Chapter 2
Mathematical Modeling of Biosystems
Moisés Alejandro Vázquez-Cruz, Alejandro Espinosa-Calderón,
Angélica Rosario Jiménez-Sánchez and Rosario Guzmán-Cruz
Abstract Mathematics is an important tool for system modeling allows us to
describe the behavior of a phenomenon or system in the real world, in particular
biological systems. This chapter gives an overview of mathematical models, their
construction, types of models, and examples of possible applications in biosystems
models. Essential for building a model is determining its scope. In addition, the
mechanistic and phenomenological mathematical models are described. Applications on fish biomass estimation, quality of fruits and crops are presented.
Contents
2.1 Introduction....................................................................................................................... 52
2.2 Building a Mathematical Model ...................................................................................... 53
2.2.1 Definition of Objectives ....................................................................................... 53
2.2.2 Quantitative Description of Hypotheses .............................................................. 54
2.2.3 Programming......................................................................................................... 54
2.2.4 Estimating Parameters .......................................................................................... 55
2.2.5 Model Evaluation.................................................................................................. 56
M. A. Vázquez-Cruz Á A. R. Jiménez-Sánchez Á R. Guzmán-Cruz (&)
Division de Estudios de Posgrado, Facultad de ingenieria, Universidad Autónoma
de Querétaro, C.U. Cerro de las Campanas S/N, Colonia Las Campanas, 76010 Santiago
de Querétaro, QRO, Mexico
e-mail: rguzman829@hotmail.com
M. A. Vázquez-Cruz
e-mail: alexvazz@hotmail.com
A. R. Jiménez-Sánchez
e-mail: jisar2604@yahoo.com.mx
A. Espinosa-Calderón
Departamento de Ing. Eléctrica y Electrónica, Instituto Tecnológico de Celaya,
Av. Tecnológico y García Cubas S/N, 38010 Celaya, GTO, Mexico
e-mail: alejandro.espinosa@uaq.mx
R. Guevara-Gonzalez and I. Torres-Pacheco (eds.), Biosystems Engineering:
Biofactories for Food Production in the Century XXI, DOI: 10.1007/978-3-319-03880-3_2,
Ó Springer International Publishing Switzerland 2014
51
Mathematical Modeling of Biosystems
Moisés Alejandro Vázquez-Cruz, Alejandro Espinosa-Calderón,
Angélica Rosario Jiménez-Sánchez and Rosario Guzmán-Cruz
Abstract Mathematics is an important tool for system modeling allows us to
describe the behavior of a phenomenon or system in the real world, in particular
biological systems. This chapter gives an overview of mathematical models, their
construction, types of models, and examples of possible applications in biosystems
models. Essential for building a model is determining its scope. In addition, the
mechanistic and phenomenological mathematical models are described. Applications on fish biomass estimation, quality of fruits and crops are presented.
Contents
2.1 Introduction....................................................................................................................... 52
2.2 Building a Mathematical Model ...................................................................................... 53
2.2.1 Definition of Objectives ....................................................................................... 53
2.2.2 Quantitative Description of Hypotheses .............................................................. 54
2.2.3 Programming......................................................................................................... 54
2.2.4 Estimating Parameters .......................................................................................... 55
2.2.5 Model Evaluation.................................................................................................. 56
M. A. Vázquez-Cruz Á A. R. Jiménez-Sánchez Á R. Guzmán-Cruz (&)
Division de Estudios de Posgrado, Facultad de ingenieria, Universidad Autónoma
de Querétaro, C.U. Cerro de las Campanas S/N, Colonia Las Campanas, 76010 Santiago
de Querétaro, QRO, Mexico
e-mail: rguzman829@hotmail.com
M. A. Vázquez-Cruz
e-mail: alexvazz@hotmail.com
A. R. Jiménez-Sánchez
e-mail: jisar2604@yahoo.com.mx
A. Espinosa-Calderón
Departamento de Ing. Eléctrica y Electrónica, Instituto Tecnológico de Celaya,
Av. Tecnológico y García Cubas S/N, 38010 Celaya, GTO, Mexico
e-mail: alejandro.espinosa@uaq.mx
R. Guevara-Gonzalez and I. Torres-Pacheco (eds.), Biosystems Engineering:
Biofactories for Food Production in the Century XXI, DOI: 10.1007/978-3-319-03880-3_2,
Ó Springer International Publishing Switzerland 2014
51