?A single infected individual enters a community of \(n\) susceptible individuals. Let \(x\) be the number of newly infected individuals at time \
Chapter 8, Problem 49(choose chapter or problem)
A single infected individual enters a community 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, \(d x / d t=k(x+1)(n-x)\) and you obtain
\(\int \frac{1}{(x+1)(n-x)} d x=\int k d t\) .
Solve for \(x\) as a function of \(t\).
Text Transcription:
n
x
t
dx/dt = k(x + 1)(n - x)
int 1 / x + 1)(n - x) dx = int k dt
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer