Pulse and constant control schemes for epidemic models with seasonality

Control schemes for infectious disease models with time-varying contact rate are analyzed. First, time-constant control schemes are introduced and studied. Specifically, a constant treatment scheme for the infected is applied to a SIR model with time-varying contact rate, which is modelled by a switching parameter. Two variations of this model are considered: one with waning immunity and one with progressive immunity. Easily verifiable conditions on the basic reproduction number of the infectious disease are established which ensure disease eradication under these constant control strategies. Pulse control schemes for epidemic models with time-varying contact rates are also studied in detail. Both pulse vaccination and pulse treatment models are applied to a SIR model with time-varying contact rate. Further, a vaccine failure model as well as a model with a reduced infective class are considered with pulse control schemes. Again, easily verifiable conditions on the basic reproduction number are developed which guarantee disease eradication. Some simulations are given to illustrate the threshold theorems developed.     

On the estimators of model-based and maximal reliability

Four estimators of the reliability for a composite score based on the factor analysis model and five estimators of the maximal reliability for the composite are presented. When the Wishart maximum likelihood is used for the estimation of the model parameters, it is shown that the five estimators of maximal reliability are the same. Asymptotic cumulants of the estimators and their logarithmic transformations are derived under arbitrary distributions with possible model misspecification. The theoretical results considering model misspecification when a model does not hold are shown to be closer to their simulated values than those neglecting model misspecification. Simulations of the confidence intervals using the normal approximation based on the asymptotically distribution-free theory and the asymptotic expansion by Hall’s method with variable transformation are performed.     

One-velocity model of a heterogeneous medium with a hyperbolic adiabatic kernel

The one-velocity model equations for a heterogeneous medium are presented that take into account the internal forces of interfractional interactions and heat and mass exchange. The shock adiabat obtained for the mixture agrees with the one-velocity model equations. For one-dimensional unsteady adiabatic flows, the characteristic equations are found and relations along characteristic directions are determined. It is shown that the model equations with allowance for interfractional interaction forces are hyperbolic. Several finite-difference and finite-volume schemes designed for integrating the model equations are discussed.     

Modelling systems with renewable resources based on functional operators with shift

A method for the study of systems with renewable resources is proposed. The individual and the group parameters are separated and a discretization of time is carried out. We obtain equilibrium proportions which are functional equations with shift. A cyclic model and an open model are considered. Conditions for the existence and uniqueness of the solution are formulated for the cyclic model. For the open model, the system’s evolution is analyzed.     

Stability preserving NSFD scheme for a delayed viral infection model with cell-to-cell transmission and general nonlinear incidence

In this paper, we designed and analysed a discrete model to solve a delayed within-host viral infection model by using non-standard finite difference scheme. The original model that we considered was a delayed viral infection model with cell-to-cell transmission, cell-mediated immune response and general nonlinear incidence. We show that the discrete model has equilibria which are exactly the same as those of the original continuous model and the conditions for those equilibria to be globally asymptotically stable are consistent with the original continuous model with no restriction on the time step size. The results imply that the discretization scheme can efficiently preserves the qualitative properties of solutions for corresponding continuous model.     

A multivariate ultrastructural errors-in-variables model with equation error

This paper deals with asymptotic results on a multivariate ultrastructural errors-in-variables regression model with equation errors. Sufficient conditions for attaining consistent estimators for model parameters are presented. Asymptotic distributions for the line regression estimators are derived. Applications to the elliptical class of distributions with two error assumptions are presented. The model generalizes previous results aimed at univariate scenarios.     

一个新锥模型信赖域算法

1引言本文考虑的无约束最优化问题为(?)f(x),(1.1)其中f(x)为连续可微函数.解此问题的很多算法一般都采用二次函数模型去逼近f(x) ([10],[15]).对于一些非二次性态强、曲率变化剧烈的函数,用二次函数模型去逼近可能效果不好,因此Davidon于1980年首次提出了解无约束优化问题的锥模型方法.锥模型是二次模型的推广,比二次函数具有更多的自由度,因此期望能够更充分地逼近原函数.对于一些在极小点附近很不对称,或曲率变化剧烈的函数,或在某个区域内变化大的函数,全部或部分用锥模型去逼近的效果可能好于用二次模型去逼近.     

