# How Epidemics Spread 4, Exercise 2: a vaccine that is too weak
# Exercise 2: a vaccine that is too weak (all values assumed).
r0, E, gamma, population, dt = 6.0, 0.8, 0.2, 10_000, 0.05
beta = r0 * gamma
print(f"threshold {1 - 1 / r0:.1%} is above E = {E:.0%}, so full coverage cannot stop spread")

def run(coverage, effectiveness):
    protected = coverage * effectiveness * population
    S, I = population - protected - 1.0, 1.0
    while I >= 0.01:
        new_inf = beta * S * I / population * dt
        S -= new_inf
        I += new_inf - gamma * I * dt
    return (population - protected - S) / population

print("coverage   share of everyone infected")
for coverage in [0.5, 0.8, 1.0]:
    print(f"{coverage:8.0%} {run(coverage, E):20.1%}")
needed = 1 - 1 / r0
print(f"A vaccine with E = {needed + 0.05:.1%} at 100% coverage:")
print(f"{1.0:8.0%} {run(1.0, needed + 0.05):20.1%}")

# Output when run:
# threshold 83.3% is above E = 80%, so full coverage cannot stop spread
# coverage   share of everyone infected
#      50%                58.2%
#      80%                30.1%
#     100%                 6.3%
# A vaccine with E = 88.3% at 100% coverage:
#     100%                 0.0%