global stability of endemic equilibrium of an epidemic model with birth and death on complex networks abstract we study global stability of endemic equilibrium of an epidemic model with birth and death on complex networks under some conditions the local asymptotic stability of the endemic equilibrium was established by zhang and jin 2011 for correlated networks and the global asymptotic stability was obtained by chen and sun 2014 for uncorrelated networks in this work we remove those conditions and prove by constructing a lyapunov function that the endemic equilibrium is globally asymptotically stable numerical simulations are also presented to illustrate the feasibility of the result

mixed si r epidemic dynamics in random graphs with general degree distributions analytical description of disease propagation on random networks has become one of the most productive fields in recent years yet more complex contact patterns and dynamics have been resorted to numerical study in this paper an epidemic model is defined in which each individual once infected has chances to recover from infection at certain rate the chance is represented by a parameter email protected 0 1 this model can be viewed as an interpolation between classical si model q 0 and sir model q 1 we develop a low dimensional system of non linear ordinary differential equations to model the mixed susceptible infected recovered si r epidemics on random network with general degree distributions both the final size of epidemics and the time dependent behaviors are derived within this simple framework in addition we present the exact transmissibility and the epidemic threshold for this model

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

epidemic thresholds of the susceptible infected susceptible model on networks a comparison of numerical and theoretical results recent work has shown that different theoretical approaches to the dynamics of the susceptible infectedsusceptible sis model for epidemics lead to qualitatively different estimates for the position of the epidemic threshold in networks here we present large scale numerical simulations of the sis dynamics on various types of networks allowing the precise determination of the effective threshold for systems of finite size n we compare quantitatively the numerical thresholds with theoretical predictions of the heterogeneous mean field theory and of the quenched mean field theory we show that the latter is in general more accurate scaling with n with the correct exponent but often failing to capture the correct prefactor

an efficient constraint handling method for genetic algorithms many real world search and optimization problems involve inequality and or equality constraints and are thus posed as constrained optimization problems in trying to solve constrained optimization problems using genetic algorithms gas or classical optimization methods penalty function methods have been the most popular approach because of their simplicity and ease of implementation however since the penalty function approach is generic and applicable to any type of constraint linear or nonlinear their performance is not always satisfactory thus researchers have developed sophisticated penalty functions specific to the problem at hand and the search algorithm used for optimization however the most difficult aspect of the penalty function approach is to find appropriate penalty parameters needed to guide the search towards the constrained optimum in this paper ga s population based approach and ability to make pair wise comparison in tournament selection operator are exploited to devise a penalty function approach that does not require any penalty parameter careful comparisons among feasible and infeasible solutions are made so as to provide a search direction towards the feasible region once sufficient feasible solutions are found a niching method along with a controlled mutation operator is used to maintain diversity among feasible solutions this allows a real parameter ga s crossover operator to continuously find better feasible solutions gradually leading the search near the true optimum solution gas with this constraint handling approach have been tested on nine problems commonly used in the literature including an engineering design problem in all cases the proposed approach has been able to repeatedly find solutions closer to the true optimum solution than that reported earlier

global stability of virus spreading in complex heterogeneous networks various networks are possessed of an obvious heterogeneity in the connectivity properties and it is of practical significance to study epidemic spreading in networks of this kind pastor satorras and vespignani established the dynamical mean field reaction rate equations for the spreading of infections in complex heterogeneous networks based on the well known sis model and figured out an epidemic threshold lambda c such that if lambda effective spreading rate is above lambda c the infection spreads and becomes endemic the significance of this result is far reaching however the authors have not found a strict mathematical proof of their conclusion in the literature in this paper we approach this problem by proving that if lambda is above lambda c the infection spreads and approaches the unique positive stationary point of the reaction rate equations as long as there exist infected nodes in the network initially i e the virus infection process is globally stable

fourth order time stepping for stiff pdes a modification of the exponential time differencing fourth order runge kutta method for solving stiff nonlinear pdes is presented that solves the problem of numerical instability in the scheme as proposed by cox and matthews and generalizes the method to nondiagonal operators a comparison is made of the performance of this modified exponential time differencing etd scheme against the competing methods of implicit explicit differencing integrating factors time splitting and fornberg and driscoll s sliders for the kdv kuramoto sivashinsky burgers and allen cahn equations in one space dimension implementation of the method is illustrated by short matlab programs for two of the equations it is found that for these applications with fixed time steps the modified etd scheme is the best

