We introduce and study a new stochastic SARS model (based on stochastic SIR model with semi-Markov regime-switchings) and investigate its behavior in averaging, merging and diffusion approximation schemes. The main method is based on general theory of random differential equations in semi-Markov...

This paper investigates the rate of occurrence of failures (ROCOF) of finite state semi-Markov systems. Firstly, a formula for evaluating the ROCOF for semi-Markov systems is derived. As a consequence of this result, we derive the ROCOF of Markov systems as well as the ROCOF of the alternating...

We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation...