Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jumpdiffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.

We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs. The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state of failure. Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function. We analyze the transient and the asymptotic behavior of the queueing system. Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs). Special attention is devoted to the case of periodic catastrophe and repair intensity functions. The first-passage-time problem through constant levels is also treated both for the queueing model and the approximating diffusion process. Finally, the goodness of the diffusive approximating procedure is discussed.

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A natural prodrug is a chemical compound or substance obtained from plants, microorganism, animal and marine sources. Natural products are small molecule source for Food and Drug Administration approved drugs and major sources for drug discovery. Most of the drugs for different ailment diseases undergo first pass metabolism, resulting in drug inactivation and the generation of toxic metabolites in body. Enormous numbers of prodrugs naturally present in plants, microorganism, animal and marine sources and those prodrugs undergoes chemical reaction to form non-toxic compounds. This review summarizes the list of prodrugs naturally present in the natural product.

Meglitinides such as repaglinide and nateglinide are useful to treat type 2 diabetes patients who follow a flexible lifestyle. They are short-acting insulin secretagogues and are associated with less risk of hypoglycemia, weight gain and chronic hyperinsulinemia compared with sulfonylureas. Meglitinides are the substrates of cytochrome P450 (CYP) enzymes and organic anion transporting polypeptide 1B1 (OATP1B1 transporter) and the coadministration of the drugs affecting them will result in pharmacokinetic drug interactions. This article focuses on the drug interactions of meglitinides involving CYP enzymes and OATP1B1 transporter. To prevent the risk of hypoglycemic episodes, prescribers and pharmacists must be aware of the adverse drug interactions of meglitinides.