stability of a novel stochastic epidemic model with double epidemic hypothesis abstract in this paper a novel sir disease transmission model is formulated under double epidemic hypothesis and stochastic perturbation we present the stability conditions of the disease free equilibrium of the sir model without stochastic perturbation and with stochastic perturbation we obtain the deterministic stability threshold 1 and 2 of the disease free equilibrium under which the disease free equilibrium is stochastically stable such that the disease will disappear finally leaving all the population susceptible the results show that double epidemic hypothesis and stochastic perturbation have significant effects on the dynamics behaviors of the model

exclusion and persistence in deterministic and stochastic chemostat models abstract we first introduce and analyze a variant of the deterministic single substrate chemostat model in this model microbe removal and growth rates depend on biomass concentration with removal terms increasing faster than growth terms using a comparison principle we show that persistence of all species is possible in this scenario then we turn to modelling the influence of random fluctuations by setting up and analyzing a stochastic differential equation in particular we show that random effects may lead to extinction in scenarios where the deterministic model predicts persistence on the other hand we also establish some stochastic persistence results

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

a warm start approach for large scale stochastic linear programs we describe a way of generating a warm start point for interior point methods in the context of stochastic programming our approach exploits the structural information of the stochastic problem so that it can be seen as a structure exploiting initial point generator we solve a small scale version of the problem corresponding to a reduced event tree and use the solution to generate an advanced starting point for the complete problem the way we produce a reduced tree tries to capture the important information in the scenario space while keeping the dimension of the corresponding reduced deterministic equivalent small we derive conditions which should be satisfied by the reduced tree to guarantee a successful warm start of the complete problem the implementation within the hopdm and oops interior point solvers shows remarkable advantages

a riccati based primal interior point solver for multistage stochastic programming we propose a new method for certain multistage stochastic programs with linear or nonlinear objective function combining a primal interior point approach with a linear quadratic control problem ov

on consistency of stochastic dominance and mean semideviation models we analyze relations between two methods frequently used for modeling the choice among uncertain outcomes stochastic dominance and mean risk approaches new necessary conditions for stochastic dominance are developed these conditions compare values of a certain functional which contains two components the expected value of a random outcome and a risk term represented by the central semideviation of the corresponding degree if the weight of the semideviation in the composite objective does not exceed the weight of the expected value maximization of such a functional yields solutions which are efficient in terms of stochastic dominance the results are illustrated graphically

a stochastic model of aids and condom use in this paper we introduce stochasticity into a model of aids and condom use via the technique of parameter perturbation which is standard in stochastic population modelling we show that the model established in this paper possesses non negative solutions as desired in any population dynamics we also carry out a detailed analysis on asymptotic stability both in probability one and in pth moment our results reveal that a certain type of stochastic perturbation may help to stabilise the underlying system

stationary distribution and threshold dynamics of a stochastic sirs model with a general incidence abstract in this paper we consider a stochastic epidemic model with relapse cure and a non linear incidence rate function firstly we show the existence and uniqueness of a global positive solution then in terms of a stochastic threshold r s 0 we prove the extinction of the disease when r s 0 1 we also establish the persistence in mean of the epidemic in the case of r s 0 1 furthermore we prove the existence of a stationary distribution and its asymptotic stability finally we present numerical simulations for the stochastic model to support the theoretical results

newton like method for nonlinear banded block diagonal system we present an efficient newton like method for solving systems of nonlinear equations with banded block diagonal structure such systems arise in economic models the main idea of this method is to exploit the special structure of the jacobian in a newton like method the proposed algorithm uses an iterative method for calculation of the approximation of diagonal blocks in the jacobian depending on dimensions of blocks significant reduction in computational cost is obtained and the algorithm can be easily parallelized local convergence of the proposed method is proved and some numerical results are presented

stability of a stochastic sir system abstract we propose a stochastic sir model with or without distributed time delay and we study the stability of disease free equilibrium the numerical simulation of the stochastic sir model shows that the introduction of noise modifies the threshold of system for an epidemic to occur and the threshold stochastic value is found

analysis of a discontinuous galerkin method for the biot s consolidation problem in this paper a fully discrete stabilized discontinuous galerkin method is proposed to solve the biot s consolidation problem the existence and uniqueness of the finite element solution are obtained the stability of the fully discrete solution is discussed the corresponding error estimates for the approximation of displacement and pressure in a mesh dependent norm are obtained the error estimate for the approximation of pressure in l 2 norm is also obtained

