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

Question

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

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Sadie 2 weeks 2021-11-19T19:00:23+00:00 1 Answer 0 views 0

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    2021-11-19T19:01:55+00:00

    Answer:

    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

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