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Please i need some help in Partial Fractions

  1. Nov 13, 2005 #1
    Partial Fractions:
    A single infected individual enters a comunnity of n susceptible individuals. Let x be the number of newly infected individuals at time t. The common epidemic model assumes that the disease spreads at a rate proportional to the product of the total number infected and the number not yet infected.So
    [tex] \frac {dx} {dt} = k(x+1) (n-x) [/tex] and you obtain [tex] \int\frac {1} {(x+1)(n-x)} dx = \int k dt [/tex] I need to know how to set up the problem and then work from there.

    Any suggestions.
     
    Last edited: Nov 13, 2005
  2. jcsd
  3. Nov 13, 2005 #2

    Tide

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    Homework Helper

    You have already "set up" the problem.

    I think you're looking for this:

    [tex]\frac {1}{(x+1)(n-x)} = \frac {1}{n+1} \left( \frac {1}{x+1} + \frac {1}{n-x}\right)[/tex]
     
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