Question

A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 90% probability that an infected mouse will overcome the virus, and during the same week there is a 40% probability that a noninfected mouse will become infected. Two hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks

Answer 1

1. How many will be infected next week

From the information, there are 1000 mice in the lab.

200 mice are infected. It is expected that 90% of the mice are expected to overcome the infection and 40% uninfected mice will be infected.

If 200 mice are infected, then number of uninfected mice is:

= 1000 - 200 = 800

90% of infected mice get cured. Out of 200 mice who are infected, the number of mice getting cures is:

N(E) = P(E)×N(S)

= 0.90*200

= 180

The number of mice still infected is 200 - 180 = 20

Out of 800 uninfected mice, 40% will get infected. Number of infected mice is:

N(E) = P(E) * N(S)

= 0.40 * 800

= 320

​Total number of infected mice is 320 + 20 = 340 . Thus, the number of infected mice next week is 340

2. How many will be infected in 3 weeks

After three week, the number of infected mice is 340. Therefore, the number of uninfected mice is 1000 - 340 = 660

Now, out of 340 mice, it is expected that 90% will recover. This indicates that 10% will remain infected. Then the number of infected mice is

N(E) = P(E) * N(S)

= 0.10 * 340

= 34

​

Out of 660 mice, 40% will be infected. The number of mice becoming infected is

N(E) = P(E) * N(S)

= 0.40 * 660

= 264

Total number of infected mice is 264 + 34 =298. Thus, the number of infected mice after two weeks is 298.