Units of parameters in differential equation

Question

Suppose I have the system $$I'(t) = \frac{\alpha\beta I}{r+\alpha I} (1-I) - \mu I$$ where $I$ is a unitless quantity giving the portion of a population (in this case, total infected/total population, so $I \le 1$). Suppose the units of $\alpha$ is $h/m$, where $h$ and $m$ are two arbitrary quantities. The same is true for $\beta$. That is, $\beta$ has units $h/m$. $\mu$ is a probability, so the final expression is unitless. However, $I'(t)$ is obviously the derivative of $I$ with respect to time, so its units should be $1/t$, as $I$ is unitless. How is this possible? How do I find the units of $r$ (the force of mortality)?