Parameter identification and estimation for stage-structured population models

[EN] A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.This work has been partially supported by the Spanish grant MTM2013-43678-P.Coll, C.; Sánchez, E. (2019). Parameter identification and estimation for stage-structured population models. International Journal of Applied Mathematics and Computer Science. 29(2):327-336. https://doi.org/10.2478/amcs-2019-0024S32733629

Quarantine in an epidemic model with seasonality

[EN] In this work, we focus on the periodicity of recurrent epidemic patterns and propose a periodic model that includes quarantine as a control strategy. So, we consider that susceptible individuals can be quarantined (Q) and then return to the recovered class once it is determined that they are not infected. We use the basic reproductive number R0 to analyze the spread of the disease. To study the effectiveness of quarantine in the spread of the disease, a new parameter Rq is introduced. This is defined as the average number of new infections that a case generates, in a totally susceptible population when quarantine is applied to individuals during the time they are infectious. The value of Rq will be closely related to both the intensity of the intervention and the severity of the epidemic in the absence of such intervention. The behavior in absence of control will be determined by the value of the basic reproductive number R-0.This work is supported by Spanish Grant MTM2013-43678-P.Coll, C.; Sánchez, E. (2019). Quarantine in an epidemic model with seasonality. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 114(1):1-12. https://doi.org/10.1007/s13398-019-00753-xS112114

An N-periodic control for coupled systems

[EN] This paper analyses the stabilisation of two coupled systems described by difference equations via an N-periodic feedback control. For this, it is considered a discrete-time approach with two compartmental systems, where each system has communication with the other one. An N-periodic controller is proposed to attenuate the interconnections affecting to stability of the process. It is designed so in each interval of amplitude N, the control is only added at initial time and there is no control in the rest of the time. This feedback control ensures the stability of the closed-loop system. Finally, an example is given to illustrate the theoretical results.MINECO/MTM2013-43678-PColl, C.; Sánchez, E. (2018). An N-periodic control for coupled systems. International Journal of Systems Science. 49(5):1040-1046. https://doi.org/10.1080/00207721.2018.1441468S1040104649

Discrete mathematical models in the analysis of splitting iterative methods for linear systems

AbstractSplitting methods are used to solve most of the linear systems, Ax=b, when the conventional method of Gauss is not efficient. These methods use the factorization of the square matrix A into two matrices M and N as A=M−N where M is nonsingular. Basic iterative methods such as Jacobi or Gauss–Seidel define the iterative scheme for matrices that have no zeros along its main diagonal.This paper is concerned with the development of an iterative method to approximate solutions when the coefficient matrix A has some zero diagonal entries. The algorithm developed in this paper involves the analysis of a discrete-time descriptor system given by the equation Me(k+1)=Ne(k), e(k) being the error vector

Weighted G-Drazin inverses and a new pre-order on rectangular matrices

[EN] This paper deals with weighted G-Drazin inverses, which is a new class of matrices introduced to extend (to the rectangular case) G-Drazin inverses recently considered by Wang and Liu for square matrices. First, we define and characterize weighted G-Drazin inverses. Next, we consider a new pre-order defined on complex rectangular matrices based on weighted G-Drazin inverses. Finally, we characterize this pre-order and relate it to the minus partial order and to the weighted Drazin pre-order. (C) 2017 Elsevier Inc. All rights reserved.This paper was partially supported by Universidad Nacional de La Pampa, Facultad de Ingenieria, grant resol. no. 155/14. The first and third authors were partially supported by Ministerio de Economia y Competitividad of Spain (grant no. DGI MTM2013-43678-P) and the third author was also partially supported by Ministerio de Economia y Competitividad of Spain (Red de Excelencia MTM2015-68805-REDT).Coll, C.; Lattanzi, M.; Thome, N. (2018). Weighted G-Drazin inverses and a new pre-order on rectangular matrices. Applied Mathematics and Computation. 317:12-24. https://doi.org/10.1016/j.amc.2017.08.047S122431

