American Institute of Mathematical Sciences

Advanced
2009, 2009(Special): 230-239. doi: 10.3934/proc.2009.2009.230

Parameter identification and quantitative comparison of differential equations that describe physiological adaptation of a bacterial population under iron limitation

Hedia Fgaier 1, and  Hermann J. Eberl 2,

1. 

Dept. Mathematics and Statistics, University of Guelph, Guelph, On, Canada, N1G 2W1, Canada
2. 

Department of Mathematics and Statistics, University of Guelph, Guelph, On, N1G 2W1, Canada

Received  August 2008 Revised  April 2009 Published  September 2009

The onset of a typical bacterial growth curve shows a period of very slow increase in population counts. This is a period of physiological adaptation to new environmental conditions. While in mathematical biology much progress was made in recent years to describe physiologically structured populations, these models typically have too many degrees of freedom to easily allow a model identification against experimental data. Therefore, and for all practical purposes, microbiologists have proposed simpler models of physiological adaptation in the past, usually in connection with standard growth curves. In this paper we compare the performance of four such lag-time models, each of which described by a scalar differential equation, when combined with a model of a siderophore producing bacterial population under iron limitation. In each case this yields a system of five nonlinear ordinary differential equations that we compare against experimental data, by solving the associated vector optimization problem. Our main finding is that a big step in accuracy is made already by including a simple lag-time model that only introduces one additional degree of freedom in the parameter identification problem (the initial state of health of the population), and that this can be reliably improved if a further degree of freedom, describing the dynamics of the physiological recovery process, is included. The vector optimization problem is solved by scalarizing it with a linear functional and solving the resulting scalar optimization problem. The growth parameters that are identified in this procedure are found to be robust with respect to the scalarization coefficient.
Keywords: Mathematical biology, computation, lag time, parameter identification.
Mathematics Subject Classification: Primary: 92D25; Secondary: 34A55.
Citation: Hedia Fgaier, Hermann J. Eberl. Parameter identification and quantitative comparison of differential equations that describe physiological adaptation of a bacterial population under iron limitation. Conference Publications, 2009, 2009 (Special) : 230-239. doi: 10.3934/proc.2009.2009.230
[1]

Edward J. Allen. Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology. Mathematical Biosciences & Engineering, 2014, 11 (3) : 403-425. doi: 10.3934/mbe.2014.11.403
[2]

Qinqin Chai, Ryan Loxton, Kok Lay Teo, Chunhua Yang. A unified parameter identification method for nonlinear time-delay systems. Journal of Industrial & Management Optimization, 2013, 9 (2) : 471-486. doi: 10.3934/jimo.2013.9.471
[3]

Eugene Kashdan, Dominique Duncan, Andrew Parnell, Heinz Schättler. Mathematical methods in systems biology. Mathematical Biosciences & Engineering, 2016, 13 (6) : i-ii. doi: 10.3934/mbe.201606i
[4]

Avner Friedman. Conservation laws in mathematical biology. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3081-3097. doi: 10.3934/dcds.2012.32.3081
[5]

Avner Friedman. PDE problems arising in mathematical biology. Networks & Heterogeneous Media, 2012, 7 (4) : 691-703. doi: 10.3934/nhm.2012.7.691
[6]

Antonio Magaña, Alain Miranville, Ramón Quintanilla. On the time decay in phase–lag thermoelasticity with two temperatures. Electronic Research Archive, 2019, 27: 7-19. doi: 10.3934/era.2019007
[7]

Monique Chyba, Benedetto Piccoli. Special issue on mathematical methods in systems biology. Networks & Heterogeneous Media, 2019, 14 (1) : ⅰ-ⅱ. doi: 10.3934/nhm.20191i
[8]

Yuepeng Wang, Yue Cheng, I. Michael Navon, Yuanhong Guan. Parameter identification techniques applied to an environmental pollution model. Journal of Industrial & Management Optimization, 2018, 14 (2) : 817-831. doi: 10.3934/jimo.2017077
[9]

Pingping Niu, Shuai Lu, Jin Cheng. On periodic parameter identification in stochastic differential equations. Inverse Problems & Imaging, 2019, 13 (3) : 513-543. doi: 10.3934/ipi.2019025
[10]

Zhuangyi Liu, Ramón Quintanilla. Time decay in dual-phase-lag thermoelasticity: Critical case. Communications on Pure & Applied Analysis, 2018, 17 (1) : 177-190. doi: 10.3934/cpaa.2018011
[11]

Lesia V. Baranovska. Pursuit differential-difference games with pure time-lag. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1021-1031. doi: 10.3934/dcdsb.2019004
[12]

Erika T. Camacho, Christopher M. Kribs-Zaleta, Stephen Wirkus. The mathematical and theoretical biology institute - a model of mentorship through research. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1351-1363. doi: 10.3934/mbe.2013.10.1351
[13]

Thorsten Hüls. Numerical computation of dichotomy rates and projectors in discrete time. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 109-131. doi: 10.3934/dcdsb.2009.12.109
[14]

Heiko Enderling, Alexander R.A. Anderson, Mark A.J. Chaplain, Glenn W.A. Rowe. Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Mathematical Biosciences & Engineering, 2006, 3 (4) : 571-582. doi: 10.3934/mbe.2006.3.571
[15]

John D. Nagy. The Ecology and Evolutionary Biology of Cancer: A Review of Mathematical Models of Necrosis and Tumor Cell Diversity. Mathematical Biosciences & Engineering, 2005, 2 (2) : 381-418. doi: 10.3934/mbe.2005.2.381
[16]

Lei Wang, Jinlong Yuan, Yingfang Li, Enmin Feng, Zhilong Xiu. Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness. Numerical Algebra, Control & Optimization, 2014, 4 (2) : 103-113. doi: 10.3934/naco.2014.4.103
[17]

Qinxi Bai, Zhijun Li, Lei Wang, Bing Tan, Enmin Feng. Parameter identification and numerical simulation for the exchange coefficient of dissolved oxygen concentration under ice in a boreal lake. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1463-1478. doi: 10.3934/jimo.2018016
[18]

Mickael Chekroun, Michael Ghil, Jean Roux, Ferenc Varadi. Averaging of time - periodic systems without a small parameter. Discrete & Continuous Dynamical Systems - A, 2006, 14 (4) : 753-782. doi: 10.3934/dcds.2006.14.753
[19]

Ling Yun Wang, Wei Hua Gui, Kok Lay Teo, Ryan Loxton, Chun Hua Yang. Time delayed optimal control problems with multiple characteristic time points: Computation and industrial applications. Journal of Industrial & Management Optimization, 2009, 5 (4) : 705-718. doi: 10.3934/jimo.2009.5.705
[20]

Ciprian Preda. Discrete-time theorems for the dichotomy of one-parameter semigroups. Communications on Pure & Applied Analysis, 2008, 7 (2) : 457-463. doi: 10.3934/cpaa.2008.7.457

 Impact Factor: 

Tools

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences