A stochastic model for internal HIV dynamics

In this paper we analyse a stochastic model representing HIV internal virus dynamics. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. We show that the model established in this paper possesses non-negative solutions as this is essential in any population dynamics model. We also carry out analysis on the asymptotic behaviour of the model. We approximate one of the variables by a mean reverting process and find out the mean and variance of this process. Numerical simulations conclude the paper.     

HIV/AIDS Model with Delay and the Effects of Stochasticity

We present a deterministic HIV/AIDS model with delay. We then extend the model by adjoining terms capturing stochastic effects. The intensity of the fluctuations in the stochastic system is analytically evaluated using Fourier transform methods. We carry out simulations to assess differences in the dynamical behavior of the deterministic and stochastic models. Simulation results show that they are no significant differences in the behavior of the two models.     

A stochastic model for the HIV epidemic in homosexual populations involving age and race

In this paper, we derive a stochastic model for the HIV epidemic in homosexual populations involving age and race. To account for effects of different mixing patterns, a low risk selection rule is introduced. The model is then formulated in terms of chain multinomial distributions by means of which the means are derived. Some simulation studies by computer indicate clearly that age and race have a significant impact on the HIV epidemic.     

Stochastic dynamics of an HIV/AIDS epidemic model with treatment

Abstract

We investigate a stochastic HIV/AIDS epidemic model with treatment. The model allows for two stages of infection namely the asymptomatic phase and the symptomatic phase. We prove existence of global positive solutions. We show that the solutions are stochastically ultimately bounded and stochastically permanent. We also study asymptotic behaviour of the solution to the stochastic model around the disease-free equilibrium of the underlying deterministic model. Our theoretical results are illustrated by way of numerical simulations.     

Stochastic models of HIV epidemic in homosexual populations—the effects of mixing patterns

Extending my previous work [1–3], in this paper I proceed to develop a stochastic model for HIV epidemic in a homosexual population under general conditions. Through computer generated data, I assess various deterministic models as compared with the expected numbers of the stochastic models. It is shown that different mixing patterns have significant impacts on the HIV epidemic except possibly restricted mixing. Thus, in populations with preferred mixing (mixing proportion less than 1) and with proportional mixing, the numbers of S people, L people, I people and A people differ significantly from the corresponding expected numbers of the stochastic models. For the L people, I people and A people, the numbers of the deterministic models first appear to be smaller and later appear to be larger than the corresponding mean numbers of the stochastic models, indicating that while in the short run the deterministic models would underestimate the true numbers, in the long run the deterministic models would overestimate the true numbers.     

Optimal control of stochastic differential equations with dynamical boundary conditions

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problems with nonstandard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with nonstandard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.     

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system

The influence of interplay of external and internal noise on the detection of weak stimulus in a cell system was studied by using a mesoscopic stochastic model. When the stimulus was too weak to fire calcium spikes for the cell, separately, we found that calcium spikes could be induced by the external noise or internal noise, and internal signal stochastic resonance (ISSR) or internal noise stochastic resonance (INSR) occurred, respectively, so that the cell system could detect the weak stimulus through intracellular calcium spikes with the help of external noise or internal noise. When considering both of the noises, we found that internal noise could suppress ISSR, while external noise could enhance INSR in a certain range of external noise intensity. Interestingly, when the INSR occurs, the optimal size matched well with the real cell size, this was of significant biological meaning.     

A stochastic recirculation system with random access

A model for a stochastic recirculation system with randomly accessed multiple heterogeneous servers, no waiting rooms, and exponentially-distributed service times is provided. In this system the units are assigned to one of the servers upon arrival by random mechanism. Units which find all servers busy recirculate and combine with the incoming arrivals and join those already in the system to initiate the next cycle. The equilibrium behavior of the internal and external stochastic processes of the system is analyzed using a two parameter approximation. A simulation model is also developed and its behavior is compared against the analytical model at the steady state. The model with randomly-accessed servers is compared to a single server model already established in the literature. The performance of the model is then examined for a wide range of parameter values to obtain conclusions about its optimal performances.     

Internal modelling of objective functions for global optimization

Global optimization requires an adequate internal representation of the objective function for success in a reasonable number of function evaluations. A method for determining the location of a new function evaluation, based on a representation using a stationary stochastic process model, is investigated and some results are given.     

Dynamics of the Stochastic Chemostat Model with Monod-Haldane Response Function

This paper is devoted to the asymptotic dynamics of stochastic chemostat model with Monod-Haldane response function. We first prove the existence of random attractors by means of the conjugacy method and further construct a general condition for internal structure of the random attractor, implying extinction of the species even with small noise. Moreover, we show that the attractors of Wong-Zakai approximations converges to the attractor of the stochastic chemostat model in an appropriate sense.     

Stochastic flocking dynamics of the inertial spin model with state-dependent noises

We study stochastic flocking dynamics of the inertial spin (IS) model with state-dependent noises. The IS model was considered to describe the collective behaviors of starling flocks moving with constant speed. Unlike mechanical flocking models extensively studied in the literature, this model incorporates an internal dynamic observable, namely spin (internal angular momentum) in addition to mechanical observables (position and velocity), and it describes how spin interacts with mechanical observables. In previous works, emergent dynamics of the deterministic counterparts for the IS model and its mean-field limit have been investigated under some specific setting in which network topology is multiplicatively separable. In this work, we present sufficient frameworks for stochastic flocking dynamics of the IS model, which state-dependent noises vanish at the equilibria of the deterministic IS model. The proposed frameworks are in terms of coupling strength, friction, and inertial coefficients, and our asymptotic convergence results for sample paths are given in both an almost sure and an expectation sense. We have also conducted several numerical experiments to verify our analytical results and to explore what can be studied further in future work     