Structured parametric epidemic models

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton-Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number Script capital R-0 and the stability of the model in the equilibrium is studied using Script capital R-0 in terms of the model parameters.This work has been partially supported by MTM2010-18228. The authors wish to express their thanks to the reviewers for helpful comments and suggestions.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2014). Structured parametric epidemic models. International Journal of Computer Mathematics. 91(2):188-197. https://doi.org/10.1080/00207160.2013.800864188197912Allen, L. J. S., & Thrasher, D. B. (1998). The effects of vaccination in an age-dependent model for varicella and herpes zoster. IEEE Transactions on Automatic Control, 43(6), 779-789. doi:10.1109/9.679018Ben-Zvi, A., McLellan, P. J., & McAuley, K. B. (2004). Identifiability of Linear Time-Invariant Differential-Algebraic Systems. 2. The Differential-Algebraic Approach. Industrial & Engineering Chemistry Research, 43(5), 1251-1259. doi:10.1021/ie030534jBoyadjiev, C., & Dimitrova, E. (2005). An iterative method for model parameter identification. Computers & Chemical Engineering, 29(5), 941-948. doi:10.1016/j.compchemeng.2004.08.036Cantó, B., Coll, C., & Sánchez, E. (2011). Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations. Mathematical Problems in Engineering, 2011, 1-12. doi:10.1155/2011/510519Cao, H., & Zhou, Y. (2012). The discrete age-structured SEIT model with application to tuberculosis transmission in China. Mathematical and Computer Modelling, 55(3-4), 385-395. doi:10.1016/j.mcm.2011.08.017Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28(4). doi:10.1007/bf00178324Dion, J.-M., Commault, C., & van der Woude, J. (2003). Generic properties and control of linear structured systems: a survey. Automatica, 39(7), 1125-1144. doi:10.1016/s0005-1098(03)00104-3Emmert, K. E., & Allen, L. J. S. (2004). Population Persistence and Extinction in a Discrete-time, Stage-structured Epidemic Model. Journal of Difference Equations and Applications, 10(13-15), 1177-1199. doi:10.1080/10236190410001654151Farina, L., & Rinaldi, S. (2000). Positive Linear Systems. doi:10.1002/9781118033029Van den Hof, J. M. (1998). Structural identifiability of linear compartmental systems. IEEE Transactions on Automatic Control, 43(6), 800-818. doi:10.1109/9.679020T. Kailath,Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.Li, C.-K., & Schneider, H. (2002). Applications of Perron-Frobenius theory to population dynamics. Journal of Mathematical Biology, 44(5), 450-462. doi:10.1007/s002850100132Li, X., & Wang, W. (2005). A discrete epidemic model with stage structure☆. Chaos, Solitons & Fractals, 26(3), 947-958. doi:10.1016/j.chaos.2005.01.063Ma, J., & Earn, D. J. D. (2006). Generality of the Final Size Formula for an Epidemic of a Newly Invading Infectious Disease. Bulletin of Mathematical Biology, 68(3), 679-702. doi:10.1007/s11538-005-9047-7Wang, W., & Zhao, X.-Q. (2004). An epidemic model in a patchy environment. Mathematical Biosciences, 190(1), 97-112. doi:10.1016/j.mbs.2002.11.00

Epidemic dynamics of an infection through the pathogen density in the environment

[EN] We propose a mathematical model for the indirect transmission via a contaminated environment by a disease agent and we analyze the possibility that the initial infection can spread in the population. We have used the significance of the basic reproduction number, since the disease free state is either stable or unstable depending on its value, to obtain an explicit expression for $R_0$. This expression is found to give threshold conditions for the stability of the disease- free equilibrium or the existence of an endemic equilibrium in a population.This research was partially supported by Ministerio de Economia y Competitividad under grant MTM2013-43678-P.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2016). Epidemic dynamics of an infection through the pathogen density in the environment. Proceeding of the Bulgarian Academy of Sciences. 69(7):835-844. http://hdl.handle.net/10251/99651S83584469

Stage-Structured Periodic Population Model for the Florida Leafwing

The Florida leafwing is an endemic butterfly which is distributed in South Florida and the lower Keys. Stage-structured population models are a useful tool for the management and conservation of Florida leafwing. In this work we use a discrete-time periodic control system for describing a leafwing population. One of the main differences between this model and classical stage-structured models is that in the current model we can alter the number of adults contributing to eggs production. This allows us to control the population. The solution of the problem is obtained using invariant formulations of positive periodic systems.Coll, C.; Horvitz, CC.; Mcelderry, R. (2012). Stage-Structured Periodic Population Model for the Florida Leafwing. International Journal of Complex Systems in Science. 2(1):1-5. http://hdl.handle.net/10251/80716S152

Análisis del proceso de aplicación de un programa de competencia familiar en el ámbito de protección de menores

