extinction and stationary distribution of a stochastic sirs epidemic model with standard incidence rate and partial immunity abstract in this paper a stochastic sirs model with standard incidence rate and partial temporary immunity is proposed the sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established our results reveal that random perturbations in the environment can restrain the spread of disease that is the deterministic model neglecting random perturbations overestimates the ability of the disease to spread the numerical simulations are carried out to demonstrate the analytical results

the analysis of an epidemic model on networks abstract the paper consider an epidemic model with birth and death on networks we derive the epidemic threshold r0 dependent on birth rate b death rate d natural death and from the infectious disease and natural death and cure rate and the stability of the equilibriums the disease free equilibrium and endemic equilibrium are analysed finally the effects of various immunization schemes are studied and compared we show that both targeted and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness for active immunization the threshold is easier to apply practically to illustrate our theoretical analysis some numerical simulations are also included

the analytic formulas of the ripple free tracking problem abstract the forward pulse transfer function of the controlled system always contains at least one zero at infinity two formulas can be found which define the order of the unspecified polynomial in the design of ripple free digital control systems some fundamental concepts are introduced in this paper and a new method which has been widely applied to teaching and research is developed

an iterative multi level algorithm for solving nonlinear ill posed problems the convergence analysis of landweber s iteration for the solution of nonlinear ill posed problem has been developed recently by hanke neubauer and scherzer in concrete applications sufficient conditions for convergence of the landweber iterates developed there although quite natural turned out to be complicated to verify analytically however in numerical realizations when discretizations are considered sufficient conditions for local convergence can usually easily be stated this paper is motivated by these observations initially a discretization is fixed and a discrete landweber iteration is implemented until an appropriate stopping criterion becomes active the output is used as an initial guess for a finer discretization an advantage of this method is that the convergence analysis can be considered in a family of finite dimensional spaces the numerical performance of this multi level algorithm is compared with landweber s iteration

simultaneous deadbeat tracking controller synthesis abstract a direct and simple design algorithm for the problem of simultaneously deadbeat tracking a prespecified class of inputs by only one controller is presented this novel approach is based on polynomial algebra and the principle of system realizability without solving linear polynomial diophantine equations the proposed procedure consists of solving a set of linear equations depending on system dynamics and yields the deadbeat controller in a compact form well suited for system with inaccessible states and changeable reference signals since all solutions are described in a parametric form some performance criteria can be easily incorporated as well examples are presented to illustrate the usefulness and computational easiness of this simple design algorithm

epidemic dynamics in finite size scale free networks many real networks present a bounded scale free behavior with a connectivity cutoff due to physical constraints or a finite network size we study epidemic dynamics in bounded scale free networks with soft and hard connectivity cutoffs the finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes the induced epidemic threshold is very small even at a relatively small cutoff showing that the neglection of connectivity fluctuations in bounded scale free networks leads to a strong overestimation of the epidemic threshold we provide the expression for the infection prevalence and discuss its finite size corrections the present paper shows that the highly heterogeneous nature of scale free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes

the method of conjugate residuals for solving the galerkin equations associated with symmetric positive semidefinite ill posed problems for the numerical solution of the galerkin equations associated with linear ill posed problems that are symmetric and positive semidefinite the method of conjugate residuals is considered an a posteriori stopping rule is introduced and associated estimates for the approximations are provided which are order optimal with respect to noise in the right hand side and with respect to the discretization error

generalized cross validation applied to conjugate gradient for discrete ill posed problems in this paper we propose a new method to apply the generalized cross validation gcv as a stopping rule for the conjugate gradient cg in general to apply gcv to an iterative method one must estimate the trace of the so called influence matrix which appears in the denominator of the gcv function in the case of cg unlike what happens with stationary iterative methods the regularized solution has a nonlinear dependence on the noise which affects the data of the problem this fact is often pointed out as a cause of poor performance of gcv to overcome this drawback our proposal linearizes the dependence by computing the derivatives through iterative formulas we compare the proposed method with other methods suggested in the literature by an extensive numerical experimentation on both 1d and 2d test problems

accelerated landweber iterations for the solution of ill posed equations in this paper the potentials of so calledlinear semiiterative methods are considered for the approximate solution of linear ill posed problems and ill conditioned matrix equations several efficient two step methods are presented most of which have been introduced earlier in the literature stipulating certain conditions concerning the smoothness of the solution a notion of optimal speed of convergence may be formulated various direct and converse results are derived to illustrate the properties of this concept if the problem s right hand side data are contaminated by noise semiiterative methods may be used asregularization methods assuming optimal rate of convergence of the iteration for the unperturbed problem the regularized approximations will be of order optimal accuracy to derive these results specific properties of polynomials are used in connection with the basic theory of solving ill posed problems rather recent results onfast decreasing polynomials are applied to answer an open question of brakhage numerical examples are given including a comparison to the method of conjugate gradients

