# How Epidemics Spread 1, Exercise 1: incidence and prevalence from a case list
# A village of 200 people (assumed). Each case is (first day ill, last day ill).
# Find, for days 1 to 12: new cases (incidence), people ill that day (prevalence),
# the cumulative incidence at day 12, and check prevalence against the
# running total of new cases minus recoveries.
population = 200
cases = [(1, 4), (2, 6), (2, 5), (3, 7), (3, 8), (4, 8), (4, 9),
         (5, 9), (5, 10), (6, 10), (7, 11), (8, 12)]

for day in range(1, 13):
    incidence = sum(1 for start, end in cases if start == day)
    prevalence = sum(1 for start, end in cases if start <= day <= end)
    recovered_before = sum(1 for start, end in cases if end < day)
    started_by = sum(1 for start, end in cases if start <= day)
    assert prevalence == started_by - recovered_before
    print(f"day {day:2d}  new {incidence}  ill {prevalence:2d}")

print("cumulative incidence at day 12:", len(cases) / population)
print("mean duration:", round(sum(e - s + 1 for s, e in cases) / len(cases), 2), "days")
print("peak prevalence:", max(sum(1 for s, e in cases if s <= d <= e) for d in range(1, 13)))

# Output when run:
# day  1  new 1  ill  1
# day  2  new 2  ill  3
# day  3  new 2  ill  5
# day  4  new 2  ill  7
# day  5  new 2  ill  8
# day  6  new 1  ill  8
# day  7  new 1  ill  8
# day  8  new 1  ill  8
# day  9  new 0  ill  6
# day 10  new 0  ill  4
# day 11  new 0  ill  2
# day 12  new 0  ill  1
# cumulative incidence at day 12: 0.06
# mean duration: 5.08 days
# peak prevalence: 8