def infectious_from_cases(cases, R0) -> float:
    """
    Initializes the "infectious" component of a SIR model from the current
    number of cases.

    This formula assumes a perfect exponential growth.
    """
    if R0 <= 1:
        raise ValueError(f"R0 must be greater than one (got {R0})")

    seed = 1
    return (cases * (R0 - 1) + seed) / (2 * R0 - 1)