nested decomposition of multistage nonlinear programs with recourse nested decomposition is extended to the case of arborescent nonlinear programs duals of extensive forms of nonlinear multistage stochastic programs constitute a particular class of those problems the method is tested on a set of problems of that type

a sirs epidemic model with infection age dependence based on j mena lorca and h w hethcote s epidemic model a sirs epidemic model with infection age dependent infectivity and general nonlinear contact rate is formulated under general conditions the unique existence of its global positive solutions is obtained moreover under more general assumptions than the existing the existence and asymptotical stability of its equilibria are discussed in the end the condition on the stability of endemic equilibrium is verified by a special model

global stability and stochastic permanence of a non autonomous logistic equation with random perturbation abstract this paper discusses a randomized non autonomous logistic equation d n t n t a t b t n t d t t d b t where b t is a 1 dimensional standard brownian motion in d q jiang n z shi a note on non autonomous logistic equation with random perturbation j math anal appl 303 2005 164 172 the authors show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0 we show that this equation is stochastically permanent and the solution n p t is globally attractive provided a t b t and t are continuous t periodic functions a t 0 b t 0 and min t 0 t a t max t 0 t 2 t by the way the similar results of a generalized non autonomous logistic equation with random perturbation are yielded

decomposition methods in stochastic programming stochastic programming problems have very large dimension and characteristic structures which are tractable by decomposition we review basic ideas of cutting plane methods augmented lagrangian and splitting methods and stochastic decomposition methods for convex polyhedral multi stage stochastic programming problems

belief rule based system for portfolio optimisation with nonlinear cash flows and constraints a belief rule based brb system is a generic nonlinear modelling and inference scheme it is based on the concept of belief structures and evidential reasoning er and has been shown to be capable of capturing complicated nonlinear causal relationships between antecedent attributes and consequents the aim of this paper is to develop a brb system that complements the riskmetrics wealthbench system for portfolio optimisation with nonlinear cash flows and constraints two optimisation methods are presented to locate efficient portfolios under different constraints specified by the investors numerical studies demonstrate the effectiveness and efficiency of the proposed methodology

a note on nonautonomous logistic equation with random perturbation abstract this paper discusses a randomized nonautonomous logistic equation d n t n t a t b t n t d t t d b t where b t is 1 dimensional standard brownian motion we show that e 1 n t has a unique positive t periodic solution e 1 n p t provided a t b t and t are continuous t periodic functions a t 0 b t 0 and 0 t a s 2 s d s 0

asymptotic behaviour of the stochastic lotka volterra model this paper examines the asymptotic behaviour of the stochastic extension of a fundamentally important population process namely the lotka volterra model the stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart indeed the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations

solving non linear portfolio optimization problems with the primal dual interior point method stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning the deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets time stages and scenarios per time stage so far models treated by mathematical programming approaches have been limited to simple linear or quadratic models due to the inability of currently available solvers to solve nlp problems of typical sizes however stochastic programming problems are highly structured the key to the efficient solution of such problems is therefore the ability to exploit their structure interior point methods are well suited to the solution of very large non linear optimization problems in this paper we exploit this feature and show how portfolio optimization problems with sizes measured in millions of constraints and decision variables featuring constraints on semi variance skewness or non linear utility functions in the objective can be solved with the state of the art solver

the threshold of a stochastic sis epidemic model with vaccination this paper is concerned with the long time behavior of a stochastic sis epidemic model with vaccination sufficient conditions for extinction and persistence in mean are obtained we find a threshold of the stochastic model which determines the outcome of the disease in case the white noises are small at last some numerical simulations are carried out to support our results

global stability of an sir epidemic model with constant infectious period in this paper we derive and study an sir epidemic model with constant infectious period which is incorporated as a time delay both trivial and endemic equilibrium are found and their stability is investigated using lyapunov functional approach sufficient conditions for global stability of endemic equilibrium is obtained

stochastic delay lotka volterra model we reveal in this paper that the environmental noise will not only suppress a potential population explosion in the stochastic delay lotka volterra model but will also make the solutions to be stochastically ultimately bounded to reveal these interesting facts we stochastically perturb the delay lotka volterra model x t diag x1 t xn t b ax t into the ito form dx t diag x1 t xn t b ax t dt x t dw t and show that although the solution to the original delay equation may explode to infinity in a finite time with probability one that of the associated stochastic delay equation does not we also show that the solution of the stochastic equation will be stochastically ultimately bounded without any additional condition on the matrix a

