A two-state recurrent stochastic model with time-dependent transition rates.

The two-state recurrent stochastic model with time-independent transition rates is generalized to a model with time-dependent transition rates. The rates can be any general function of external time, that is, any general function of the calendar time in which the process unfolds. Formulas for the state transition probabilities, the proportion of individuals in a particular state at time t, the distribution function, and the expectation of the number of individuals in a particular state at time t are derived.