Mathematical analysis of a food chain: prey - predator - biological control


  • Jhelly Pérez Núñez
  • Roxana López Cruz



Predator - Prey, Food Chain, Biological Control, Scenarios Extinction, Asymptotic Stability, Runge - Kutta


In this work, we present the dynamics of biological control through a mathematical model using a simple food chain of three trophic levels. This mathematical model is based on a ratio-dependent predator-prey model with Holling type II functional response, adding a top predator so this model is a system of three ordinary differential equations. We study the existence and uniqueness, invariance and boundary of solutions. The information given in this work could also be useful for the design of development plans that meet the needs of the agricultural sector to guide the non-pollution of the environment in the country through the use of biological control to control pests.


Burden, R. L., and Faires, J. D. Numerical Analysis. Brooks/Cole Cenage learning, USA, 2010.

Hsu, S. B., Hwang, T. W., and Kuang, Y. A Ratio-Dependent Food Chain Model and Its Applications to Biological Control. Mathematical Biosciences 181 (2003), 55–83.

López, R. Structured SI epidemic models with applications to HIV edipemic. PhD thesis, Arizona State University, Arizona - USA, 2006.

Nicholis, C. I. Control biológico de insectos: un enfoque agroecológico. Editorial Universidad de Antioquia, 2008.

Pérez, J. R. Dinámica del Control Biológico Basado en un Modelo de Cadena Alimenticia Con Tres Niveles Tróficos, Tesis de licenciatura, UNMSM, Lima Perú, 2014.

SNSA. Control Biológico, SENASA Perú, Recuperado el 12 de marzo del 2017, de:

USDA. 20th Century Insect Control. Recuperado el 18 de marzo del 2014, de:, 1992.

van den Bosch, R., Gutierrez, A. P., and Messenger, P. S. An introduction to biologicalcontrol. Plenum Press, 1982.



How to Cite

Pérez Núñez, J., & López Cruz, R. (2017). Mathematical analysis of a food chain: prey - predator - biological control. Selecciones Matemáticas, 4(01), 112-123.