dual stochastic dominance and related mean risk models we consider the problem of constructing mean risk models which are consistent with the second degree stochastic dominance relation by exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions this allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation we also provide stochastic linear programming formulations of these models

robust ranking and portfolio optimization the portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out of sample performance due to estimation errors in the expected returns a practical method for portfolio construction is to use assets ordering information expressed in the form of preferences over the stocks instead of the exact expected returns due to the fact that the ranking itself is often described with uncertainty we introduce a generic robust ranking model and apply it to portfolio optimization in this problem there are n objects whose ranking is in a discrete uncertainty set we want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking this robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general to solve this robust ranking problem we apply the constraint generation method where constraints are efficiently generated by solving a network flow problem for empirical tests we use post earnings announcement drifts to obtain ranking uncertainty sets for the stocks in the djia index we demonstrate that our robust portfolios produce smaller risk compared to their non robust counterparts

the dynamics of a new sir epidemic model concerning pulse vaccination strategy abstract a new sir epidemic model with vertical and horizontal transmission is proposed and the dynamics of this disease model under constant and pulse vaccination are analyzed firstly global stability of the endemic equilibrium states of the model with constant vaccination is thereby established further we show that there exists a stable infection free periodic solution when the period of impulsive effect is less than some critical value the condition for the permanence of the system with pulse vaccination is also given which implies the periodic bursts of epidemic occurs numerical simulation shows system with pulse vaccination has more complex dynamic behavior for positive periodic oscillation infection free quasi periodic oscillation than system with constant vaccination finally we compare validity of the strategy of pulse vaccination with no vaccination and constant vaccination and conclude that pulse vaccination strategy is more effective than no vaccination and continuous vaccination

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

an epidemic model of a vector borne disease with direct transmission and time delay abstract this paper considers an epidemic model of a vector borne disease which has direct mode of transmission in addition to the vector mediated transmission the incidence term is assumed to be of the bilinear mass action form we include both a baseline ode version of the model and a differential delay model with a discrete time delay the ode model shows that the dynamics is completely determined by the basic reproduction number r 0 if r 0 1 the disease free equilibrium is globally stable and the disease dies out if r 0 1 a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region the delay in the differential delay model accounts for the incubation time the vectors need to become infectious we study the effect of that delay on the stability of the equilibria we show that the introduction of a time delay in the host to vector transmission term can destabilize the system and periodic solutions can arise through hopf bifurcation

reoptimization with the primal dual interior point method reoptimization techniques for an interior point method applied to solving a sequence of linear programming problems are discussed conditions are given for problem perturbations that can be absorbed in merely one newton step the analysis is performed for both short step and long step feasible path following methods a practical procedure is then derived for an infeasible path following method it is applied in the context of crash start for several large scale structured linear programs numerical results with oops a new object oriented parallel solver demonstrate the efficiency of the approach for large structured linear programs crash start leads to about 40 reduction in the number of iterations and translates into a 25 reduction of the solution time the crash procedure parallelizes well and speed ups between 3 1 3 8 on four processors are achieved

the ergodicity and extinction of stochastically perturbed sir and seir epidemic models with saturated incidence abstract in this paper we include stochastic perturbations into sir and seir epidemic models with saturated incidence and investigate their dynamics according to the basic reproduction number r 0 the long time behavior of the two stochastic systems is studied mainly we utilize stochastic lyapunov functions to show under some conditions the solution has the ergodic property as r 0 1 while exponential stability as r 0 1 at last we make simulations to conform our analytical results

threshold behavior of a stochastic sis model with levy jumps in this paper the dynamics of a stochastic sis model with levy jumps are investigated we first prove that this model has a unique global positive solution starting from the positive initial value then taking the accumulated jump size into account we find a threshold of the model denoted by r 0 which completely determines the extinction and prevalence of the disease if r 0 1 the disease dies out exponentially with probability one if r 0 1 the solution of the model tends to a point in time average which leads to the stochastical persistence of the disease from the view of epidemiology the existence of threshold is useful in determining treatment strategies and forecasting epidemic dynamics moreover we find that levy noise can suppress disease outbreak finally we introduce some numerical simulations to support the main results obtained