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Abstract: In this paper, we will employ some dynamic inequalities of Opial’s type on time scales to prove several results related to the spacing between consecutive zeros of a solution of a second order dynamic equation with a damping term. We also obtain several results related to the spacing between a zero of the solution and/or a zero of its derivative. As a special case, we will establish some new results for differential and difference equations with damping terms. For illustration, we will derive some well-known results obtained for differential equations without damping terms. The results yield conditions for disfocality and disconjugacy for dynamic equations with damping terms on time scales. [Copyright &y& Elsevier]

Abstract: A nonautonomous two dimensional competitive Lotka–Volterra system is considered in this paper. Average conditions on the coefficients are given to guarantee the principle of competitive exclusion in the system. It is shown that our results are extensions of those of the counterpart of periodic system. [Copyright &y& Elsevier]

Abstract: This paper shows that every well-defined solution of the difference equation , where is eventually periodic with period two. [Copyright &y& Elsevier]

Abstract: In this paper, with the compounded rate of removed errors, a new software reliability model is proposed. By the least squares and first-order differential methods, the approximate parameters of the model are obtained. The applicability of proposed model is demonstrated on three well-known real software data sets. The results show that our model has a good capability of fitting and predicting. Moreover, when we own enough history failure data of software, predicting results will be fairly accurate. [Copyright &y& Elsevier]

Abstract: In this paper we propose a mathematical model to manage a Service Center (SC) which is based on a system of ordinary differential equations. By resorting to this model, the manager of the SC can design planning strategies to satisfy customer orders, under strict deadlines and human resource constraints. After describing the model, we introduce criteria which optimize the processing time and supply a more accurate description of working behavior. Finally, we conclude presenting some numerical simulations which demonstrate the usefulness of the proposed model to reach correct decisions in managing a SC. [Copyright &y& Elsevier]

Abstract: In this paper, a non-linear mathematical model for the effects of awareness programs on the spread of infectious diseases such as flu has been proposed and analyzed. In the modeling process it is assumed that disease spreads due to the contact between susceptibles and infectives only. The growth rate of awareness programs impacting the population is assumed to be proportional to the number of infective individuals. It is further assumed that due to the effect of media, susceptible individuals form a separate class and avoid contact with the infectives. The model is analyzed by using stability theory of differential equations. The model analysis shows that the spread of an infectious disease can be controlled by using awareness programs but the disease remains endemic due to immigration. The simulation analysis of the model confirms the analytical results. [ABSTRACT FROM AUTHOR]

Abstract: The subject of this paper are analytic approximate methods for pantograph stochastic differential equations with Markovian switching, as well as their counterparts without Markovian switching. Approximate equations are defined on equidistant partitions of the time interval, and their coefficients are Taylor approximations of the coefficients of the initial equation. In the case with Markovian switching we will present the approximate method based on Taylor approximation of coefficients in two arguments and show that the appropriate approximate solutions converge in the -norm to the solution of the initial equation. Then we will present the other approximate method which deals with Taylor approximation in the first argument. In both cases the closeness between the approximate solution and the solution of the initial equation depends on the number of degrees in Taylor approximations of coefficients, although the presence of the Markov chain affects it. These approximate methods are then adapted to the case without Markovian switching. The first method gives the possibility of proving convergence as well as a.s. convergence of the appropriate sequence of approximate solutions to the solution of the initial equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we have constructed a mathematical model to interpret the spread of wild avian influenza from the birds to the humans, after the emergence of mutant avian influenza, with nonautonomous ordinary differential equations and distributed time delay due to the intracellular delay between initial infection of a cell and the release of new virus particles. The bird population is divided into two classes: susceptible birds and infected birds with wild avian influenza, by a compartmental model. The human population is divided into four classes, namely susceptible humans, humans infected with wild avian influenza, humans infected with mutant avian influenza, and recovered humans from mutant avian influenza, by a compartmental model. Here, we have established some sufficient conditions on the permanence and extinction of the disease by using inequality analytical techniques. By a Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness. [ABSTRACT FROM AUTHOR]

Abstract: In this paper an age-structured mathematical model for respiratory syncytial virus (RSV) is proposed where children younger than one year old, who are the most affected by this illness, are specially considered. Real data of hospitalized children in the Spanish region of Valencia are used in order to determine some seasonal parameters of the model. Once the parameters are determined, we propose a complete stochastic network model to study the seasonal evolution of the respiratory syncytial virus (RSV) epidemics. In this model every susceptible individual can acquire the disease after a random encounter with any infected individual in the social network. The edges of a complete graph connecting every pair of individuals in the network simulate these encounters and a season dependent probability, , determines whether the healthy susceptible individual becomes infected or not. We show that the prediction of this model is compatible with the above mentioned age-structured model based upon differential equations, but sharper peaks are obtained in the case of the network. Then, on the network model, we propose the vaccination of children at 2 months, 4 months and 1 year old, and we study the cost of this vaccination strategy, which is emerging as the most plausible one to be applied when the vaccine hits the market. It is worth to note that this vaccination strategy is simulated in the network model because to implement it in the continuous model is very difficult and increases its complexity. [ABSTRACT FROM AUTHOR]

