We study the asymptotic periodic distribution of queues with time- varying periodic transition rates and catastrophes that occur randomly according to an exponential distribution with time-varying periodic rate. When a disaster occurs, the system resets, all customers are lost and an exponentially distributed period of time elapses before the repair is complete. Service is governed by a phase distribution. The asymptotic periodic distribution of the queue process is analogous to the steady state distribution for a system with constant transition rates.