In this study, a mathematical model of bacterial resistance considering the immune system response and antibiotic therapy is examined under random conditions. A consisting differential equations obtained by using existing deterministic model. Similarly, stochastic effect terms are added to form equations. The results from models also compared with investigate behavior components

In this study, an extended model of type (s,S) is considered and a semi-Markovian random walk with Gaussian distribution summands, which mathematically describes model, constructed. Moreover, under some weak assumptions the ergodicity process discussed. addition, characteristic function ergodic expressed by means appropriating boundary functional S N . Using relation, exact formulas for first four moments are obtained asymptotic expansions derived up to three terms, as β=S−s→∞....

In this study, we constructed a stochastic process ( X t )) that expresses semi‐Markovian inventory model of type s , S ) and it is shown ergodic under some weak conditions. Moreover, obtained exact asymptotic expressions for the n th order moments = 1,2,3, … distribution ), as − → ∞ . Finally, tested how close approximation formulas are to expressions. Copyright © 2012 John Wiley & Sons, Ltd.

The deterministic stability of a model Hepatitis C which includes term defining the effect immune system is studied on both local and global scales. Random added to investigate random behavior model. numerical characteristics such as expectation, variance confidence interval are calculated for effects with two different distributions from results simulations. In addition, compliance examined.

In this study, a semi-Markovian random walk with discrete interference of chance (X(t)) is considered and under some weak assumptions the ergodicity process discussed. The exact formulas for first four moments ergodic distribution X(t) are obtained when variable ζ1, which describes chance, has gamma parameters (α, λ), α > 1, λ 0. Based on these results, asymptotic expansions X(t), as → Furthermore, skewness kurtosis established. Finally, it discussed that alternative estimations stationary...

Type-2 fuzzy sets were initially given by Zadeh as an extension of type-1 sets. There is a growing interest in type-2 set and its memberships (named secondary memberships) to handle the uncertainty primary membership values. However, arithmetical operators on have computational complexity due third dimension these In this study, we present some mathematical which can be easily applied numbers. Also, functions numbers are according their monotonicity. These adapted reliability distribution...

In this study, a renewal-reward process with discrete interference of chance is constructed and considered. Under weak conditions, the ergodicity X(t) proved exact formulas for ergodic distribution its moments are found. Within some assumptions in general form, two-term asymptotic expansions all obtained. Additionally, kurtosis coefficient, skewness coefficient variation computed. As special case, semi-Markovian inventory model type (s, S) investigated.

In this paper, a stochastic process with discrete interference of chance and generalized reflecting barrier $\left(X\left(t\right)\right)$ is constructed the ergodicity proved. Using basic identity for random walk processes, characteristic function ergodic distribution written help characteristics boundary functional $S_{N_{1} (x)} $. Moreover, weak convergence theorem standardized $Y_{\lambda} (t)\equiv X(t)/\lambda$ proved, as $\lambda \to \infty $ limit form found.

Abstract In this article, a semi-Markovian random walk with delay and discrete interference of chance (X(t)) is considered. It assumed that the variables ζ n , = 1, 2,…, which describe form an ergodic Markov chain distribution gamma parameters (α, λ). Under assumption, asymptotic expansions for first four moments process X(t) are derived, as λ → 0. Moreover, by using Riemann zeta-function, coefficients these expressed means numerical characteristics summands, when considered Gaussian small...

Probabilistic processing times, times between breakdowns and repair make the amount of stock in buffers stations production lines behave as a stochastic process. Too much or too little buffer reduces system economy efficiency, respectively. We obtain optimum capacities initial levels for employing mathematical random walk approach based on maximum minimum values process time window. Two approximations are developed, each useful under different risk-acceptance assumptions. Simulation results...