On the basis of part i) above, you know that Sus[0] >= Sus[t]fort >= 0. Now look

Question

On the basis of part i) above, you know that Sus[0] >= Sus[t]fort >= 0.

Now look at the key ingredient of the model: Inf'[t] = a Sus[t] Inf[t] - b Inf[t] = (a Sus[t] - b) Inf[t].

Explain the statements:
-> If Sus[0] < b/a, then the model predicts no epidemic because in this case Inf[t] goes down as t goes up.

-> If Sus[0] > b/a, then the model predicts that the disease will spread and the infected population will increase until S[t] gets small enough that Sus[t] < b/a. In other words, if Sus[0] > b/a, then an epidemic is in the cards.

On the basis of part i) above, you know that Sus[0)2 Susit] for t 20 Now look at the key ingredient of the model: Inf It] -a Sus[t] Inf[t]-b Inf [t] = (a Sus[t]-b) Inf[t] Explain the statements If Suso then the model predicts no epidemie because in this case Inf[t] goes down as t goes up. If Susto then the model predicts that the disease will spread and the infected population will increase until St) gets small enough that Sust] In other words, if Sus[0] >- , then an epidemic is in the cards.

Explanation / Answer

Explanation:

Given Sus[0] >= Sus[t]fort >= 0.
Key ingredient of the model: Inf'[t] = a Sus[t] Inf[t] - b Inf[t] = (a Sus[t] - b) Inf[t].

1) Consider the first statement,

If Sus[0] < b/a, then the model predicts no epidemic because in this case Inf[t] goes down as t goes up.

Let us simply this statement using an example.

Inf'[t] = (a Sus[t] - b) Inf[t]

when you take "a" as common the you will get the below statement.

Inf'[t] = (Sus[t] - b/a) (a) Inf[t]

According to the statement 1, when Sus[0]<b/a

Inf'[0] = (Sus[0] - b/a) (a) Inf[0]

consider b/a as 1/3 then Sus[0] is 1/4 then substitute the same in the above equation.

Inf'[0] = (1/4-1/3) (a) Inf[0]

Inf'[0] = (-1/12)(a) Inf[0] which is very small... So the model predicts no epidemic because in this case Inf[t] goes down as t goes up.

2) Consider the second statement,

If Sus[0]>b/a

then again consider b/a as 1/3 and Sus[0] as 1

Inf'[0] = (Sus[0] - b/a) (a) Inf[0]

Inf'[0] = (1-1/3) (a) Inf[0]

Inf'[0] = 2/3 (a) Inf[0] which is increasing until S[t] gets small enough that Sus[t] < b/a.

So the model predicts that the disease will spread

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