Question

dI/dt = βSI – mI  .

dI/dt is the rate of growth of the infected population

β is the transmission coefficient

S is the number of uninfected hosts

m is the death and recovery (with immunity) rate

Now suppose that the transmission rate (β) of both groups is different.The transmission rate of the first group (where m = 0.7) is really 0.003 (higher than in the question above). The transmission rate of the second group (where m = 0.2) is really 0.0005 (lower than in the question above). You must choose between allowing the three individuals with the more virulent disease or the three with the less virulent disease to enter the town. You cannot choose all or none of them. If your goal is to preserve the lives of the townspeople, which group do you allow into the town? Why?

Answer 1

Question:

Answer:

For group 1:

β = 0.003

m =0.7

dI/dt = βSI – mI

Let take population size = 1000

Rate of growth of infected person because of group 1 (R1, dI/dt) =

R1 = (1000*0.003) – 0.7

R1 = 2.3 per 1000 people

For group 2:

β = 0.0005

m =0.2

dI/dt = βSI – mI

Let take population size = 1000

Rate of growth of infected person because of group 2 (R2, dI/dt) =

R2 = (1000*0.0005) – 0.2

R2 = 0.3 per 1000 people

To preserve lives of town people I will allow group2 people into town. Because rate of growth of infected person is 0.3/1000 people which is less than because of R1 (2.3/1000 people).