Numerical methods and mathematical modelling in biology, medicine and social sciences

It is with pleasure that we offer the readers of the International Journal of Computer Mathematics this special issue consisting of some of the most significant contributions to computational methods and mathematical modelling with applications in biology, medicine and social sciences presented at the International Conference on Mathematical Modelling in Engineering & Human Behaviour 2012, held at the Instituto Universitario de Matemática, Multidisciplinar, Polytechnic City of Innovation in Valencia, Spain, September 4–7, 2012, cf. http://jornadas.imm.upv.es/2012/

Since its founding the International Conference on Mathematical Modelling in Engineering & Human Behaviour has been a truly multi-disciplinary conference, covering all aspects of applied mathematics in a very broad field of areas of science and engineering with its increasing level of complexity. The aim of this conference series is to encourage cross-fertilization between different disciplines and to gain new insights into the emerging research trends in mathematical modelling and engineering methods.

In the first paper of this special issue, Solis and Gonzalez [15] consider a model for cervical cancer and propose an advection diffusion reaction model for basal cells of the cervix corresponding to different stages ranging from normal cells to the formation of precancerous lesions. A nonstandard numerical method to analyse the model is developed.

The article Structured parametric epidemic models, by Cantó et al. [3], analyses a stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages. The identifiability of the parameters allows us to determine uniquely the basic reproduction number R0 and the stability of the model in the equilibrium is studied using R0 in terms of the model parameters.

The third article, Asymptotic behaviour of a mathematical model of hematopoietic stem cell dynamics [1], deals with the asymptotic behaviour of a numerical method adapted for the solution of a mathematical model of hematopoiesis which describes the dynamics of a stem cell population.

The research by García-Mora et al. [7] is concerned with the sum of two independent phase-type (PH) distributed variables, each of them being associated with a Markovian process with one absorbing state. The obtained results are applied to bladder carcinoma data.

In the article by Náhlík and Štys, Microscope point spread function, focus and calculation of optimal microscope set-up [9], the authors propose a method for automatic focusing of the microscope by estimating the 3D distortion modelled by a Point Spread Function (PSF) approach. In their work, Predicting workaholism in Spain: a discrete mathematical model, de la Poza et al. [11] propose a discrete mathematical model to forecast the development of workaholism in Spain in the next few years. A questionnaire is used in order to measure and classify the sample in sub-populations by their level of addiction, and different economic scenarios are simulated. The authors state economic and social consequences of this addiction and suggest public health recommendations.

In Modelling the dynamics of the students’ academic performance in the German region of the North Rhine-Westphalia: an epidemiological approach with uncertainty [5], the authors develop a model based on a system of differential equations to describe the student's academic underachievement in the German region of North Rhine-Westphalia. This model allows us to forecast student academic performance by means of confidence intervals over the next few years.

In the work Application of simultaneous equation models to temporary disability prescriptions in primary health care centres [10] the authors use a structural two-equation model to explain which primary health-care centre factors impact prescriptions more. The results suggest the need to improve centres’ management (clinical guidelines) and labour market regulations, and to control the disability benefits paid.

Ribes-Giner and Fuentes-Blasco [12] by using the Structural Equation methodology measure empirically the influence of the main variables affecting the voting intentions of the electorate, taking as reference the poll results during the months preceding the 2008 American General Elections.

In the article An economic dispatch algorithm of combined cycle units, Bayón et al. [2] consider a method to solve the economic dispatch (ED) problem for thermal unit systems involving combined cycle units. The ED problem finds the optimal generation of each unit in order to minimize the total generation cost while satisfying total demand and generating capacity constraints.

Computing the so-called Pagerank in a social network is an important issue in today's highly connected societies. NewFriends: an algorithm for computing the minimum number of friends required by a user to get the highest PageRank in a social network [8] proposes a novel algorithm, based on the classical PageRank method, to determine the minimum number of new friends required by a user of a social network to become the user with the highest PageRank in the network. The authors provide some experiments based on synthetic and real data.

In Discovering social structures of influence using tweetStimuli, by Tejeda-Gómez et al. [16], the authors investigate ‘word-of-mouth’ diffusion mechanism where one message could reach large populations from individual to individual and it can influence peoples’ opinion. Microblogs, such as twitter, have become interesting platforms to study how diffusion takes place. This research is supported by a new application tweetStimuli, to visualize, identify, rank and find the local influence on twitter. This software tool is available at http://tweetstimuli.com.

The authors of Centralities of a network and its line graph: an analytical comparison by means of their irregularity [6] use the centrality of a given network to estimate the centrality and show that the error committed is bounded by some measure of the irregularity of the network. Sanchis et al. [13] analyse the so-called choice overload problem referring to the discomfort or paralysis experienced by individuals when facing a choice within a large set of alternatives. The authors introduce a rational model of time allocation to analyse how increasing the number of options may change a consumer's optimal time allocation and in turn affect his/her welfare.

In their article related to nuclear safety analysis Improvements in the decay heat model in the thermalhydraulic code TRAC-BF1, Soler et al. [14] present a novel numerical study based on the analytical resolution of the decay heat equation which takes into account the number of reactor operation histories, the number of fissionable nuclides and the number of groups per fissile. Furthermore, this work describes the influence of the short-term power histories on the total decay heat power calculation due to the high interest in the simulation of severe transients.

The research underlying the article by Chen-Charpentier and Stanescu [4] is focused on the topic errors, uncertainties and variations in mathematical models. The authors consider a system having random coefficients whose distribution and moments are unknown a priori. Next, a polynomial chaos representation is applied and the parameters can be determined by establishing the best-fit values of the random variables that represent them.

Finally, we thank all the authors and referees for their excellent contributions to this special volume. We also express our gratitude to Helen Gray and Lucy from the Taylor & Francis Group for their continuous support in preparing this special issue.