Calibrating a large network model describing the transmission dynamics of the human papillomavirus (HPV) using a Particle Swarm Optimization (PSO) algorithm in a distributed computing environment

[EN] Working in large networks applied to epidemiological-type models has led us to design a simple but e↵ective computed distributed environment to perform a large amount of model simulations in a reasonable time in order to study the behavior of these models and to calibrate them. Finding the model parameters that best fit the available data in the designed distributed computing environment becomes a challenge and it is necessary to implement reliable algorithms for model calibration. In this paper, we have adapted the random PSO algorithm to our distributed computing environment to be applied to the calibration of a Papillomavirus transmission dynamics model on a lifetime sexual partners network. And we have obtained a good fitting saving time and calculations compared with the exhaustive searching strategy we have been using so far.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work has been partially supported by the Ministerio de Economa y Competitividad Grants MTM2013-41765-P and TIN 2014-54806-R.Acedo Rodríguez, L.; Burgos-Simon, C.; Hidalgo, J.; Sánchez-Alonso, V.; Villanueva Micó, RJ.; Villanueva-Oller, J. (2018). Calibrating a large network model describing the transmission dynamics of the human papillomavirus (HPV) using a Particle Swarm Optimization (PSO) algorithm in a distributed computing environment. International Journal of High Performance Computing Applications. 32(5):721-728. https://doi.org/10.1177/1094342017697862S721728325Acedo, L., Lamprianidou, E., Moraño, J.-A., Villanueva-Oller, J., & Villanueva, R.-J. (2015). Firing patterns in a random network cellular automata model of the brain. Physica A: Statistical Mechanics and its Applications, 435, 111-119. doi:10.1016/j.physa.2015.05.017Acedo, L., Moraño, J.-A., Villanueva, R.-J., Villanueva-Oller, J., & Díez-Domingo, J. (2011). Using random networks to study the dynamics of respiratory syncytial virus (RSV) in the Spanish region of Valencia. Mathematical and Computer Modelling, 54(7-8), 1650-1654. doi:10.1016/j.mcm.2010.11.068Castellsagué, X., Iftner, T., Roura, E., Vidart, J. A., Kjaer, S. K., … Bosch, F. X. (2012). Prevalence and genotype distribution of human papillomavirus infection of the cervix in Spain: The CLEOPATRE study. Journal of Medical Virology, 84(6), 947-956. doi:10.1002/jmv.23282Cortés, J.-C., Colmenar, J.-M., Hidalgo, J.-I., Sánchez-Sánchez, A., Santonja, F.-J., & Villanueva, R.-J. (2016). Modeling and predicting the Spanish Bachillerato academic results over the next few years using a random network model. Physica A: Statistical Mechanics and its Applications, 442, 36-49. doi:10.1016/j.physa.2015.08.032Elbasha, E. H., Dasbach, E. J., & Insinga, R. P. (2007). Model for Assessing Human Papillomavirus Vaccination Strategies. Emerging Infectious Diseases, 13(1), 28-41. doi:10.3201/eid1301.060438González-Parra, G., Villanueva, R.-J., Ruiz-Baragaño, J., & Moraño, J.-A. (2015). Modelling influenza A(H1N1) 2009 epidemics using a random network in a distributed computing environment. Acta Tropica, 143, 29-35. doi:10.1016/j.actatropica.2014.12.008Khemka, N., & Jacob, C. (2010). Exploratory Toolkit for Evolutionary and Swarm-Based Optimization. The Mathematica Journal, 11(3), 376-391. doi:10.3888/tmj.11.3-

Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty

[EN] Recently, the transmission dynamics of the Human Papillomavirus (HPV) has been studied. In previous works, we have designed and implemented a computational model (agent-based simulation model) where the contagion of the HPV is described on a network of lifetime sexual partners. The run of a single simulation of this computational model, composed of a network with 500 000 nodes, takes about one hour and a half. In addition to set an adequate model, finding out the model parameters that best fit the proposed model to the available data of prevalence is a crucial goal. Taking into account that the necessary number of simulations to perform the calibration of the model may be very high, the aforementioned goal may become unaffordable. In this paper, we present a procedure to fit the proposed HPV model to the available data and the design of an asynchronous version of the Particle Swarm Optimization (PSO) algorithm adapted to the distributed computing environment. In the process, the number of particles used in PSO should be set carefully looking for a compromise between quality of the solutions and computation time. Another feature of the procedure presented here is that we want to capture the intrinsic uncertainty in the data (data come from a survey) when calibrating the model. To do so, we also propose the design of an algorithm to select the model parameter sets obtained during the calibration that best capture the data uncertainty.This work has been supported by the Spanish Ministerio de Economia y Competitividad grants MTM2017-89664-P, TIN2014-54806-R and RTI2018-095180-B-I00, Grants Y2018/NMT-4668 (Micro-Stres-MAP-CM) and GenObIA-CM (S2017/BMD-3773) financed by the Community of Madrid, Spain and co-financed with EU Structural Funds, Spain, and by GLENO project financed by Fundacion Eugenio Rodriguez Pascual, Spain.Villanueva Micó, RJ.; Hidalgo, J.; Cervigon, C.; Villanueva-Oller, J.; Cortés, J. (2019). Calibration of an agent-based simulation model to the data of women infected by Human Papillomavirus with uncertainty. Applied Soft Computing. 80:546-556. https://doi.org/10.1016/j.asoc.2019.04.015S5465568

Building networks of sexual partners. Application for the study of the transmission dynamics of Human Papillomavirus (HPV)

[ES] Desde tiempos inmemorables en la historia de la humanidad las enfermedades de transmisión sexual (ETSs) han sido una gran amenaza para la salud pública. Las preocupaciones comienzan en la edad moderna con pandemias tales como la sífilis, cuya propagación ocurre en Europa a comienzos del siglo XVI. El virus de papiloma humano (VPH) es la causa directa de más de medio millón de casos nuevos de cáncer de cuello de útero, el segundo más maligno entre mujeres y una de las principales causas de muerte por cáncer en todo el mundo. Además causa verrugas anogenitales y otras enfermedades relacionadas. En este trabajo estudiamos el contagio del VPH en una red de contactos sexuales. Para predecir la evolución de este tipo de enfermedades, necesitamos un modelo fiable de la red social subyacente sobre el que la infección prolifera. Hemos construido una red de parejas sexuales durante toda la vida basada en datos demográficos y encuestas sobre hábitos sexuales. La mayoría de los enfoques para modelizar ETSs por lo general y del VPH en particular, se hacen usando modelos clásicos donde la hipótesis de mezcla homogénea (todo el mundo puede transmitir a todo el mundo) es asumida de manera implícita. Sin embargo, la mezcla homogénea no es una hipótesis razonable y las consecuencias de estas suposiciones se ven de hecho, en que los efectos de los calendarios de vacunación contra el VPH se detectan en Australia mucho antes de lo que los modelos clásicos predijeron. Hay un debate sobre la conveniencia de la vacunación de los niños. Elbasha et al. encontraron evidencias de que la vacunación en niños podría llegar a ser coste-efectiva. En nuestro modelo consideramos poblaciones tanto de hombres que solo tienen relaciones con mujeres y que las tienen entre ellos, permitiéndonos sacar conclusiones al respecto. Con nuestro modelo simulamos y llevamos a cabo campañas de vacunación de modo que podemos sacar conclusiones atendiendo a las mejores estrategias. Estos resultados pueden ayudar a los responsables de Salud Pública a tomar decisiones apropiadas con respecto al VPH.