A Within-Host Stochastic Model for Nematode Infection

We propose a stochastic model for the development of gastrointestinal nematode infection in growing lambs under the assumption that nonhomogeneous Poisson processes govern the acquisition of parasites, the parasite-induced host mortality, the natural (no parasite-induced) host mortality and the death of parasites within the host. By means of considering a number of age-dependent birth and death processes with killing, we analyse the impact of grazing strategies that are defined in terms of an intervention instant t 0 , which might imply a move of the host to safe pasture and/or anthelmintic treatment. The efficacy and cost of each grazing strategy are defined in terms of the transient probabilities of the underlying stochastic processes, which are computed by means of Strang–Marchuk splitting techniques. Our model, calibrated with empirical data from Uriarte et al and Nasreen et al., regarding the seasonal presence of nematodes on pasture in temperate zones and anthelmintic efficacy, supports the use of dose-and-move strategies in temperate zones during summer and provides stochastic criteria for selecting the exact optimum time instant t 0 when these strategies should be applied.

Monte Carlo Simulation for Optimization of Object Operation Process and Reliability / SYMULACJA MONTE CARLO W OPTYMALIZACJI PROCESU EKSPLOATACJI ORAZ NIEZAWODNOŚCI OBIEKTU TECHNICZNEGO

This paper presents the computer simulation technique related to the reliability of an object under variable operation conditions. The Monte Carlo simulation is performed and, consequently, the unknown parameters for the considered object operation process and its main reliability characteristics are identified. The optimal transient probabilities of the object operation process at the particular operation states and its optimal unconditional reliability function are determined.

Exact transient solution of a state-dependent birth-death process

A power series expression in closed form for the transient probabilities of a state-dependent birth-death process is presented with suitable illustrations.

Transient solution to the time-dependent multiserver Poisson queue

We derive an integral equation for the transient probabilities and expected number in the queue for the multiserver queue with Poisson arrivals, exponential service for time-varying arrival and departure rates, and a time-varying number of servers. The method is a straightforward application of generating functions. We can express pĉ−1(t), the probability that ĉ − 1 customers are in the queue or being served, in terms of a Volterra equation of the second kind, where ĉ is the maximum number of servers working during the day. Each of the other transient probabilities is expressed in terms of integral equations in pĉ−1(t) and the transition probabilities of a certain time-dependent random walk. In this random walk, the rate of steps to the right equals the arrival rate of the queue and the rate of steps to the left equals the departure rate of the queue when all servers are busy.

Transient solution to the time-dependent multiserver Poisson queue

We derive an integral equation for the transient probabilities and expected number in the queue for the multiserver queue with Poisson arrivals, exponential service for time-varying arrival and departure rates, and a time-varying number of servers. The method is a straightforward application of generating functions. We can express p ĉ−1(t), the probability that ĉ − 1 customers are in the queue or being served, in terms of a Volterra equation of the second kind, where ĉ is the maximum number of servers working during the day. Each of the other transient probabilities is expressed in terms of integral equations in p ĉ−1(t) and the transition probabilities of a certain time-dependent random walk. In this random walk, the rate of steps to the right equals the arrival rate of the queue and the rate of steps to the left equals the departure rate of the queue when all servers are busy.