Differential Equation (Application)

In a ‘simple’ epidemic, the rate at which the number of susceptible, s, in a population of total size n+1, become infected is given by \displaystyle \frac{ds}{dt}=-cs(n+1-s), where c is a positive constant.

Show that, if an epidemic is ‘simple’, the number of new cases of the disease recorded per unit time will be given by:

    \[\frac{cn\left(n+1\right)^{2}\,e^{\left(n+1\right)ct}}{\left[ n + e^{\left(n+1\right)ct}\right]^{2}}\]

Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 44: Question 7, p. 132)

Author: ascklee

Dr. Lee teaches at the Wee Kim Wee School of Communication and Information at the Nanyang Technological University in Singapore. He founded The Mathematics Digital Library in 2013.

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