[CA] Des de temps inmemorables en la història de la humanitat les malalties de transmissió sexual (MTSs) han sigut una gran amenaça per a la salut pública. Les preocupacions comencen en l'edat moderna amb pandèmies com ara la sífilis, la propagació de la qual ocorre a Europa al començament del segle XVI. El virus de papilloma humà (VPH) és el causant directe de més de mig milió de casos nous de càncer de coll d'úter, el segon mes maligne entre dones i una de les principals causes de mort per càncer en tot el món. A més causa berrugues anogenitales i altres malalties relacionades. En este treball estudiem la dinàmica de transmissió del VPH en una xarxa de contactes sexuals. Per a predir l'evolució d'este tipus de malalties, necessitem un model fiable de la xarxa social subjacent sobre la qual la infecció prolifera. Hem construït un xarxa de parelles sexuals durant tota la vida basada en dades demogràfiques i enquestes sobre hàbits sexuals. La majoria dels enfocaments per a modelizar MTSs generalment i del VPH en particular, es fan usant models clàssics on la hipótesi de mescla homogènia (tot el món pot transmetre a tot el món) és assumida de manera implícita. No obstant això la mescla homogènia no és una hipòtesi raonable i les conseqüències d'estes suposicions es veuen de fet, en que els efectes dels calendaris de vacunació contra el VPH es detecten a Austràlia molt abans del que els models clàssics van predir.[EN] Sexually transmitted diseases (STDs) have been a major public health threat for a long time in human history. Modern concerns about STD began with the pandemic of syphilis which spread over Europe in the early sixteenth century. The human papillomavirus (HPV) is the direct cause of more than half million new cases of cervical cancer, the second most common malignancy among women and a leading cause of cancer death worldwide. It also causes anogenital warts and other related diseases. In this work we have studied the transmission dynamics of HPV over a sexual contacts network. In order to predict the evolution of these kind of diseases, we need a reliable model of the underlying social network in which the infection spreads. We have built a lifetime sexual partners (LSP) network based on demographic data and surveys about sexual habits. Most of the modeling approaches to STD in general and HPV in particular, are done using classical models where the hypothesis of homogeneous mixing (everybody can transmit a disease to everybody) is assumed. However, homogeneous mixing is not a reasonable hypothesis and consequences of this assumption can be seen, for instance, in that the effects of vaccination schedules against HPV have been detected in Australia much sooner than what the classical models predicted. There is a debate concerning the vaccination of young men. Elbasha et al. found some evidences that the vaccination of boys could also be cost-effective. In our model we consider both heterosexual men, and men who have sex with men (MSM) populations and the connections among them letting us to study this matter. With our model simulate and carry out vaccination campaigns in order to figure out the best strategies. All these results can be useful for policy makers in Public Health to make appropriate decisions respect to HPV.Sánchez Alonso, V. (2019). Building networks of sexual partners. Application for the study of the transmission dynamics of Human Papillomavirus (HPV) [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/124344TESI