approximation accuracy of the krylov subspaces for linear discrete ill posed problems abstract for the large scale linear discrete ill posed problem min a x b or a x b with b contaminated by gaussian white noise the lanczos bidiagonalization based krylov solver lsqr and its mathematically equivalent cgls the conjugate gradient cg method implicitly applied to a t a x a t b are most commonly used and cgme the cg method applied to min a a t y b or a a t y b with x a t y and lsmr which is equivalent to the minimal residual minres method applied to a t a x a t b have also been choices these methods exhibit typical semi convergence feature and the iteration number k plays the role of the regularization parameter however there has been no definitive answer to the long standing fundamental question can lsqr and cgls find 2 norm filtering best possible regularized solutions the same question is for cgme and lsmr too at iteration k lsqr cgme and lsmr compute different iterates from the same k dimensional krylov subspace a first and fundamental step towards answering the above question is to accurately estimate the accuracy of the underlying k dimensional krylov subspace approximating the k dimensional dominant right singular subspace of a assuming that the singular values of a are simple we present a general sin theorem for the 2 norm distances between these two subspaces and derive accurate estimates on them for severely moderately and mildly ill posed problems we also establish some relationships between the smallest ritz values and these distances numerical experiments justify the sharpness of our results

environmental variability in a stochastic epidemic model abstract in this paper we investigate the stochastic dynamics of a simple epidemic model incorporating the mean reverting ornstein uhlenbeck process analytically and numerically we define two threshold parameters the stochastic demographic reproduction number r d s and the stochastic basic reproduction number r 0 s to utilize in identifying the stochastic extinction and persistence of the disease we find that the stochastic disease dynamics can be determined by the environment fluctuations which measured by the intensity of volatility and the speed of reversion the larger intensity of volatility or the smaller speed of reversion can suppress the outbreak of the disease the smaller intensity of volatility or the the higher speed of reversion can enhance the outbreak of the disease furthermore via numerical simulations we find that the stochastic model has an endemic stationary distribution which leads to the stochastic persistence of the disease our results show that mean reverting process is a well established way of introducing stochastic environmental noise into biologically realistic population dynamic models

spreading of epidemics on scale free networks with nonlinear infectivity abstract in this paper we study the spreading of epidemics on scale free networks with infectivity which is nonlinear in the connectivity of nodes we will show that the nonlinear infectivity is more appropriate than constant or linear ones and give the epidemic threshold of the sis model on a scale free network with nonlinear infectivity in addition we compare the effects of nonlinear infectivity on the epidemic threshold with two other cases on infinite and finite scale free networks and find some new results such as with unit recovery rate and nonlinear irrational infectivity the epidemic threshold is always positive and the epidemic threshold can increase with network size on finite networks contrary to the findings in all previous work

ripple free tracking problem in the deadbeat control of discrete plants originating from continuous ones it is important to have exact tracking not only at the sampling instants but also in between the instants this paper investigates such a problem in the general case of a reference signal that can vary within a pre specified class the design procedure proposed here is based on a polynomial algebra approach an internally stable closed loop system is derived by means of an algorithm where the transfer function of the controller originates from the solution of a set of linear equations algebraic conditions are given to determine the minimum time control scheme numerical examples are reported to show the feasibility of the method and the simplicity of including other specific requirements into the control law

the instability of some gradient methods for ill posed problems for the solution of linear ill posed problems some gradient methods like conjugate gradients and steepest descent have been examined previously in the literature it is shown that even though these methods converge in the case of exact data their instability makes it impossible to base a priori parameter choice regularization methods upon them

behavior of susceptible infected susceptible epidemics on heterogeneous networks with saturation we investigate saturation effects in susceptible infected susceptible models of the spread of epidemics in heterogeneous populations the structure of interactions in the population is represented by networks with connectivity distribution p k including scale free sf networks with power law distributions p k approximately k gamma considering cases where the transmission of infection between nodes depends on their connectivity we introduce a saturation function c k which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k a mean field approximation with the neglect of degree degree correlation then leads to a finite threshold lambda c 0 for sf networks with 2 gamma 3 we also find in this approximation the fraction of infected individuals among those with degree k for lambda close to lambda c we investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean field theory with and without neglect of degree degree correlations

epidemic dynamics and endemic states in complex networks we study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks in networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null on the contrary on a wide range of scale free networks we observe the absence of an epidemic threshold and its associated critical behavior this implies that scale free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess these results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks

a stochastic differential equation sis epidemic model incorporating ornstein uhlenbeck process abstract in this paper based on the results of gray et al 2011 we propose a new sde sis model incorporating mean reverting ornstein uhlenbeck process and prove that the stochastic basic reproduction number r 0 s can be used to identify the stochastic extinction and persistence for the sde mode if r 0 s 1 under mild extra conditions the disease will be extinct a s while if r 0 s 1 the disease will persist a s epidemiologically we find that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak thus in order to control the spread of the disease we must decrease the speed of reversion or increase the intensity of volatility

