global stability of an hiv 1 infection model with saturation infection and intracellular delay in this paper an hiv 1 infection model with a saturation infection rate and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated by analyzing the characteristic equations the local stability of an infection free equilibrium and a chronic infection equilibrium of the model is established by using suitable lyapunov functionals and the lasalle invariant principle it is proved that if the basic reproduction ratio is less than unity the infection free equilibrium is globally asymptotically stable if the basic reproduction ratio is greater than unity the chronic infection equilibrium is globally asymptotically stable

a stochastic differential equation sis epidemic model with two independent brownian motions abstract in this paper we introduce two perturbations in the classical deterministic susceptible infected susceptible epidemic model greenhalgh and gray 4 in 2011 use a perturbation on in sis model based on their previous work we consider another perturbation on the parameter and formulate the original model as a stochastic differential equation sde with two independent brownian motions for the number of infected population we then prove that our model has a unique and bounded global solution i t also we establish conditions for extinction and persistence of the infected population i t under the conditions of persistence we show that there is a unique stationary distribution and derive its mean and variance computer simulations illustrate our results and provide evidence to back up our theory

theory and multipliers of stable algebras the main theorem is that if a is a c algebra with a countable approximate identity consisting of projections then the unitary group of m a k is contractible this gives a realization via the index map of ko a as components in the set of fredholm operators on ha for a c algebra a let ha ai i ai e a and eai ai converges in norm then ha becomes a right a module under the action ai b aib with the a valued inner product ai b1 ea bi ha is a hilbert a module y ha is the c algebra of operators on ha that have an adjoint k ha is an ideal of y ha called the compact operators on ha set 11 2 definition 4 operators in ha invertible modulo 3f ha are called fredholm and have an index that takes its values in ko a the paper is divided into two parts in part 1 we show that index a ko a is an isomorphism where t denotes the set of path components of the set of fredholm operators in part 2 we show that the unitary group of m a k is contractible when a has a countable approximate identity consisting of projections as 2 ha m a k this in particular implies that the unitary group of s ha is connected when a is unital this latter result is used to prove the isomorphism mentioned above the results of this paper were announced in 14 see remark 2 5 2 this research is based on the author s doctoral work done at dalhousie university under the supervision of professor p a fillmore the author also wishes to thank w j phillips for many useful suggestions part 1 the index of a fredholm operator 1 1 we describe the index map from fredholm operators on hilbert c modules to the corresponding k groups the principal ingredients of this construction have been discussed by several authors kasparov 12 miscenko and fomenko 15 and pimsner popa and voiculescu 17 however as we shall need refinements and variations of these constructions we will give a detailed account of the index map throughout this paper k or y h will denote the c algebra of compact operators on a separable infinite dimensional hilbert space h for any two c algebras a and b a b will denote the completion of the algebraic tensor product aob in the spatial or minimal c norm see e g effros and lance 8 2 received by the editors july 28 1983 and in revised form december 27 1985 1980 mathematics subject classification 1985 revision primary 46l05 46m20 01987 american mathematical society 0002 9947 87 1 00 25 per page

stability and hopf bifurcation in a delayed competition system abstract in this paper hopf bifurcation for two species lotka volterra competition systems with delay dependence is investigated by choosing the delay as a bifurcation parameter we prove that the system is stable over a range of the delay and beyond that it is unstable in the limit cycle form i e there are periodic solutions bifurcating out from the positive equilibrium our results show that a stable competition system can be destabilized by the introduction of a maturation delay parameter further an explicit algorithm for determining the direction of the hopf bifurcation and the stability of the bifurcating periodic solutions is derived by using the theory of normal forms and center manifolds and numerical simulations supporting the theoretical analysis are also given

asymptotic speeds of spread and traveling waves for integral equations and delayed reaction diffusion models abstract the theory of asymptotic speeds of spread and monotone traveling waves is generalized to a large class of scalar nonlinear integral equations and is applied to some time delayed reaction and diffusion population models

dynamics in a stochastic heroin model with seasonal variation abstract in this paper a stochastic non autonomous heroin model is formulated we obtain sufficient conditions for extinction and permanence in mean with probability one of the positive solutions in addition we prove that there exists at least one positive periodic solution under some conditions finally numerical simulations are performed to illustrate our theoretical results

