# How Epidemics Spread 3, Exercise 2: steps that are too big
# Exercise 2: steps that are too big. High transmission (assumed beta = 2.0, gamma = 0.2).
population, beta, gamma = 10_000, 2.0, 0.2

def run(dt, guard, days=60):
    S, I, R = population - 1.0, 1.0, 0.0
    lowest_S = S
    for _ in range(int(days / dt)):
        new_inf = beta * S * I / population * dt
        if guard:
            new_inf = min(new_inf, S)
        new_rec = gamma * I * dt
        S -= new_inf
        I += new_inf - new_rec
        R += new_rec
        lowest_S = min(lowest_S, S)
    return lowest_S, I

for dt in [1.0, 0.5, 0.1, 0.01]:
    for guard in [False, True]:
        low, I = run(dt, guard)
        note = "  <- negative people!" if low < 0 else ""
        print(f"dt {dt:5.2f} guard {str(guard):5s} lowest S {low:10.1f}  I at day 60 {I:10.1f}{note}")

# Output when run:
# dt  1.00 guard False lowest S     -762.3  I at day 60        0.1  <- negative people!
# dt  1.00 guard True  lowest S        0.0  I at day 60        0.1
# dt  0.50 guard False lowest S        0.0  I at day 60        0.1
# dt  0.50 guard True  lowest S        0.0  I at day 60        0.1
# dt  0.10 guard False lowest S        0.3  I at day 60        0.2
# dt  0.10 guard True  lowest S        0.3  I at day 60        0.2
# dt  0.01 guard False lowest S        0.4  I at day 60        0.2
# dt  0.01 guard True  lowest S        0.4  I at day 60        0.2