dynamics of an saits alcoholism model on unweighted and weighted networks abstract a novel saits alcoholism model on networks is introduced in which alcoholics are divided into light problem alcoholics and heavy problem alcoholics susceptible individuals can enter into the compartment of heavy problem alcoholics directly by contacting with light problem alcoholics or heavy problem alcoholics and the heavy problem alcoholics who receive treatment can relapse into the compartment of heavy problem alcoholics are also considered first the dynamics of our model on unweighted networks including the basic reproduction number existence and stability of equilibria are studied second the models with fixed weighted and adaptive weighted networks are introduced and investigated at last some simulations are presented to illustrate and extend our results our results show that it is very important to treat alcoholics to quit the drinking

convergence rate results for steepest descent type method for nonlinear ill posed equations convergence rate result for a modified steepest descent method and a modified minimal error method for the solution of nonlinear ill posed operator equation have been proved with noisy data to our knowledge convergence rate result for the steepest descent method and minimal error method with noisy data are not known we provide a convergence rate results for these methods with noisy data the result in this paper are obtained under less computational cost when compared to the steepest descent method and minimal error method we present an academic example which satisfies the assumptions of this paper

dynamics for an seirs epidemic model with time delay on a scale free network abstract a new seirs epidemic model with time delay on a scale free network is introduced the basic reproduction number r 0 is defined and it does not depend on time delay by analyzing the characteristic equation of equilibria and constructing suitable lyapunov functionals the stability of steady states is proved system does not occur hopf bifurcation around disease free equilibrium e 0 uniform immunization and targeted immunization are investigated numerical simulations and sensitivity analysis are performed results indicate that time delay plays a significant part in propagation process of epidemics on a scale free network

qualitative study of a stochastic sis epidemic model with vertical transmission abstract in this paper we study a stochastic sis epidemic model with vertical infection by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of a stationary probability measure of the model in addition we also establish sufficient conditions for extinction and persistence of the disease

epidemic spreading with nonlinear infectivity in weighted scale free networks abstract in this paper we investigate the epidemic spreading for the sir model in weighted scale free networks with the nonlinear infectivity and weighted transmission rate concretely we introduce the infectivity exponent and the weight exponent into the epidemic system then examine the impact of and on the epidemic spreading we show that one can adjust the values of and to rebuild a nonzero finite epidemic threshold furthermore we also find the infectivity exponent has a stronger effect not only on the epidemic threshold but also on the epidemic prevalence in addition it is also interesting to see that the absence of the epidemic threshold appears not very dejected since the prevalence grows much more slowly as the transmission rate increases

a taxonomy for conjugate gradient methods the conjugate gradient method of hestenes and stiefel is an effective method for solving large sparse hermitian positive definite hpd systems of linear equations ax b generalizations to non hpd matrices have long been sought the recent theory of faber and manteuffel gives necessary and sufficient conditions for the existence of a cg method this paper uses these conditions to develop and organize such methods it is shown that any cg method for ax b is characterized by an hpd inner product matrix b and a left preconditioning matrix c at each step the method minimizes the b norm of the error over a krylov subspace this characterization is then used to classify known and new methods finally it is shown how eigenvalue estimates may be obtained from the iteration parameters generalizing the well known connection between cg and lanczos such estimates allow implementation of a stopping criterion based more nearly on the true error

stability of an sairs alcoholism model on scale free networks abstract a new sairs alcoholism model with birth and death on complex heterogeneous networks is proposed the total population of our model is partitioned into four compartments the susceptible individual the light problem alcoholic the heavy problem alcoholic and the recovered individual the spread of alcoholism threshold r 0 is calculated by the next generation matrix method when r 0 1 the alcohol free equilibrium is globally asymptotically stable then the alcoholics will disappear when r 0 1 the alcoholism equilibrium is global attractivity then the number of alcoholics will remain stable and alcoholism will become endemic furthermore the modified sairs alcoholism model on weighted contact network is introduced dynamical behavior of the modified model is also studied numerical simulations are also presented to verify and extend theoretical results our results show that it is very important to treat alcoholics to control the spread of the alcoholism

pattern formation of a diffusive predator prey model with strong allee effect and nonconstant death rate abstract this paper is concerned with the pattern formation of a diffusive predator prey model with strong allee effect in the prey population and nonconstant death rate for the predator the necessary and sufficient conditions of turing instability are explicitly obtained by regarding the diffusion coefficient d 2 of the predator as bifurcation parameter we demonstrate that at the critical value of the bifurcation parameter d 2 a turing bifurcation occurs i e a pattern arises the conditions for the stability of the pattern are also derived in detail our results show that strong allee effect in our model plays a crucial role in the formation of stationary pattern which is a strong contrast to the case without strong allee effect