# How Epidemics Spread 2, Exercise 2: generations to reach a size, and how uncertain R0 changes the answer
import math

# Part A: generations needed for one case to lead to 1000 cases in a single
# generation, and the days that takes if a generation lasts 5 days (assumed).
T = 5
print("   R0  generations  days")
for r0 in [1.2, 1.5, 2.0, 2.5, 3.0]:
    generations = math.log(1000) / math.log(r0)
    print(f"{r0:5.1f}  {generations:10.1f}  {generations * T:5.0f}")

# Part B: how much does the uncertainty in R0 matter? Measles is often quoted
# at 12 to 18 and seasonal influenza near 1.3 (Wikipedia, as fetched).
for name, r0 in [("measles low", 12), ("measles high", 18), ("influenza", 1.3)]:
    print(f"{name:13s} R0 {r0:4}: cases in generation 3 = {r0 ** 3:,.0f}")

# Output when run:
#    R0  generations  days
#   1.2        37.9    189
#   1.5        17.0     85
#   2.0        10.0     50
#   2.5         7.5     38
#   3.0         6.3     31
# measles low   R0   12: cases in generation 3 = 1,728
# measles high  R0   18: cases in generation 3 = 5,832
# influenza     R0  1.3: cases in generation 3 = 2