This week, we are going to work together as a class to assist the Lone Star Cent

Question

This week, we are going to work together as a class to assist the Lone Star Center for Disease Control. They have identified a closed population of 10,000 individuals, where a particularly nasty strain of flu virus has started to spread. What we know about this particular virus:

1) It spreads at a rate that is jointly proportional to both the number of infected individuals and then number of uninfected individuals.

2) When 1,000 individuals are infected, the rate at which individuals are becoming infected is 500 individuals per day.

3) There are currently 200 individuals infected. The LSCDC has determined that it is critical for relief efforts that they know how long it will take, based upon available information, for 90% of the population to become infected with the virus. You are not required to solve this entire problem on your own. Post at least the equivalent of 50 words that contributes to us solving this together throughout the course of the week.

Explanation / Answer

let the populatin be a
no. of infected be x
no of uninfected will be. a-x

1)given rate=kx*(a-x)
2) rate per day =500 when infected is 1000
= 500=k*1000*9000
k=1/18000
3)
right now 200 are infected
asked to find time for 9000 to be infected

dx/dt=k*(ax-x^2)

we can solvve it by solving the above diff. eq.
integral dx/(ax-x^2) =k*dT
with limits x=200 to 9000 and T=0 to t

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