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

dynamics of a competing two strain sis epidemic model on complex networks with a saturating incidence rate this paper studies a two strain sis epidemic model with a competing mechanism and a saturating incidence rate on complex networks this type of incidence rate can be used to reflect the crowding effect of the infective individuals we first obtain the associated reproduction numbers for each of the two strains which determine the existence of the boundary equilibria the stability of the disease free and boundary equilibria are further examined besides this we also show that the two competing strains can coexist under certain conditions interestingly the saturating incidence rate can have specific effects on not only the stability of the boundary equilibria but also the existence of the coexistence equilibrium numerical simulations are presented to support the theoretical results

behaviors of susceptible infected epidemics on scale free networks with identical infectivity in this paper we propose a susceptible infected model with identical infectivity in which at every time step each node can only contact a constant number of neighbors we implemented this model on scale free networks and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate furthermore by numerical simulation we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible infected model finally we investigate a fast spreading strategy when only local information is available different from the extensively studied path finding strategy the strategy preferring small degree nodes is more efficient than that preferring large degree nodes our results indicate the existence of an essential relationship between network traffic and network epidemic on scale free networks

a modified primal dual logarithmic barrier method for solving the optimal power flow problem with discrete and continuous control variables abstract the aim of solving the optimal power flow problem is to determine the optimal state of an electric power transmission system that is the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system while satisfying its physical and operating constraints the optimal power flow problem is modeled as a large scale mixed discrete nonlinear programming problem this paper proposes a method for handling the discrete variables of the optimal power flow problem a penalty function is presented due to the inclusion of the penalty function into the objective function a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem the obtained nonlinear programming problems are solved by a primal dual logarithmic barrier method numerical tests using the ieee 14 30 118 and 300 bus test systems indicate that the method is efficient

genetic algorithm based technique for solving chance constrained problems management and measurement of risk is an important issue in almost all areas that require decisions to be made under uncertain information chance constrained programming ccp have been used for modelling and analysis of risks in a number of application domains however the resulting mathematical problems are non trivial to represent using algebraic modelling languages and pose significant computational challenges due to their non linear non convex and the stochastic nature we develop and implement c classes to represent such ccp problems we propose a framework consisting of genetic algorithm and monte carlo simulation in order to process the problems the non linear and non convex nature of the ccp problems are processed using genetic algorithm whereas the stochastic nature is addressed through simulation the computational investigations have shown that the framework can efficiently represent and obtain good solutions for seven test problems

dynamics of a network based sis epidemic model with nonmonotone incidence rate abstract this paper studies the dynamics of a network based sis epidemic model with nonmonotone incidence rate this type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels we first find a threshold value for the transmission rate this value completely determines the dynamics of the model and interestingly the threshold is not dependent on the functional form of the nonlinear incidence rate furthermore if the transmission rate is less than or equal to the threshold value the disease will die out otherwise it will be permanent numerical experiments are given to illustrate the theoretical results we also consider the effect of the nonlinear incidence on the epidemic dynamics

the benders decomposition algorithm a literature review the benders decomposition algorithm has been successfully applied to a wide range of difficult optimization problems this paper presents a state of the art survey of this algorithm emphasizing its use in combinatorial optimization we discuss the classical algorithm the impact of the problem formulation on its convergence and the relationship to other decomposition methods we introduce a taxonomy of algorithmic enhancements and acceleration strategies based on the main components of the algorithm the taxonomy provides the framework to synthesize the literature and to identify shortcomings trends and potential research directions we also discuss the use of the benders decomposition to develop efficient meta heuristics describe the limitations of the classical algorithm and present extensions enabling its application to a broader range of problems

