dynamics of the deterministic and stochastic siqs epidemic model with non linear incidence the deterministic and stochastic siqs models with non linear incidence are introduced for deterministic model the basic reproductive rate r 0 is derived moreover if r 0 1 there exists a unique endemic equilibrium which is globally asymptotically stable for stochastic model sufficient condition for extinction of the disease that is regardless of the value of r 0 is presented in addition if the intensities of the white noises are sufficiently small and r 0 1 then there exists a unique stationary distribution to stochastic model numerical simulations are also carried out to confirm the analytical results

a local proof for the characterization of young measures generated by sequences in bv this work presents a new proof of the recent characterization theorem for generalized young measures generated by sequences in bv by kristensen and rindler 2010 14 the present argument is based on a localization technique together with a local hahn banach argument in novel function spaces combined with an application of alberti s rank one theorem this strategy avoids employing a relaxation theorem as in the previously known proof and the new tools introduced in its course should prove useful in other contexts as well in particular we introduce homogeneous young measures separately at regular and singular points which exhibit rather different behavior than the classical homogeneous young measures as an application we show how for bv young measures with an atomic part one can find a generating sequence respecting this structure

quasiconvex elastodynamics weak strong uniqueness for measure valued solutions a weak strong uniqueness result is proved for measure valued solutions to the system of conservation laws arising in elastodynamics the main novelty brought forward by the present work is that the underlying stored energy function of the material is assumed strongly quasiconvex the proof employs tools from the calculus of variations to establish general convexity type bounds on quasiconvex functions and recasts them in order to adapt the relative entropy method to quasiconvex elastodynamics

complete global stability for an sirs epidemic model with generalized non linear incidence and vaccination abstract this paper deals with global dynamics of an sirs epidemic model for infections with non permanent acquired immunity the sirs model studied here incorporates a preventive vaccination and generalized non linear incidence rate as well as the disease related death lyapunov functions are used to show that the disease free equilibrium state is globally asymptotically stable when the basic reproduction number is less than or equal to one and that there is an endemic equilibrium state which is globally asymptotically stable when it is greater than one

an algorithmic introduction to numerical simulation of stochastic differential equations a practical and accessible introduction to numerical methods for stochastic differential equations is given the reader is assumed to be familiar with euler s method for deterministic differential equations and to have at least an intuitive feel for the concept of a random variable however no knowledge of advanced probability theory or stochastic processes is assumed the article is built around 10 matlab programs and the topics covered include stochastic integration the euler maruyama method milstein s method strong and weak convergence linear stability and the stochastic chain rule

measure valued solutions to the ericksen leslie model equipped with the oseen frank energy abstract in this article we prove the existence of measure valued solutions to the ericksen leslie system equipped with the oseen frank energy we introduce a suitable concept of generalized gradient young measures for this system via a galerkin approximation we show the existence of weak solutions to a regularized system and attain measure valued solutions for vanishing regularization additionally it is shown that the measure valued solution fulfills an energy inequality

dynamics of a stochastic siqr epidemic model with standard incidence abstract in this paper a stochastic siqr epidemic model with quarantine and standard incidence is investigated we first consider the existence and uniqueness of the global positive solution to the stochastic system further we obtain conclusions that the large noise can make the disease die out exponentially and the stationary distribution will exist under certain conditions

an upper bound for the height for regular affine automorphisms of mathbb a n kawaguchi math ann 335 2 285 310 359 374 2006 proved a height inequality for h bigl f p bigr when f is a regular affine automorphism of mathbb a 2 and he conjectured that a similar estimate is also true for regular affine automorphisms of mathbb a n for n 3 in this paper we prove kawaguchi s conjecture this implies that kawaguchi s theory of canonical heights for regular affine automorphisms of projective space is true in all dimensions

oscillations and concentrations in weak solutions of the incompressible fluid equations the authors introduce a new concept of measure valued solution for the 3 d incompressible euler equations in order to incorporate the complex phenomena present in limits of approximate solutions of these equations one application of the concepts developed here is the following important result a sequence of leray hopf weak solutions of the navier stokes equations converges in the high reynolds number limit to a measure valued solution of 3 d euler defined for all positive times the authors present several explicit examples of solution sequences for 3 d incompressible euler with uniformly bounded local kinetic energy which exhibit complex phenomena involving both persistence of oscillations and development of concentrations an extensions of the concept of young measure is developed to incorporate these complex phenomena in the measure valued solutions constructed here

