A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is a 60% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Four hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks

Number of mice that will be infected next week

N₁ = 220

in 3 weeks

N₃ = 149.8

Step-by-step explanation:

Let A represent the number of infected mice and B represent the number of noninfected mice at a particular time.

Initially;

A₀ = 400

B₀ = 1000-400 = 600

Probability that an infected mouse will overcome the virus Pa = 60%

probability that a noninfected mouse will become infected Pb = 10%

The number of mice that would be infected in the next week is N;

N₁ = A - APa + BPb

N₁ = 400 - 0.60 (400) + 0.10 (600)

N₁ = 400 - 240 + 60

N₁ = 220

Second week;

A₁ = 220

B₁ = 1000-220 = 780

N₂ = 220 - 0.60 (220) + 0.10 (780)

N₂ = 220 - 132 + 78

N₂ = 166

Three weeks after;

A₂ = 166

B₂ = 1000-166 = 834

N₃ = 166 - 0.60 (166) + 0.10 (834)

N₃ = 149.8

A₃ = 149.8