ABSTRACT
In = 5, 000− 3, 000(0.9)n ⇒ I14 = 4314 (ii) The number of cases will eventually stabilize to 5000 for large n (n
→ ∞.
11. (i) r - recovery rate, In - infected people at time t
In+1 = In − rIn + αIn(N − In) (ii)
(a) In+1 = In − rIn + α1I2n ( 1− In
N
)2 (b) In+1 = (1− r)In + α2I22
( 1− I
N2
) (c) In+1 = (1− r)In + α3Ine−In/N
(iii) r = 8%, N = 106, In = 1000 In+1 = 1500
In+1 = In(1− 0.8) + kIn(106 − In) ⇒ 1500 = 0.2× 1000 + k × 103(106 − 103)
⇒ k = 1.3/(106 − 103) ⇒ In+1 = 0.2In + 1.3013In − 1.3013× 10−6I2n.