Modelling the dynamics of frequent users of electronic commenrce in Spain using optimization techniques for inverse problems with uncertainty

[EN] In this paper, we retrieve data about the frequent users of electronic commerce during the period 2011-2016 from the Spanish National Institute of Statistics. These data,coming from surveys, have intrinsic uncertainty that we describe using appropriate random variables. Then, we propose a stochastic model to study the dynamics of frequent users of electronic commerce. The goal of this paper is to solve the inverse problem that consists of determining themodel parameters as suitable parametric random variables, in such a way the model output be capable of capturing the data uncertainty, at the time instantswhere sample data are available, via adequate probability density functions. To achieve the aforementioned goal, we propose a computational procedure that involves building a nonlinear objective function, based on statistical moment measures, to be minimized using a variation of the particle swarm optimization algorithm.This work has been supported by the Ministerio de Economía, Industria y Competitividad Grant MTM2017-89664-P.Burgos-Simon, C.; Cortés, J.; Lombana, IC.; Martínez Rodríguez, D.; Villanueva Micó, RJ. (2018). Modelling the dynamics of frequent users of electronic commenrce in Spain using optimization techniques for inverse problems with uncertainty. Journal of Optimization Theory and Applications. 158(3):1-12. https://doi.org/10.1007/s10957-018-1382-6S1121583Dorini, F.A., Cecconello, M.S., Dorini, M.B.: On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density. Commun. Nonlinear Sci. Numer. Simul. 33, 160–173 (2016). https://doi.org/10.1016/j.cnsns.2015.09.009Hussein, A., Selim, M.M.: Solution of the stochastic radiative transfer equation with Rayleigh scattering using RVT technique. Appl. Math. Comput. 218(13), 7193–7203 (2012). https://doi.org/10.1016/j.amc.2011.12.088Dorini, F., Cunha, M.: Statistical moments of the random linear transport equation. J. Comput. Phys. 227(19), 8541–8550 (2008). https://doi.org/10.1016/j.jcp.2008.06.002Xu, Z., Tipireddy, R., Lin, G.: Analytical approximation and numerical studies of one-dimensional elliptic equation with random coefficients. Appl. Math. Model. 40(9–10), 5542–5559 (2016). https://doi.org/10.1016/j.apm.2015.12.04Mourad, K., Debbouche, A.: Complete controllability of nonlocal fractional stochastic differential evolution equations with Poisson jumps in Hilbert spaces. Int. J. Adv. Appl. Math. Mech. 3(1), 41–48 (2015)Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: A comprehensive probabilistic solution of random SIS-type epidemiological models using the random variable transformation technique. Commun. Nonlinear Sci. Numer. Simul. 32, 199–210 (2016). https://doi.org/10.1016/j.cnsns.2015.08.009Casabán, M.C., Cortés, J.C., Navarro-Quiles, A., Romero, J.V., Roselló, M.D., Villanueva, R.J.: Computing probabilistic solutions of the Bernoulli random differential equation. J. Comput. Appl. Math. 309, 396–407 (2017). https://doi.org/10.1016//j.cam.2016.02.034Cortés, J.C., Santonja, F.J., Tarazona, A.C., Villanueva, R.J., Villanueva-Oller, J.: A probabilistic estimation and prediction technique for dynamic continuous social science models: the evolution of the attitude of the basque country population towards ETA as a case study. Appl. Math. Comput. 264, 13–20 (2015). https://doi.org/10.1016/j.amc.2015.03.128Spanish INE: Encuesta sobre equipamiento y uso de tecnologías de información y comunicación en los hogares (Survey on equipment and use of the information technologies and communication in the household. http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736176741&menu=resultados&idp=1254735576692 . Accessed 20 June 2018Spanish INE: Indicadores demográficos básicos (Basic demographic indicators). http://www.ine.es/dyngs/INEbase/es/operacion.htm?c=Estadistica_C&cid=1254736177003&menu=resultados&idp=1254735573002 . Accessed 20 June 2018Christakis, N.A., Fowler, J.H.: Connected: The Surprising Power of Our Social Networks and How They Shape Our Lives. Little, Brown and Company, Boston (2009)Brauer, F., Castillo-Chávez, C.: Mathematical Models in Population Biology and Epidemiology. Springer, New York (2001). https://doi.org/10.1007/978-1-4757-3516-1Norman, L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions. Wiley, London (1994)Khemka, N., Jacob, C.: Exploratory toolkit for evolutionary and swarm-based optimization. Math. J. 11(3), 376–391 (2010). https://doi.org/10.3888/tmj.11.3-5Acedo, L., Burgos, C., Hidalgo, J.I., Sánchez-Alonso, V., Villanueva, R.J., Villanueva-Oller, J.: Calibrating a large network model describing the transmission dynamics of the human papillomavirus using a particle swarm optimization algorithm in a distributed computing environment. Int. J. High Perf. Comput. Appl. (2017). https://doi.org/10.1177/109434201769786

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

Diffusion of tin from TEC-8 conductive glass into mesoporous titanium dioxide in dye sensitized solar cells

The photoanode of a dye sensitized solar cell is typically a mesoporous titanium dioxide thin film adhered to a conductive glass plate. In the case of TEC-8 glass, an approximately 500 nm film of tin oxide provides the conductivity of this substrate. During the calcining step of photoanode fabrication, tin diffuses into the titanium dioxide layer. Scanning Electron Microscopy and Electron Dispersion Microscopy are used to analyze quantitatively the diffusion of tin through the photoanode. At temperatures (400 to 600 °C) and times (30 to 90 min) typically employed in the calcinations of titanium dioxide layers for dye sensitized solar cells, tin is observed to diffuse through several micrometers of the photoanode. The transport of tin is reasonably described using Fick\u27s Law of Diffusion through a semi-infinite medium with a fixed tin concentration at the interface. Numerical modeling allows for extraction of mass transport parameters that will be important in assessing the degree to which tin diffusion influences the performance of dye sensitized solar cells