State and prove monotone convergence theorem... | Filo

SOLVED: a) The monotone convergence theorem implies that if a function f is monotone (increasing or decreasing) and bounded on [0,x], then limₜ→ₓ f(t) exists. Use this to show that limₜ→ₓ S(t), limₜ→ₓ I(t), and limₜ→ₓ R(t) all exist. Denote these limits by S₀, I₀, and R₀. This means the situation stabilizes over time. Hint: Consider S and R first and remember the total population size is N. Solution:b) It is a fact that if limₜ→ₓ f'(t) > 0, then limₜ→ₓ f