# How Epidemics Spread 2, Exercise 1: doubling time and growth rate from daily counts
import math

# Daily new cases for days 1 to 6 (assumed, invented to show the method).
new_cases = [12, 15, 19, 24, 30, 38]

ratios = [b / a for a, b in zip(new_cases, new_cases[1:])]
print("day-to-day ratios:", [round(x, 3) for x in ratios])

# Geometric mean of the ratios = the average daily growth factor.
factor = (new_cases[-1] / new_cases[0]) ** (1 / (len(new_cases) - 1))
growth_pct = (factor - 1) * 100
doubling = math.log(2) / math.log(factor)
print(f"average daily growth: {growth_pct:.1f}%")
print(f"doubling time: {doubling:.2f} days (rule of 70 says {70 / growth_pct:.2f})")

# Day on which new cases per day first reach 1000 if growth never changes.
day = 6
level = new_cases[-1]
while level < 1000:
    level *= factor
    day += 1
print("new cases a day reach 1000 on day", day)
print("same answer by formula:", 6 + math.ceil(math.log(1000 / new_cases[-1]) / math.log(factor)))

# Output when run:
# day-to-day ratios: [1.25, 1.267, 1.263, 1.25, 1.267]
# average daily growth: 25.9%
# doubling time: 3.01 days (rule of 70 says 2.70)
# new cases a day reach 1000 on day 21
# same answer by formula: 21