of an epidemic
Reference Page A Modified Discrete SIR Model, Jennifer Switkes, The College Mathematics Journal, Vol. 34, No. 5 (Nov., 2003), pp. 399-402. W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics, Proc. Roy. Soc. A 115 (1927), 700-721; 138 (1932), 55-83; 141 (1933), 92-122. J. D. Murray, Mathematical Biology, Springer, 1993. Callahan, J. "The Spread of a Contagious Illness." http://maven.smith.edu/~callahan/ili/pde.html.