Abstract: Mathematical models are very important in epidemiology. Many of the models are given by differential equations and most consider that the parameters are deterministic variables. But in practice, these parameters have large variability that depends on the measurement method and its inherent error, on differences in the actual population sample size used, as well as other factors that are difficult to account for. In this paper the parameters that appear in SIR and SIRS epidemic model are considered random variables with specified distributions. A stochastic spectral representation of the parameters is used, together with the polynomial chaos method, to obtain a system of differential equations, which is integrated numerically to obtain the evolution of the mean and higher-order moments with respect to time. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a mathematical model for alcohol consumption in Spanish population is proposed. Its parameters are estimated by fitting the model to real data from Spanish Ministry of Health. Predictions about the future behavior of the alcohol consumption in Spain are presented using this model. Results are applied to estimate the economic costs (sanitary and non-sanitary) assumed by Spanish society that are derived from this consumption. [ABSTRACT FROM AUTHOR]

Abstract: Recently we developed a model composed of five impulsive differential equations that describes the changes in drinking patterns (that persist at epidemic level) amongst college students. Many of the model parameters cannot be measured directly from data; thus, an inverse problem approach, which chooses the set of parameters that results in the “best” model to data fit, is crucial for using this model as a predictive tool. The purpose of this paper is to present the procedure and results of an unconventional approach to parameter estimation that we developed after more common approaches were unsuccessful for our specific problem. The results show that our model provides a good fit to survey data for 32 campuses. Using these parameter estimates, we examined the effect of two hypothetical intervention policies: (1) reducing environmental wetness, and (2) penalizing students who are caught drinking. The results suggest that reducing campus wetness may be a very effective way of reducing heavy episodic (binge) drinking on a college campus, while a policy that penalizes students who drink is not nearly as effective. [Copyright &y& Elsevier]

Abstract: The technique used to spot information in Magnetic Resonance Imaging (MRI) uses electromagnetic fields. Even minor perturbations of these magnetic fields can disturb the imaging process and may render clinical images inaccurate or useless. Modelling and numerical simulation of the effects of static field inhomogeneities are now well established. Less attention has been paid to mathematical modelling of the effects of radio-frequency (RF) field inhomogeneities in the imaging process. When considering RF field inhomogeneities, the major difficulty is that the mathematical expression of the magnetisation vector is not anymore explicitly known in contrast with the unperturbed case. Indeed, the Bloch equation becomes an ordinary differential equation with nonconstant coefficients that cannot be solved analytically. The use of standard numerical schemes for ordinary differential equations to compute the magnetisation vector appears to be costly and not well suited for MRI image simulation. In this paper, we present an original method for solving the Bloch equation based on a truncated series expansion of the solution. The computational cost of the method reduces to the computation of the eigenelements of a block tridiagonal matrix of a very small size. [Copyright &y& Elsevier]

Abstract: This paper deals with the definition of a general framework, inspired by the discrete generalized kinetic theory, suitable for the description of the evolution of opinions within a population in the presence of some external actions. As a conceivable application, a specific model of opinion formation is formulated, relying on the interactions of single individuals within the population. Then, two examples of possible persuader’s influence are constructed. The resulting models are expressed by means of nonlinear ordinary differential equations, which are then investigated both analytically and computationally. [Copyright &y& Elsevier]

Abstract: In this paper, we study the generalized strong vector quasi-equilibrium problem without assuming that the dual of the ordering cone has a weak∗ compact base. We establish an existence theorem of solutions for the generalized strong vector quasi-equilibrium problem by using Kakutani–Fan–Glicksberg fixed point theorem and discuss the closedness of the strong solution set. Moreover, we also derive a stability result for this problem. [Copyright &y& Elsevier]

Abstract: In this paper, stability criteria of impulsive switched systems with time-invariant delays are introduced. We proposed a class of impulsive switched systems with time delays and parameter uncertainties. Based on the result of Theorem 3.1 in [X.Z. Liu, G. Ballinger, Uniform asymptotic stability of impulsive delay differential equations, Computer and Mathematics with Applications 41 (2001) 903–915], sufficient stability conditions of the impulsive delay switched systems are obtained. The validity of the results is shown by an example and its simulation. [Copyright &y& Elsevier]

Abstract: In this paper, we study the steady state solutions for viscous reactive flows through channels with a sliding wall. The reaction is assumed to be strongly exothermic under Arrhenius kinetics, neglecting the consumption of the material. Approximate solutions are constructed for the governing nonlinear boundary value problem using regular perturbation techniques together with a special type of Hermite–Padé approximants, and important properties of the temperature field including bifurcations and thermal criticality conditions are discussed. [Copyright &y& Elsevier]

Abstract: In this paper we study global existence of solutions of a mathematical model for drug transport in tumor multicell spheroids. The model is a free boundary problem of a system of partial differential equations. It contains one nonlinear first-order equation describing the distribution of live tumor cells, and two nonlinear reaction diffusion equations describing the evolution of nutrient concentration and drug concentration, respectively. By using the method of characteristics for first-order equations, the -theory for parabolic equations, the Banach fixed point theorem and the extension method, we prove that this problem has a unique global solution. [Copyright &y& Elsevier]

Abstract: Nonexponential evolution equations can be treated using a formalism involving the evolution operator method, which, unlike the ordinary case, is not expressed in terms of exponential operators. The use of this technique requires particular care associated with the operator ordering. In this paper, we will present a first systematic approach to this type of problems. [Copyright &y& Elsevier]

In our paper, we are interested in the generalization of the famous Lotka-Volterra models by the help of stochastic nonlinear differential equations (called diffusion type processes). We propose by Ito's rule some two- and multidimensional systems of stochastic differential equation, which can be used in statistical inference. For this reason, we give the Radon-Nikodym derivative of measures, the related linear stochastic models, and the discussion of the stability problems. We use the author's earlier results in parameter estimation, stochastic control, and Ka´lma´n filtering. [Copyright &y& Elsevier]