Effects of centralization on expected profits in a multi-location newsboy problem

This paper develops a single-period, single-product inventory model with several individual sources of demand. It is a multi-location problem with an opportunity for centralization. Both decentralized and centralized inventory systems are also examined to extend the Ravindram, Phillips and Solberg (RPS) model to constitute a new inventory model. Two theorems that include the results of the RPS model are proved in the new inventory model.     

Analytical and numerical investigations of a batch crystallization model

This article is concerned with the analytical and numerical investigations of a one-dimensional population balance model for batch crystallization processes. We start with a one-dimensional batch crystallization model and prove the local existence and uniqueness of the solution of this model. For this purpose Laplace transformation is used as a basic tool. A semi-discrete high resolution finite volume scheme is proposed for the numerical solution of the current model. The issues of positivity (monotonicity), consistency, stability and convergence of the proposed scheme for the current model are analyzed and proved. Finally, we give a numerical test problem. The numerical results of the proposed high resolution scheme are compared with the solution of the reduced four-moments model and the first-order upwind scheme.     

Bayesian Ising Graphical Model for Variable Selection

In this article, we propose a new Bayesian variable selection (BVS) approach via the graphical model and the Ising model, which we refer to as the “Bayesian Ising graphical model” (BIGM). The BIGM is developed by showing that the BVS problem based on the linear regression model can be considered as a complete graph and described by an Ising model with random interactions. There are several advantages of our BIGM: it is easy to (i) employ the single-site updating and cluster updating algorithm, both of which are suitable for problems with small sample sizes and a larger number of variables, (ii) extend this approach to nonparametric regression models, and (iii) incorporate graphical prior information. In our BIGM, the interactions are determined by the linear model coefficients, so we systematically study the performance of different scale normal mixture priors for the model coefficients by adopting the global-local shrinkage strategy. Our results indicate that the best prior for the model coefficients in terms of variable selection should place substantial weight on small, nonzero shrinkage. The methods are illustrated with simulated and real data. Supplementary materials for this article are available online.     

Global dynamics of a discretized SIRS epidemic model with time delay

We derive a discretized SIRS epidemic model with time delay by applying a nonstandard finite difference scheme. Sufficient conditions for the global dynamics of the solution are obtained by improvements in discretization and applying proofs for continuous epidemic models. These conditions for our discretized model are the same as for the original continuous model.     

Building up a Sequence of Optimum Media Schedules

A mathematical model is proposed for finding the response to an advertising campaign. Although, hypothetically, there is no restriction on the media involved, the assumptions made are more suited to a campaign in newspapers or magazines, rather than, for example, on television. The deficiencies in the model are discussed, and the use of such a model is compared with the use of simulation techniques. Two previous attempts to optimize similar models are discussed, and a technique for building up a sequence of optimum schedules with an example and a proof of the optimum properties are presented.     

An agent-based model of supply chains with dynamic structures

This paper proposes a common agent-based model for the simulation of MTS and MTO supply chains with dynamic structures. Based on the model, scholars can model supply chains easily. Basic characters of supply chains are proposed in the model. Agents, who are used to simulate the members of supply chains, produce appropriate products by intelligent choices. The relationships among agents are connected by their products. Different agents’ attributes are presented by their knowledge and actions of agents are introduced in the paper. Experiments are produced to show the availability of the agent-based model. The model should be available as a toolkit for the studying of dynamic supply chains.     

Chaotic dynamics of a discrete prey–predator model with Holling type II

A discrete-time prey–predator model with Holling type II is investigated. For this model, the existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase portraits and Lyapunov exponents are obtained for different parameters of the model. The fractal dimension of a strange attractor of the model was also calculated. Numerical simulations show that the discrete model exhibits rich dynamics compared with the continuous model, which means that the present model is a chaotic, and complex one.     

