Parameter identification and estimation for stage-structured population models

• Autorzy: Coll Carmen , Sánchez Elena

Identyfikatory

DOI

10.2478/amcs-2019-0024

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

system identification; parameter estimation; dynamic population; discrete time system; rank-one matrix

PL

identyfikacja systemu; estymacja parametru; dynamika populacji; system czasu dyskretnego

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2019
• Tom: Vol. 29, no. 2
• Strony: 327--336
• Opis fizyczny: Bibliogr. 19 poz., wykr.

Twórcy

autor

Coll Carmen

• Institute of Multidisciplinary Mathematics, Polytechnic University of Valencia (UPV), Camino de Vera, 14, 46022 Valencia, Spain

autor

Sánchez Elena

• Institute of Multidisciplinary Mathematics, Polytechnic University of Valencia (UPV), Camino de Vera, 14, 46022 Valencia, Spain

Bibliografia

• [1] Baliarsingh, P. and Dutta, S. (2015). On an explicit formula for inverse of triangular matrices, Journal of the Egyptian Mathematical Society 23(1): 297–302.
• [2] Berman, A. and Plemmons, R. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA.
• [3] Boyadjiev, C. and Dimitrova, E. (2005). An iterative method for model parameter identification, Computers and Chemical Engineering 29(1): 941–948.
• [4] Cantó, B., Coll, C. and Sánchez, E. (2014). On stability and reachability of perturbed positive systems, Advances in Difference Equations 296(1): 1–11.
• [5] Cao, H. and 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.
• [6] Carnia, E., Sylviani, S., Wirmas, M. and Supriatna, A. (2015). Modeling the killer whale Orcinus orca via the Lefkovitch matrix, 3rd International Conference on Chemical, Agricultural and Medical Sciences (CAMS-2015), Singapore, pp. 18–21.
• [7] Caswell, H. (2001). Matrix Population Models: Construction, Analysis and Interpretation, Sinauer, Sunderland, MA.
• [8] Chou, I. and Voit, E. (2013). Recent developments in parameter estimation and structure identification of biochemical and genomic systems, Mathematical Biosciences 219: 57–83.
• [9] De La Sen, M. and Quesada, A. (2003). Some equilibrium, stability, instability and ocillatory results for an extended discrete epidemic model with evolution memory, Advances in Difference Equations 2013: 234.
• [10] Dion, J.M., Commault, C. and van der Woude, J. (2003). Generic properties and control of linear structured systems: A survey, Automatica 39: 1125–1144.
• [11] Emmert, H. and Allen, L. (2004). Population persistence and extinction in a discrete-time, stage-structured epidemic model, Journal of Difference Equations and Applications 10(13–15): 1177–1199.
• [12] Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.
• [13] Kajin, M., Almeida, P., Vieira, M. and Cerqueira, R. (2012). The state of the art of population projection models: From the Leslie matrix to evolutionary demography, Oecologia Australis 16(3): 13–22.
• [14] Lefkovitch, L. (1965). The study of population growth in organisms grouped by stages, Biometrika 21(1): 1–18.
• [15] Leslie, P.H. (1948). Some further notes on the use of matrices in population mathematics, Biometrika 35(3–4): 213–245.
• [16] Li, C. and Schneider, H. (2002). Applications of Perron–Frobenius theory to population dynamics, Journal Mathematical Biology 44(5): 450–462.
• [17] Li, X. and Wang, W. (2006). A discrete epidemic model with stage structure, Chaos Solitons and Fractals 26(3): 947–958.
• [18] Ljung, L. and Soderstrom, T. (1983). Theory and Practice of Recursive Identification, MIT Press, Cambridge, MA.
• [19] Verdière, N., Denis-Vidal, L., Joly-Blanchard, G. and Domurado, D. (2005). Identifiability and estimation of pharmacokinetic parameters for the ligands of the macrophage mannose receptor, International Journal Applied Mathematics and Computer Science 15(4): 517–526.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).