El Grupo de Investigación y de Formación Educativa y Social de la UIB ha adaptado el Programa de competencia familiar (Strengthening Families Program) desarrollado por la doctora K. Kumpfer, de la Universidad de Utah para su aplicación con diversos colectivos en situación de riesgo por problemas de consumo de drogas y/o dificultades sociales. Este programa persigue reducir los factores de riesgo y reforzar los factores de protección en los hijos e hijas, fomentando la normalidad en las relaciones paterno-filiales. Desde el año 2005 el Grupo GIFES de la UIB ha realizado diversas aplicaciones del PCF en colaboración con Proyecto Hombre y con centros de servicios sociales de diferentes municipios de la comunidad autónoma de las Islas Baleares. Ha sido en el año 2009 cuando se ha aplicado por primera vez con familias que están siendo tuteladas en el marco de la Dirección General de Menores del Govern de les Illes Balears. En la comunicación presentamos el análisis del proceso de esta aplicación de carácter experimental. Las características del entorno de la intervención se reflejan en las necesidades de las familias participantes. La tipología de familias, su situación de desestructuración familiar y los estilos educativos a menudo negligentes son aspectos que suman a situaciones de analfabetismo funcional y otras necesidades básicas no cubiertas (de pensiones, salarios y/o vivienda). Por otra parte, la necesaria coordinación entre los profesionales del programa y los técnicos referentes de cada familia, nos obliga a estudiar fórmulas de coordinación más efectivas que se adapten a las características organizativas del propio departamento de menores y a los requerimientos del programa para la consecución de los objetivos y resultados previstos. No obstante, se pueden destacar diferentes aspectos del programa y del proceso de implementación del mismo, que han reforzado y mantenido la participación de las familias, y los cambios funcionales que se han producido en el seno de las mismas.The Socio-Educational Training and Research Group (GIFES)2 at the UIB has adapted the Strengthening Families Program developed by Dr. K. Kumpfer of the University of Utah in order to apply it to different collectives at risk of problems related to drug consumption and/or social difficulties. This program aims to reduce children’s risk factors and reinforce protection factors, fostering normal parent- child relations. Since 2005, the GIFES group at the UIB has been implementing different applications of the FPC in collaboration with Proyecto Hombre and social service centres in different municipalities in the Autonomous Community of the Balearic Islands. 2009 was the year in which the program was applied for the first time with families who are under the tutelage of the Balearic Government’s General Directorate for Minors. This paper analyses the process of this experimental application. The characteristics of the intervention setting reflect the participating families’ needs. The types of families, their dysfunctional family situations and often negligent educational style are aspects that join situations of functional illiteracy and other unmet basic needs (pensions, salaries and/or housing). In turn, the coordination needed among the program’s professionals and each family’s referring technicians obliges us to study more effective coordination formulas that adapt to the organisational characteristics of the Department of Minors itself and to the program requirements to achieve the foreseen outcomes and objectives. Nevertheless, different aspects of the program and the process of its implementation that reinforced and maintained the participation of the families and functional changes that have taken place within them can be highlighted.peerReviewe

Superficies químicamente modificadas para la detección colorimétrica y eliminación de aniones de interés medioambiental en aguas

La presente tesis se ha desarrollado combinando conceptos de química supramolecular y ciencia de los materiales. En concreto, se planteó la Tesis Doctoral sobre la idea de desarrollar sensores sobre superficies silíceas para detectar especies de interés ambiental. En primer lugar, se ha llevado a cabo el desarrollo de un nuevo método colorimétrico en dos pasos para la detección de surfactantes aniónicos en aguas, en el cual no es necesario el uso de disolventes clorados. Para ello, se ha diseñado y preparado un sólido silíceo funcionalizado con una unidad coordinante de aniones como es el grupo imidazol. Tras producirse la interacción de dichas unidades con los surfactantes aniónicos, en un segundo paso se produce la extracción de un colorante desde la disolución al sólido preparado. La coloración del sólido es función de la concentración de surfactante presente en la muestra inicial, por lo que permite la detección a simple vista de la presencia de surfactantes en una muestra. En vista de los resultados obtenidos, se diseñó un nuevo material que fuera capaz de determinar surfactantes catiónicos. Para ello, se utilizó como unidad coordinante un derivado con un grupo sulfonato. Además de realizar un estudio de la respuesta de dichos materiales y la caracterización de los mismos, se han analizado muestra reales que indica la viabilidad de dichos sistemas para la detección de surfactantes. Basándose en los resultados anteriores, en segundo lugar se planteó la posibilidad de diseñar y preparar un material capaz de retener y eliminar surfactantes aniónicos de muestras acuosas. Se trabaja en este caso con sólidos mesoporosos que presentan una mayor superficie específica, lo que permite el anclaje de un mayor número de unidades coordinantes y por tanto eliminar mayor cantidad de surfactantes. Se estudió la capacidad de retención de los materiales funcionalizados en su superficie con grupos imidazol, amina y piridina.Coll Merino, MC. (2010). Superficies químicamente modificadas para la detección colorimétrica y eliminación de aniones de interés medioambiental en aguas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8723Palanci