optimal control and the value of information for a stochastic epidemiological sis model abstract we analyze a continuous time stochastic sis epidemiological model describing the transmission dynamics of infectious diseases where infected individuals can become susceptible again after recovery the infectivity period of infected individuals can be influenced dynamically by a decision maker with the aim to minimize the expected aggregated economic costs due to illness and drug treatment this stochastic control problem is investigated under two alternative assumptions about the information available if a complete and exact measurement of the size of the infected population is available at any time then the optimal control is sought in a state feedback form and the related hamilton jacobi bellman hjb equation can be used if no state measurement is available then the optimal control is sought in an open loop form and the problem can be reformulated as an optimal control problem for the kolmogorov forward equation in both cases deriving optimality conditions requires non standard arguments due to the degeneracy of the involved hjb and kolmogorov equations based on the obtained theoretical results the role of the information pattern is numerically investigated

explicit characterization oflp young measures the full explicit description of young measures attainable by bounded sequences from the lebesgue spacelp rm was known so far for the casep only in the paper a suitable condition characterizing such measures is isolated also for the case 1 p a generalization of thelp young measures constructed recently by diperna and majda can be thus described also but in special cases only

necessary and sufficient condition for extinction and persistence of sirs system with random perturbation abstract this paper characterizes the qualitative dynamics of a stochastic sirs epidemic model the study shows that the dynamics of the model are determined by a certain threshold quantity r s expressed in terms of the model parameters and the intensity of the noise if r s 1 the disease will be eliminated from the community whereas an epidemic occurs if r s 1 our results recover the known results in the earlier literature as special cases the presented results are illustrated by numerical simulations

stochastic asymptotic analysis of a multi host model with vector transmission abstract we present a stochastic epidemic model with vectorial transmission and multi host structure to include environmental noise we stochastically perturb biting rates with general state functional intensities so we derive a stochastic differential equation sde which describes a vector disease with two types of hosts humans and animals and give conditions to assure disease extinction and persistence finally via numerical experiments we extend and illustrate our results using literature parameters for chagas

survival and stationary distribution of a sir epidemic model with stochastic perturbations abstract in this paper the dynamics of a sir epidemic model is investigated first we show that the system admits a unique positive global solution starting from the positive initial value then when r 0 1 we show that the stochastic model has a stationary distribution under certain parametric restrictions in particular we show that random effects may lead the disease to extinction in scenarios where the deterministic model predicts persistence when r 0 1 a result on fluctuation of the solution around the disease free equilibrium of deterministic system is established under suitable conditions finally numerical simulations are carried out to illustrate the theoretical results

some geometric properties of the set of generalized young functionals this paper studies geometric properties in particular extreme points and rays of various generalizations of young measures applications of the knowledge of extreme points are illustrated on existence results for optimal control problems and on various convergence results for young measures by using the choquet theory

analysis of a saturation incidence sveirs epidemic model with pulse and two time delays in this paper we study a new sveirs infectious disease model with pulse and two time delays the pulse vaccination strategy is used as an effective strategy for the elimination of infectious disease the model consists of a set of integro differential equations the existence and global attractivity of infection free periodic solution permanence of an endemic model are investigated

numerical approach to double well problems this paper deals with two sided numerical energy estimates of a solution to two dimensional double well problems these estimates are obtained by computing the energy appropriate for the polyconvex envelope and an upper estimate of the energy appropriate for the rank one convex envelope of the energy density examples of computed laminated microstructures are shown

characterization of generalized young measures generated by symmetric gradients this work establishes a characterization theorem for generalized young measures generated by symmetric derivatives of functions of bounded deformation bd in the spirit of the classical kinderlehrer pedregal theorem our result places such young measures in duality with symmetric quasiconvex functions with linear growth the local proof strategy combines blow up arguments with the singular structure theorem in bd the analogue of alberti s rank one theorem in bv which was recently proved by the authors as an application of our characterization theorem we show how an atomic part in a bd young measure can be split off in generating sequences

global stability of a delayed sirs epidemic model with a non monotonic incidence rate in this paper we investigate a disease transmission model of sirs type with latent period 0 and the specific nonmonotone incidence rate k exp d s t i t 1 i 2 t for the basic reproduction number r0 1 applying monotone iterative techniques we establish sufficient conditions for the global asymptotic stability of endemic equilibrium of system which become partial answers to the open problem in hai feng huo and zhan ping ma dynamics of a delayed epidemic model with non monotonic incidence rate commun nonlinear sci numer simulat 15 2010 459 468 moreover combining both monotone iterative techniques and the lyapunov functional techniques to an sir model by perturbation we derive another type of sufficient conditions for the global asymptotic stability of the endemic equilibrium

dynamics of stochastic seis epidemic model with varying population size abstract we introduce the stochasticity into a deterministic model which has state variables susceptible exposed infected with varying population size in this paper the infected individuals could return into susceptible compartment after recovering we show that the stochastic model possesses a unique global solution under building up a suitable lyapunov function and using generalized ito s formula the densities of the exposed and infected tend to extinction when some conditions are being valid moreover the conditions of persistence to a global solution are derived when the parameters are subject to some simple criteria the stochastic model admits a stationary distribution around the endemic equilibrium which means that the disease will prevail to check the validity of the main results numerical simulations are demonstrated as end of this contribution