Mother-to-child transmission of HIV: a simulation-based approach for the evaluation of intervention strategies

Mother-to-child transmission (MTCT) of HIV is the most significant source of HIV infection in children below the age of 15 years. In 2000 alone, about 600 000 new infections occurred, the vast majority from mothers living in developing countries who were not aware of their HIV-positive status. To date, at least 4.3 million children have died from AIDS. In this paper, we discuss the development of an operational model that can be used to evaluate intervention options for the prevention of MTCT of HIV. The problem was approached by defining suitable pregnancy risk groups, prevention options and the required model outputs to evaluate different intervention strategies. The method chosen to approach the problem was a discrete-event, three-phase simulation, built in Visual Basic, with a stochastic semi-Markov structure. The developed model takes individual pregnant women through each stage of their pregnancy, labour and birth. Different intervention strategies may be modelled at any time, including short-course antiretroviral drugs and cessation of breastfeeding. The model is demonstrated with data from Botswana, which has one of the highest HIV-infection rates in the world.     

From deterministic to stochastic surrender risk models: Impact of correlation crises on economic capital

In this paper we raise the matter of considering a stochastic model of the surrender rate instead of the classical S-shaped deterministic curve (in function of the spread), still used in almost all insurance companies. For extreme scenarios, due to the lack of data, it could be tempting to assume that surrenders are conditionally independent with respect to a S-curve disturbance. However, we explain why this conditional independence between policyholders decisions, which has the advantage to be the simplest assumption, looks particularly maladaptive when the spread increases. Indeed the correlation between policyholders decisions is most likely to increase in this situation. We suggest and develop a simple model which integrates those phenomena. With stochastic orders it is possible to compare it to the conditional independence approach qualitatively. In a partially internal Solvency II model, we quantify the impact of the correlation phenomenon on a real life portfolio for a global risk management strategy.     

Efficient stochastic model for the point kinetics equations

A new stochastic model for the point kinetics equations with I-delayed neutron precursor groups is presented. In this stochastic model, the point kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and external neutrons source. The matrix form of the efficient stochastic model is solved by a semi-analytical method. The semi-analytical method is based on the exponential function of the coefficient matrix. The eigenvalues of the coefficient matrix and Gaussian elimination are used to calculate this exponential function. The mean and standard deviation of neutron and precursor populations of the efficient stochastic model with step, ramp, and sinusoidal reactivities are computed. The results of the efficient stochastic model are compared with the results of Allen's stochastic model for the point kinetics equations. This comparison confirms that the efficient stochastic model is an accurate model compared with the deterministic point kinetics equations. This stochastic model is efficient to study the natural behavior of neutron and precursor populations in the nuclear reactor dynamics.     

Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise

A stochastic differential equation modelling a Marchuk’s model is investigated. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Firstly, the stochastic Marchuk’s model has been simplified by applying stochastic center manifold and stochastic average theory. Secondly, by using Lyapunov exponent and singular boundary theory, we analyze the local stochastic stability and global stochastic stability for stochastic Marchuk’s model, respectively. Thirdly, we explore the stochastic bifurcation of the stochastic Marchuk’s model according to invariant measure and stationary probability density. Some new criteria ensuring stochastic pitchfork bifurcation and P-bifurcation for stochastic Marchuk’s model are obtained, respectively.     

Effect of environmental fluctuation on a detritus based ecosystem

Present paper deals with the stochastic perturbation analysis on a detritus based three dimensional food-chain in presence of gestation delays and recycling delay. We have perturbed some demographic parameters by white noise and coloured noise and then extensive numerical simulations are performed to understand the effect of fluctuating environment on the dynamics of the model system for different values of forcing intensities. We have explained how stochastic perturbation terms can be introduced in the model system. Mathematical analysis reveals the fact that the internal dynamics have no ability to suppress the environmental stochasticity and rhythmic oscillation does not persist in presence of environmental driving forces rather oscillate in a irregular fashion.     

TheM/G/1 retrial queue with the server subject to starting failures

In this paper, we study a retrial queueing model with the server subject to starting failures. We first present the necessary and sufficient condition for the system to be stable and derive analytical results for the queue length distribution as well as some performance measures of the system in steady state. We show that the general stochastic decomposition law forM/G/1 vacation models also holds for the present system. Finally, we demonstrate that a few well known queueing models are special cases of the present model and discuss various interpretations of the stochastic decomposition law when applied to each of these special cases.Partially supported by the Natural Sciences and Engineering Research Council of Canada, grant OGP0046415.Partially supported by internal research grant of Mount Saint Vincent University.     

Equilibrium models for inter‐dependent Markov systems

A Markovian model of graded systems, like the educational system, ensures internal consistency between forecasts. Sometimes merely ensuring this consistency is not enough, for the stochastic system may be operating below desired planning levels. This is highlighted. The educational system is considered and necessary conditions for equilibrium between demand and supply of teachers at first level is given. Disequilibrium conditions are shown to exist when the resulting models are applied to an autonomous education zone.     

Inventory rationing via drop-shipping in Internet retailing: A sensitivity analysis

In this paper, we study a threshold level inventory rationing policy that is of interest to e-tailers, operating in a business to consumer (B2C) environment and selling non-perishable, made-to-stock items such as books, CDs, consumer electronics, and body and bath products. A Monte Carlo simulation model is developed to examine this policy when the demand process is stochastic, lead-time is stochastic, and the e-tailer uses ‘drop-shipping’ as an order fulfillment option. The methodology presented, which includes computer simulation and a full factorial experimental design, permits understanding of the complexity of the decision-making environment and implications of different sources of uncertainty (e.g. demand variability and lead-time variability) on a profit-maximizing threshold level of inventory, a stock level below which low margin orders are drop-shipped directly from the e-tailer’s supplier rather than fulfilled from internal stock.