MATHEMATICAL MODEL FOR THE POPULATION DYNAMICS OF THE BRONZE BUG AND ITS EGG PARASITOID CLERUCHOIDES NOACKAE

Authors

DOI:

https://doi.org/10.21575/25254782rmetg2025vol10n42480

Keywords:

Hosts, Parasitoids, Mathematical Modeling, Stability Analysis

Abstract

The objective of this work is to propose a mathematical model that describes the population dynamics between the egg parasitoid Cleruchoides noackae and its host Thaumastocoris peregrinus. The interaction between these populations is modeled as a host–parasitoid system using a type II functional response. The system is formulated through a set of four ordinary differential equations. The stability of its equilibrium points is analyzed. In addition, numerical simulations are performed using experimental laboratory data, and some results are presented.

Author Biographies

  • Jhonatan Rodrigues Biller, Federal University of Pelotas

    He holds a Bachelor’s degree in Applied Mathematics from the Federal University of Rio Grande and is currently a Master’s student in Mathematical Modeling at the Federal University of Pelotas.

  • Matheus Moro Moutinho, Federal University of Pelotas

    He is a graduate student in the Mathematical Modeling Program at UFPel, a fellow in the project “Some Problems in Optimal Control and Mathematical Biology,” and a member of the Optimization, Control, and Nonlinear Analysis research group. He is also pursuing a Licentiate in Mathematics and holds pedagogical training in the field. He graduated in Applied Mathematics (FURG) and is a certified Industrial Electrician (SENAI), with experience as a teaching assistant in Calculus and participation in teaching and research projects.

  • Alexandre Molter, Federal University of Pelotas

    He holds a degree in Mathematics (Unisinos), an M.Sc. in Mathematical Modeling (UNIJUÍ), a Ph.D. in Mechanical Engineering (UFRGS), and a postdoctoral fellowship from UFRGS. He is a Full Professor at the Institute of Physics and Mathematics at UFPel and advises master’s and doctoral students in the Graduate Program in Mathematical Modeling. His work focuses on mathematical modeling, dynamical systems, control, and optimization.

References

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BECCHI, L. K. et al. Thermal requirements, fertility life table and biological parameters of Cleruchoides noackae (Hymenoptera: Mymaridae) at different temperatures. PeerJ, v. 11, p. e14911, 1–19, 2023.

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OLIVEIRA, E. B. D.; JUNIOR, J. E. P. O eucalipto e a Embrapa: quatro décadas de pesquisa e desenvolvimento. Embrapa Florestas, 2021.

ROGERS, D. Random search and insect population models. Journal of Animal Ecology, v. 41, n. 2, p. 369-383, 1972.

TREXLER, J. C.; MCCULLOCH, C. E.; TRAVIS, J. How can the functional response best be determined? Oecologia, v. 76, p. 206-214, 1988.

WILCKEN, C. F. et al. Bronze bug Thaumastocoris peregrinus Carpintero e Dellapé (Hemiptera: Thaumastocoridae) on eucalyptus in Brazil and its distribution. Journal of Plant Protection Research, p. 201-205, 2010.

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Published

2025-12-15

Issue

Vol. 10 No. 4 (2025): Edição Especial do XII ERMAC RS

Section

Edição Especial do XII ERMAC RS

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Copyright (c) 2025 Jhonatan Rodrigues Biller, Matheus Moro Moutinho, Alexandre Molter

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