Semi-parametric extensions of the Cairns–Blake–Dowd model: A one-dimensional kernel smoothing approach

Over the last few decades, there has been an enormous growth in mortality modeling as the field of mortality risk and longevity risk has attracted great attention from academic, government and private sectors. In this paper, we propose a time-varying coefficient (TVC) mortality model aiming to combine the good characteristics of existing models with efficient model calibration methods. Nonparametric kernel smoothing techniques have been applied in the literature of mortality modeling and based on the findings from Li et al.’s (2015) study, such techniques can significantly improve the forecasting performance of mortality models. In this study we take the same path and adopt a kernel smoothing approach along the time dimension. Since we follow the model structure of the Cairns–Blake–Dowd (CBD) model, the TVC model we propose can be seen as a semi-parametric extension of the CBD model and it gives specific model design according to different countries’ mortality experience. Our empirical study presented here includes Great Britain, the United States, and Australia amongst other developed countries. Fitting and forecasting results from the empirical study have shown superior performances of the model over a selection of well-known mortality models in the current literature.     

Hybrid approach for pest control with impulsive releasing of natural enemies and chemical pesticides: A plant–pest–natural enemy model

The agricultural pests can be controlled effectively by simultaneous use (i.e., hybrid approach) of biological and chemical control methods. Also, many insect natural enemies have two major life stages, immature and mature. According to this biological background, in this paper, we propose a three tropic level plant–pest–natural enemy food chain model with stage structure in natural enemy. Moreover, impulsive releasing of natural enemies and harvesting of pests are also considered. We obtain that the system has two types of periodic solutions: plant–pest-extinction and pest-extinction using stroboscopic maps. The local stability for both periodic solutions is studied using the Floquet theory of the impulsive equation and small amplitude perturbation techniques. The sufficient conditions for the global attractivity of a pest-extinction periodic solution are determined by the comparison technique of impulsive differential equations. We analyze that the global attractivity of a pest-extinction periodic solution and permanence of the system are evidenced by a threshold limit of an impulsive period depending on pulse releasing and harvesting amounts. Finally, numerical simulations are given in support of validation of the theoretical findings.     

From a cellular automaton model of tumor–immune interactions to its macroscopic dynamical equation: A drift–diffusion data analysis approach

Several models of tumor growth have been developed from various perspectives and for multiple scales. Due to the complexity of interactions, how the macroscopic dynamics formed by such interactions at the microscopic level is a difficult problem. In this paper, we focus on reconstructing a model from the output of an experimental model. This is carried out by the data analysis approach. We simulate the growth process of tumor with immune competition by using cellular automata technique adapted from previous studies. We employ an analysis of data given by the simulation output to derive an evolution equation of macroscopic dynamics of tumor growth. In a numerical example we show that the dynamics of tumor at stationary state can be described by an Ornstein–Uhlenbeck process. We show further how the result can be linked to the stochastic Gompertz model.     

Length of stay as a stochastic process: A general approach and application to hospitalization for schizophrenia†

A general approach to the study of length of stay (LOS) for hospitalization is presented. Data on first hospitalization for schizophrenia from the Maryland Psychiatric Case Register are applied to discussions of the Life Table and seven stochastic models of the LOS process. As far as possible, prior applications of the various models to this process are reviewed, and the models are conceptualized on the individual and aggregate level. The models are the exponential, mixed exponential, type XI, Weibull, gamma, lognormal and Inverse Gaussian. The lognormal and Inverse Gaussian show the best fits to the data in terms of the maximum absolute deviation. However, the Inverse Gaussian is superior due to its attractive statistical characterization. Special attention is given to the relatively new Inverse Gaussian, and there is a brief section on LOS and theory verification. Recommendations are made for future LOS research.     

Erratum to “A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling” [Appl. Math. Modell. 34 (2010) 655–670]

This study analyzes Mixed Integer Linear Program (MILP) proposed by G. Kannan, P. Sasikumar M. Devika, (2010) in their paper titled ‘A genetic algorithm approach for solving a closed loop supply chain model: A case of battery recycling’, Applied Mathematical Modelling, (34, 655–670). The model in Kannan et al. (2010) is found to be inadequate for the problem described. It is erroneous/infeasible in terms of constraints, objective and variables. In this work, we list down the flaws in the published work and propose modifications to rectify the flaws. The revised model is presented and illustrated using hypothetical problems.