global stability of endemic equilibrium for a siqrs epidemic model on complex networks abstract we study the global stability of endemic equilibrium of a siqrs epidemic model on complex networks this model was proposed by li et al 2014 the local asymptotic stability of disease free equilibrium and the permanence of the disease were proved by them by use of a combination of lyapunov function method and a monotone iterative technique we prove that the endemic equilibrium is globally asymptotically stable numerical simulations indicate that quarantine strategy is an effective measure in preventing and controlling epidemic spreading

generalized integrating factor methods for stiff pdes the integrating factor if method for numerical integration of stiff nonlinear pdes has the disadvantage of producing large error coefficients when the linear term has large norm we propose a generalization of the if method and in particular construct multistep type methods with several orders of magnitude improved accuracy we also consider exponential time differencing etd methods and point out connections with a particular application of the commutator free lie group methods we present a new fourth order etdrk method with improved accuracy the methods considered are compared in several numerical examples

a class of explicit multistep exponential integrators for semilinear problems a class of explicit multistep exponential methods for abstract semilinear equations is introduced and analyzed it is shown that the k step method achieves order k for appropriate starting values which can be computed by auxiliary routines or by one strategy proposed in the paper together with some implementation issues numerical illustrations are also provided

stability of multistep methods on variable grids this paper is concerned with the stability of multistep methods for ordinary initial value problems on grids with variable mesh sizes a necessary and sufficient condition for stability is given from which generalizations of recent results by gear et al and by zlatev can be obtained as special cases as an application the stability of the variable bdf formulas is treated

exponential integrators for large systems of differential equations we study the numerical integration of large stiff systems of differential equations by methods that use matrix vector products with the exponential or a related function of the jacobian for large problems these can be approximated by krylov subspace methods which typically converge faster than those for the solution of the linear systems arising in standard stiff integrators the exponential methods also offer favorable properties in the integration of differential equations whose jacobian has large imaginary eigenvalues we derive methods up to order 4 which are exact for linear constant coefficient equations the implementation of the methods is discussed numerical experiments with reaction diffusion problems and a time dependent schrodinger equation are included

effect of infection age on an sir epidemic model with demography on complex networks abstract for the long term population behavior demography is a very important factor impacting the disease spread infection age also helps us better understand the process of the disease transmission in this paper we incorporate these two factors in an sir epidemic model on complex networks through mathematical analysis the basic reproduction number r 0 is shown to be a sharp threshold to determine whether or not the disease spreads precisely if r 0 is less than 1 then the disease free equilibrium is globally asymptotically stable while if r 0 is larger than 1 then the endemic equilibrium is globally asymptotically stable some simulations are carried out to illustrate the theoretical results

exponential time differencing for stiff systems we develop a class of numerical methods for stiff systems based on the method of exponential time differencing we describe schemes with second and higher order accuracy introduce new runge kutta versions of these schemes and extend the method to show how it may be applied to systems whose linear part is nondiagonal we test the method against other common schemes including integrating factor and linearly implicit methods and show how it is more accurate in a number of applications we apply the method to both dissipative and dispersive partial differential equations after illustrating its behavior using forced ordinary differential equations with stiff linear parts

stability analysis of an sis epidemic model with feedback mechanism on networks abstract in this paper an epidemic model with feedback mechanism on networks is investigated we obtain the basic reproductive number r 0 and analyze the stability behaviors of disease free equilibrium e 0 and endemic equilibrium e when r 0 1 the disease free equilibrium is globally asymptotically stable and when r 0 1 the endemic equilibrium is asymptotically stable although the feedback mechanism cannot change the basic reproductive number r 0 as we prove it should be indicated that it can weaken the spreading of diseases and reduce the endemic level finally the results of the stability and the effectiveness of the feedback mechanism are illustrated by some numerical simulations