Models for optimal harvest with convex function of growth rate of a population

Two models for growth of a population, which are described by a Cauchy problem for an ordinary differential equation with right-hand side depending on the population size and time, are investigated. The first model is time-discrete, i.e., the moments of harvest are fixed and discrete. The second model is time-continuous, i.e., a crop is harvested continuously in time. For autonomous systems, the second model is a particular case of the variational model for optimal control with constraints investigated in [1]. However, the prerequisites and the method of investigation are somewhat different, for they are based on Lemma1 presented below. In this paper, the existence and uniqueness theorem for the solution of the discrete and continuous problems of optimal harvest is proved, and the corresponding algorithms are presented. The results obtained are illustrated by a model for growth of the light-requiring green alge Chlorella. Bibliography: 6 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 77, 1993, pp. 75–86.     

Managing longevity and disability risks in life annuities with long term care

The aim of the paper is twofold. Firstly, it develops a model for risk assessment in a portfolio of life annuities with long term care benefits. These products are usually represented by a Markovian Multi-State model and are affected by both longevity and disability risks. Here, a stochastic projection model is proposed in order to represent the future evolution of mortality and disability transition intensities. Data from the Italian National Institute of Social Security (INPS) and from Human Mortality Database (HMD) are used to estimate the model parameters. Secondly, it investigates the solvency in a portfolio of enhanced pensions. To this aim a risk model based on the portfolio risk reserve is proposed and different rules to calculate solvency capital requirements for life underwriting risk are examined. Such rules are then compared with the standard formula proposed by the Solvency II project.     

Simultaneous estimation of the origin–destination matrices and the parameters of a nested logit model in a combined network equilibrium model

This paper deals with the inverse problem of a type of traffic equilibrium models with combined modes. This problem consists of obtaining a parametrization of the equilibrium model from a set of observations of the outputs for the model. The inputs for the model are an origin–destination (O–D) trip matrix for the various alternatives that have been considered, and a set of parameters for a nested logit model used as a demand model.     

Forecast-driven model for prepositioning supplies in preparation for a foreseen hurricane

In this paper, we present a forecast-driven dynamic model for prepositioning relief items in preparation for a foreseen hurricane. Our model uses forecast advisories issued by the National Hurricane Center (NHC), which are issued every 6?h. Every time a new advisory is issued with updated information, our model determines the amount and location of units to be prepositioned and it also re-prepositions already prepositioned units. The model also determines the best time for starting the prepositioning activities. Our approach uses a combination of Decision Theory and stochastic programming. The outcomes of our model are presented in a way that could be easily understood by humanitarian practitioners who are ultimately the ones who would use and apply our model.     

Reduced order dynamic model of the flat-plate solar collector

Padé approximation techniques are applied to obtain a reduced order dynamic model for the partial differential system representing the dynamic behaviour of the flat-plate solar collector. According to a prespecified accuracy, the collector is divided into n sections. At any position along each section the reduced order dynamic model is decoupled second order state equation, the input of which is the output of the preceding section. Numerical solutions obtained from the reduced order dynamic model are in very close agreement with the exact solution. Moreover, the computational efforts as well as the computer storage requirements are considerably reduced in comparison with other methods.The results obtained from the dynamic model are compared with those based on a simple steady-state model. The comparison reveals that the steady-state expression may only be used for collectors having a low thermal inertia and a high fluid-stream heat capacity.     

Efficient stochastic model for the point kinetics equations

A new stochastic model for the point kinetics equations with I-delayed neutron precursor groups is presented. In this stochastic model, the point kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and external neutrons source. The matrix form of the efficient stochastic model is solved by a semi-analytical method. The semi-analytical method is based on the exponential function of the coefficient matrix. The eigenvalues of the coefficient matrix and Gaussian elimination are used to calculate this exponential function. The mean and standard deviation of neutron and precursor populations of the efficient stochastic model with step, ramp, and sinusoidal reactivities are computed. The results of the efficient stochastic model are compared with the results of Allen's stochastic model for the point kinetics equations. This comparison confirms that the efficient stochastic model is an accurate model compared with the deterministic point kinetics equations. This stochastic model is efficient to study the natural behavior of neutron and precursor populations in the nuclear reactor dynamics.