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

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

extinction and persistence of a stochastic nonlinear sis epidemic model with jumps abstract in this paper brownian motion and l e vy jumps are introduced to a sis type epidemic model with nonlinear incidence rate the dynamical behavior of the considered model is investigated in order to reveal the extinction and permanence of the disease two threshold values r 0 r 0 are showed we find that if r 0 1 the disease may die out and when r 0 1 the disease may be persistent finally the numerical simulations are presented to illustrate our mathematical results

factorizations of invertible operators and k theory of c algebras let a be a unital c algebra we describe k skeleton factorizations of all invertible operators on a hilbert c module a in particular on h 12 with the fredholm index as an invariant we then outline the isomorphisms k 0 a 2k p 0 2k gl r p a and k 1 a 2k 1 p 0 2k 1 gl r p a for k 0 where p 0 denotes the class of all compact perturbations of a projection p in the infinite grassmann space gr 022 a and gl r p a stands for the group of all those invertible operators on h a essentially commuting with p

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

periodic solutions in an epidemic model with diffusion and delay a spatial diffusion si model with delay and neumann boundary conditions are investigated we derive the conditions of the existence of hopf bifurcation in one dimension space moreover we analyze the properties of bifurcating period solutions by using the normal form theory and the center manifold theorem of partial functional differential pfds equations by numerical simulations we found that spatiotemporal periodic solutions can occur in the epidemic model with spatial diffusion which verifies our theoretical results the obtained results show that interaction of delay and diffusion may induce outbreak of infectious diseases

dynamical behavior of an epidemic model with a nonlinear incidence rate abstract in this paper we study the global dynamics of an epidemic model with vital dynamics and nonlinear incidence rate of saturated mass action by carrying out global qualitative and bifurcation analyses it is shown that either the number of infective individuals tends to zero as time evolves or there is a region such that the disease will be persistent if the initial position lies in the region and the disease will disappear if the initial position lies outside this region when such a region exists it is shown that the model undergoes a bogdanov takens bifurcation i e it exhibits a saddle node bifurcation hopf bifurcations and a homoclinic bifurcation existence of none one or two limit cycles is also discussed

stationary distribution of a stochastic sis epidemic model with vaccination abstract in this paper we consider a stochastic sis epidemic model with vaccination we prove that the densities of the distributions of the solution can converge in l 1 to an invariant density under appropriate conditions also we find the support of the invariant density

ergodic stationary distribution and extinction of a stochastic sirs epidemic model with logistic growth and nonlinear incidence abstract a stochastic sirs model with logistic growth and nonlinear incidence rate is probed in this paper we exemplify that the proposed stochastic sirs model reveals a global and positive solution by applying suitable lyapunov functions the sufficient conditions for the existence of ergodic stationary distribution of the solution to the stochastic sirs model are derived furthermore we acquire the sufficient conditions for extinction of the infectious disease

deformation of a projection in the multiplier algebra and projection lifting from the corona algebra of a non simple c algebra let x be a unit interval or a unit circle and let b be a p unital purely infinite simple c algebra such that its multiplier algebra m b has real rank zero then we determine necessary and sufficient conditions for a projection in the corona algebra of c x b to be liftable to a projection in the multiplier algebra this generalizes a result proved by l brown and the author brown and lee 2012 3 the main technical tools are divided into two parts the first part is borrowed from the author s result lee 2011 14 theorem 3 3 the second part is a proposition showing that we can produce a sub projection with an arbitrary rank which is prescribed as k theoretical data of a projection or a co projection in the multiplier algebra of c x b under a suitable infinite rank and co rank condition

asymptotic behavior and stability of a stochastic model for aids transmission a stochastic model for aids transmission is presented in this paper the existence and uniqueness of its solution is proved and the solution belongs to an interval satisfying the actual condition furthermore the disease equilibrium can be demonstrated to be existent and both its almost surely exponential stability and its pth moment exponential stability can be concluded based on parameter analysis the first quadrant can be integrated into several parts according to the comparison between almost surely exponential stability and pth moment exponential stability and the potential meaning of the stability is further demonstrated finally based on the above theoretical analysis some conditions for aids to decrease and then to die out are obtained by computer simulation

a method for the numerical solution of the one dimensional inverse stefan problem in this paper we suggest the use of complete families of solutions of the heat equation for the numerical solution of the inverse stefan problem our approach leads to linear optimization problems which can be established and solved easily convergence results are proved in a final section the method is applied to some examples

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

the extinction and persistence of the stochastic sis epidemic model with vaccination abstract in this paper we discuss the dynamics of a stochastic sis epidemic model with vaccination when the noise is large the infective decays exponentially to zero regardless of the magnitude of r 0 when the noise is small sufficient conditions for extinction exponentially and persistence in the mean are established the results are illustrated by computer simulations