explicit exponential runge kutta methods for semilinear parabolic problems the aim of this paper is to analyze explicit exponential runge kutta methods for the time integration of semilinear parabolic problems the analysis is performed in an abstract banach space framework of sectorial operators and locally lipschitz continuous nonlinearities we commence by giving a new and short derivation of the classical nonstiff order conditions for exponential runge kutta methods but the main interest of our paper lies in the stiff case by expanding the errors of the numerical method in terms of the solution we derive new order conditions that form the basis of our error bounds for parabolic problems we show convergence for methods up to order four and we analyze methods that were recently presented in the literature these methods have classical order four but they do not satisfy some of the new conditions therefore an order reduction is expected we present numerical experiments which show that this order reduction in fact arises in practical examples based on our new conditions we finally construct methods that do not suffer from order reduction

improving benders decomposition using a genetic algorithm we develop and investigate the performance of a hybrid solution framework for solving mixed integer linear programming problems benders decomposition and a genetic algorithm are combined to develop a framework to compute feasible solutions we decompose the problem into a master problem and a subproblem a genetic algorithm along with a heuristic are used to obtain feasible solutions to the master problem whereas the subproblem is solved to optimality using a linear programming solver over successive iterations the master problem is refined by adding cutting planes that are implied by the subproblem we compare the performance of the approach against a standard benders decomposition approach as well as against a stand alone solver cplex on miplib test problems

global stability and attractivity of a network based sis epidemic model with nonmonotone incidence rate abstract in this paper we study the global stability and attractivity of the endemic equilibrium for a network based sis epidemic model with nonmonotone incidence rate the model was introduced in li 2015 we prove that the endemic equilibrium is globally asymptotically stable if a parameter of this model is sufficiently large and is globally attractive if the transmission rate satisfies c 1 2 where c is the epidemic threshold some numerical experiments are also presented to illustrate the theoretical results

spectra of laplacian matrices of weighted graphs structural genericity properties this article deals with the spectra of laplacians of weighted graphs in this context two objects are of fundamental importance for the dynamics of complex networks the second eigenvalue of such a spectrum called the algebraic connectivity and its associated eigenvector the so called fiedler vector here we prove that given a laplacian matrix it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a fiedler vector composed of only nonzero entries these structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones for which arbitrary structural perturbations are allowed these results open the opportunity to understand the impact of structural changes on the dynamics of complex systems

a note on global stability of the virose equilibrium for network based computer viruses epidemics abstract it has been recently conjectured in yang et al 2013 27 that the unique virose equilibrium of a network based model is globally asymptotically stable in the feasible region the aim of this paper is to investigate the global stability of the virose equilibrium by using the direct lyapunov method and appropriate grouping techniques for lyapunov function derivatives some sufficient conditions are established which improves the relevant results moreover we provide a new brief proof for global stability of the virus free equilibrium by using comparison method and discuss quantitatively the effect of various immunization schemes including uniform immunization targeted immunization and high risk immunization on the viruses spread which suggests promising strategy to halt viruses spread in computer networks

large scale mixed integer programming benders type heuristics abstract the limited success of exact methods for solving integer programming problems has prompted the development of heuristic procedures which have performed surprisingly well in their search for near optimal solutions the present paper constitutes an attempt to generalize these procedures to the mixed integer case the approach is based on the utilization of the benders partitioning method bpm which separates the integer from the continuous variables a number of alternatives are presented for integrating ip heuristics in the bpm thus alleviating its main limitation the necessity of solving a sequence of integer master problems the rationale and its usefulness are illustrated on large scale applications from the fields of power systems and network flows