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

canonical height functions for affine plane automorphisms let open image in new window be a polynomial automorphism of dynamical degree 2 over a number field k we construct height functions defined on open image in new window that transform well relative to f which we call canonical height functions for f these functions satisfy the northcott finiteness property and a open image in new window valued point on open image in new window is f periodic if and only if its height is zero as an application we give an estimate on the number of points with bounded height in an infinite f orbit

dynamics of a stochastic sir epidemic model with saturated incidence in this paper the dynamics of a stochastic sir epidemic model with saturated incidence is investigated firstly we prove that the system has a unique global positive solution with any positive initial value then we verify that random effect may lead the disease to extinction under a simple condition thirdly we establish a sufficient condition for persistence in the mean of the disease moreover we show that there is a stationary distribution to the stochastic system under certain parametric restrictions finally some numerical simulations are carried out to confirm the analytical results

young measures generated by ideal incompressible fluid flows in their seminal paper diperna and majda commun math phys 108 4 667 689 1987 introduced the notion of a measure valued solution for the incompressible euler equations in order to capture complex phenomena present in limits of approximate solutions such as persistence of oscillation and development of concentrations furthermore they gave several explicit examples exhibiting such phenomena in this paper we show that any measure valued solution can be generated by a sequence of exact weak solutions in particular this gives rise to a very large arguably too large set of weak solutions of the incompressible euler equations

asymptotic properties of hybrid diffusion systems in response to the increasing needs for control and optimization of hybrid systems this work is concerned with such asymptotic properties as recurrence also known as weak stochastic stability in the literature and ergodicity of regime switching diffusions using liapunov functions necessary and sufficient conditions for positive recurrence are developed then ergodicity of positive recurrent regime switching diffusions is obtained by constructing cycles using the associated discrete time markov chains

consequences of denseness of dirac young measures 1 introductiona fundamental property of the set of dirac young measures is itsdenseness in the set of all young measures when the underlying measurespace is nonatomic e g see 11 theorem iv 2 6 6 in what would wx appear to be its most general form this result was stated for a completelyregular suslin space of control points 3 moreover a simple observation wxstemming directly from the proof of the result states that such densenessof the dirac young measures is maintained under a finite number ofcertain integral functional inequalities 3 corollary 3 for this reason awxrecent characterization of

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

stability of sirs system with random perturbations epidemiological models with bilinear incidence rate si usually have an asymptotically stable trivial equilibrium corresponding to the disease free state or an asymptotically stable non trivial equilibrium i e interior equilibrium corresponding to the endemic state in this paper we consider an epidemiological model which is an sirs model with or without distributed time delay influenced by random perturbations we present the stability conditions of the disease free equilibrium of the associated stochastic sirs system

behavior of a stochastic sir epidemic model with saturated incidence and vaccination rules abstract in this paper the threshold behavior of a susceptible infected recovered sir epidemic model with stochastic perturbation is investigated firstly it is obtained that the system has a unique global positive solution with any positive initial value random effect may lead to disease extinction under a simple condition subsequently sufficient condition for persistence has been established in the mean of the disease finally some numerical simulations are carried out to confirm the analytical results

the equidistribution of small points for strongly regular pairs of polynomial maps in this paper we prove the equidistribution of periodic points of a regular polynomial automorphism f mathbb a n rightarrow mathbb a n defined over a number field k let f be a regular polynomial automorphism defined over a number field k and let v in m k then there exists an f invariant probability measure mu f v on mathrm berk bigl mathbb p n mathbb c v bigr such that the set of periodic points of f is equidistributed with respect to mu f v

strong convergence of the partially truncated euler maruyama scheme for a stochastic age structured sir epidemic model abstract we study in this paper strong convergence of the partially truncated euler maruyama scheme for an age structured susceptible infected removed sir epidemic model with environmental noise using the semigroup theory the existence and uniqueness of global positive solution for the model is first proved we then define a truncated function and develop a partially truncated em numerical solutions to the stochastic age structured sir epidemic model we present the pth moment boundedness of the partially truncated em numerical approximate solutions under appropriate conditions furthermore the strong lq convergence is established for the condition of 2 q