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

the long time behavior of di sir epidemic model with stochastic perturbation in this paper we present a di sir epidemic model with two categories stochastic perturbations the long time behavior of the two stochastic systems is studied mainly we show how the solution goes around the infection free equilibrium and the endemic equilibrium of deterministic system under different conditions

brief paper dynamics of a multigroup sir epidemic model with stochastic perturbation in this paper we introduce stochasticity into a multigroup sir susceptible infective and recovered model the stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modeling in the deterministic models the basic reproduction number r 0 is a threshold which completely determines the persistence or extinction of the disease we carry out a detailed analysis on the asymptotic behavior of the stochastic model also regarding of the value of r 0 if r email protected 1 the solution of the model is oscillating around a steady state which is the disease free equilibrium of the corresponding deterministic model whereas if r 0 1 there is a stationary distribution which means that the disease will prevail

an approximation technique for the numerical solution of a stefan problem a nonlinear approximation technique for the numerical solution of certain free boundary problems is proposed the method is shown for a degenerate one dimensional stefan problem for this problem an error estimate which is independent of the used algorithm is derived numerical examples are discussed

persistence and distribution of a stochastic susceptible infected removed epidemic model with varying population size abstract in this paper the dynamics of a stochastic susceptible infected removed model in a population with varying size is investigated we firstly show that the stochastic epidemic model has a unique global positive solution with any positive initial value then we verify that random perturbations lead to extinction when some conditions are being valid moreover we prove that the solution of the stochastic epidemic model is persistent in the mean by building up a suitable lyapunov function and using generalized ito s formula further the stochastic epidemic model admits a stationary distribution around the endemic equilibrium when parameters satisfy some sufficient conditions to end this contribution and to check the validity of the main results numerical simulations are separately carried out to illustrate these results

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

an implementation of a discretization method for semi infinite programming for linear semi infinite programming problems a discretization method is presented a first coarse grid is successively refined in such a way that the solution on the foregoing grids can be used on the one hand as starting points for the subsequent grids and on the other hand to considerably reduce the number of constraints which have to be considered in the subsequent problems this enables an efficient treatment of large problems with moderate storage requirements a numerically stable simplex algorithm is used to solve the lp subproblems numerical examples from bivariate chebyshev approximation are presented

homotopy classification of homogeneous projections in the corona algebra of c x b for a graph x abstract in this paper we consider certain projections in the corona algebra of c x b for x a directed graph and b a stable c algebra of which the multiplier algebra has real rank zero assuming a kind of homogeneity on the projections we characterize when two such projections are homotopy equivalent as a result for a simple graph we show that such projections are always homotopic

pattern formation of an epidemic model with time delay abstract one of the central issues in epidemiology is the study of the distribution of disease and time delay widely exists in the process of disease spread thus in this paper we presented an epidemic model with spatial diffusion and time delay by mathematical analysis we find two different types of instability one is the diffusion induced instability and the other one is delay induced instability moreover we derive the corresponding patterns by performing a series of numerical simulations the obtained results show that the interaction of diffusion and time delay may give rise to rich dynamics in epidemic systems

dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth abstract in this paper we investigate the dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model then we obtain sufficient conditions for extinction of the disease in two cases that is the first case is that the susceptible population survival and infected and exposed populations extinction the second case is that all the populations extinction

a stochastic model for the evolution of bone metastasis persistence and recovery abstract bone metastasis is a complex disease that modifies the natural dynamics of the bone remodeling process which is vital for maintaining a healthy bone structure nowadays there are deterministic differential models that describe the bone metastasis evolution by considering interaction mechanisms between cancer cells and basic bone cells such as osteoclasts and osteoblasts based on these deterministic models a stochastic differential model is proposed to describe the bone metastasis evolution in order to analyze the effect of environmental fluctuations inclusions conditions for the existence and uniqueness of a nonnegative solution of the proposed stochastic model are given to characterize whether the invasion of cancer persists or is eradicated finally we illustrate different dynamical behaviors of the stochastic solution by means of numerical simulations

dynamics of a stochastic sis model with double epidemic diseases driven by levy jumps abstract this paper is to investigate the dynamics of a stochastic sis epidemic model with saturated incidence rate and double epidemic diseases which make the research more complex the environment variability in this study is characterized by white noise and jump noise sufficient conditions for the extinction and persistence in the mean of two epidemic diseases are obtained it is shown that the two diseases can coexist under appropriate conditions finally numerical simulations are introduced to illustrate the results developed

global behavior of a multi group sis epidemic model with age structure abstract we study global dynamics of a system of partial differential equations the system is motivated by modelling the transmission dynamics of infectious diseases in a population with multiple groups and age dependent transition rates existence and uniqueness of a positive endemic equilibrium are established under the quasi irreducibility assumption which is weaker than irreducibility on the function representing the force of infection we give a classification of initial values from which corresponding solutions converge to either the disease free or the endemic equilibrium the stability of each equilibrium is linked to the dominant eigenvalue s a where a is the infinitesimal generator of a quasi irreducible semigroup generated by the model equations in particular we show that if s a 0 then the disease free equilibrium is globally stable if s a 0 then the unique endemic equilibrium is globally stable