a 17th order radau iia method for package radau applications in mechanical systems a new radau iia code with an order of 17 is programmed for the well known implicit runge kutta program package radau several numerical examples are reported in this article to demonstrate the performance and efficiency of the new algorithm they are real stiff problems obtained from the simulation of mechanical systems

an improved benders decomposition algorithm for the tree of hubs location problem abstract the tree of hubs location problem is a particularly hard variant of the so called hub location problems when solving this problem by a benders decomposition approach it is necessary to deal with both optimality and feasibility cuts while modern implementations of the benders decomposition method rely on pareto optimal optimality cuts or on rendering feasibility cuts based on minimal infeasible subsystems a new cut selection scheme is devised here under the guiding principle of extracting useful information even when facing infeasible subproblems the proposed algorithm outperforms two other modern variants of the method and it is capable of optimally solving instances five times larger than the ones previously reported on the literature

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 on scale free networks with piecewise linear infectivity and immunization we examine epidemic thresholds for disease spread using susceptible infected susceptible models on scale free networks with variable infectivity infectivity between nodes is modeled as a piecewise linear function of the node degree rather than the less realistic linear transformation considered previously with this nonlinear infectivity we derive conditions for the epidemic threshold to be positive the effects of various immunization schemes including ring and targeted vaccination are studied and compared we find that both targeted and ring immunization strategies compare favorably to a proportional scheme in terms of effectiveness

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

infection dynamics on scale free networks we discuss properties of infection processes on scale free networks relating them to the node connectivity distribution that characterizes the network considering the epidemiologically important case of a disease that confers permanent immunity upon recovery we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual s degree of connectivity within the population as in an earlier study r pastor satorras and a vesipignani phys rev lett 86 3200 2001 phys rev e 63 006117 2001 for an infection that did not confer immunity upon recovery the epidemic process in contrast with many traditional epidemiological models does not exhibit threshold behavior and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale free network finally we discuss effects that arise from finite population sizes showing that networks of finite size do exhibit threshold effects infections cannot spread for arbitrarily low transmission probabilities

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

an analysis of transmission dynamics of drug resistant disease on scale free networks in this paper we present an sir drug resistant model on scale free networks the model has a disease free equilibrium which is globally asymptotically stable when a threshold quantity is less than one the model has a wild strain equilibrium and a resistant strain equilibrium which are asymptotically stable when their respective reproduction number is great than one when treatment leads to resistance development the model can have a unique coexistence equilibrium and we also prove the persistence of infection the effects of two immunization schemes including proportional immunization scheme and targeted immunization scheme are studied and compared we find that targeted strategy compare favorably to a proportional immunization has prominent effect to control the disease spread on scale free networks

the feasibility pump in this paper we consider the np hard problem of finding a feasible solution if any exists for a generic mip problem of the form min ctx ax b xj integer j trivially a feasible solution can be defined as a point x p x ax b that is equal to its rounding where the rounded point is defined by x j if j and x j otherwise and represents scalar rounding to the nearest integer replacing equal with as close as possible relative to a suitable distance function x suggests the following feasibility pump fp heuristic for finding a feasible solution of a given mip we start from any x p and define its rounding at each fp iteration we look for a point x p that is as close as possible to the current by solving the problem min x x p assuming x is chosen appropriately this is an easily solvable lp problem if x 0 then x is a feasible mip solution and we are done otherwise we replace by the rounding of x and repeat we report computational results on a set of 83 difficult 0 1 mips using the commercial software ilog cplex 8 1 as a benchmark the outcome is that fp in spite of its simple foundation proves competitive with ilog cplex both in terms of speed and quality of the first solution delivered interestingly ilog cplex could not find any feasible solution at the root node for 19 problems in our test bed whereas fp was unsuccessful in just 3 cases

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

the architecture of complex weighted networks networked structures arise in a wide array of different contexts such as technological and transportation infrastructures social phenomena and biological systems these highly interconnected systems have recently been the focus of a great deal of attention that has uncovered and characterized their topological complexity along with a complex topological structure real networks display a large heterogeneity in the capacity and intensity of the connections these features however have mainly not been considered in past studies where links are usually represented as binary states i e either present or absent here we study the scientific collaboration network and the world wide air transportation network which are representative examples of social and large infrastructure systems respectively in both cases it is possible to assign to each edge of the graph a weight proportional to the intensity or capacity of the connections among the various elements of the network we define appropriate metrics combining weighted and topological observables that enable us to characterize the complex statistical properties and heterogeneity of the actual strength of edges and vertices this information allows us to investigate the correlations among weighted quantities and the underlying topological structure of the network these results provide a better description of the hierarchies and organizational principles at the basis of the architecture of weighted networks

variable step implementation of etd methods for semilinear problems abstract spatial discretization of many evolutionary partial differential equations leads to stiff semilinear systems of ordinary differential equations exponential integrators solve exactly the linear part which is assumed to be responsible of the stiffness of the problem while the nonlinear terms are approximated numerically in this paper a variable step implementation of the exponential time differencing methods of multistep type is considered a local error estimate of exponential type whose computation is for free is introduced and some implementation issues for diagonalizable matrices are addressed numerical results showing the behaviour of the proposed variable step implementation are provided too

global stability analysis of an sir epidemic model with demographics and time delay on networks abstract in this paper a susceptible infected recovery sir epidemic model is governed with demographics and time delay on networks firstly the basic reproduction number r 0 is derived dependent on birth rate death rate recovery rate and transmission rate the disease free equilibrium of the model is stable when r 0 1 and unstable when r 0 1 secondly based on a jacobian matrix calculated along with the disease free equilibrium we find that the system does not occur hopf branch under the disease free equilibrium thirdly the global asymptotic stability of a disease free equilibrium and a unique endemic equilibrium are proved by structuring two lyapunov functions finally numerical simulations are performed to illustrate the analysis results

a fractional order model for ebola virus infection with delayed immune response on heterogeneous complex networks abstract most of the biological systems have long range temporal memory and modeling of such systems by fractional order differential equations has more advantages than classical models with integer orders in this paper we provide a fractional order ebola virus epidemic model with delayed immune response on heterogeneous complex networks the time delay is introduced in the cytotoxic t lymphocyte ctls term based on fractional laplace transform some conditions on stability are derived for the model the analysis shows that the fractional order time delay can effectively enrich the dynamics and strengthen the stability condition of fractional order infection model finally the derived theoretical results are justified by some numerical simulations

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

a new class of time discretization schemes for the solution of nonlinear pdes we consider issues of stability of time discretization schemes withexacttreatment of thelinear part elp schemes for solving nonlinear pdes a distinctive feature of elp schemes is the exact evaluation of the contribution of the linear term that is if the nonlinear term of the equation is zero then the scheme reduces to the evaluation of the exponential function of the operator representing the linear term computing and applying the exponential or other functions of operators with variable coefficients in the usual manner requires evaluating dense matrices and is highly inefficient it turns out that computing the exponential of strictly elliptic operators in the wavelet system of coordinates yields sparse matrices for a finite but arbitrary accuracy this observation makes our approach practical in a number of applications in particular we consider applications of elp schemes to advection diffusion equations we study the stability of these schemes and show that both explicit and implicit elp schemes have distinctly different stability properties if compared with known implicit explicit schemes for example we describe explicit schemes with stability regions similar to those of typical implicit schemes used for solving advection diffusion equations

the analysis of an epidemic model with time delay on scale free networks abstract a new epidemic s i s model with time delay on scale free networks is presented we give the formula of the basic reproductive number for the model and prove that the disease dies out when the basic reproductive number is less than unity and the disease is uniformly persistent when the basic reproductive number is more than unity the effects of various immunization schemes are studied numerical simulations are given to demonstrate the main results