Mathematical Modeling of Plants, Herbivore and Natural Enemies of Herbivores Interaction with Harvesting

Isaac K. Barasa *

Kaimosi Friends University, Kenya.

Samuel B. Apima

Kaimosi Friends University, Kenya.

*Author to whom correspondence should be addressed.


Plant-herbivore-natural enemies of herbivores interaction is one of the basic interactions that drives of the ecosystem yields. In this interaction, plants are the primary food source for herbivores while natural enemies of herbivores depends on herbivores for food and on plants for shelter. Harvesting of every species which is common in many habitat may affect the population densities of the species and even the entire ecosystem. Therefore, conservation and maintenance of the harvested species is critical for ecosystem balance. In this paper, a model of plant-herbivore-natural enemies interactions with the constant effort harvesting of every species was developed and analyzed. The positive invariant set, the conditions of existence and locally asymptotically, stability of the equilibria were determined using the stability theory of ordinary differential equations. The results shows that the species being harvested would become extinct if harvesting effort exceeded a threshold value for the given population. While maintaining the coexistence of populations in the ecosystem requires sensible harvesting practices. Therefore, it is fair to choose a reasonable harvesting effort to allow all species to coexist in order to govern the species’ dynamic behavior. The insights of the solutions of this study are of great essence to ecologists and policy developers in environmental conservation. The authorities to pay attention to the minimum number required based on the area coverage in deciding when to harvest and also be cautious to the amount and effort of harvesting in view of conserving the species and the environment.

Keywords: Ecology, harvesting, extinction

How to Cite

Barasa, I. K., & Apima, S. B. (2023). Mathematical Modeling of Plants, Herbivore and Natural Enemies of Herbivores Interaction with Harvesting. Asian Research Journal of Mathematics, 19(10), 7–15.


Download data is not yet available.


Murray JD. Mathematical biology: An introduction. Third Edition. Springer Verlag, Berlin; 2002.

Barasa KI, Apima SB, Wanjara AO. Mathematical modeling of plants-pathogen-herbivore interaction

incorporating allee effect and harvesting. JAMCS. 2022;39(9).

Bandyopadhyay M, Saha T. Plant-herbivore model. J. Appl. Math and Computing. 2005;19(1-2):327-344.

Jones CG, Lawton JH, Shachak M. Organisms as ecosystem engineers. Oikos. 1994;69:373-386.

Asfaw MD, Kassa SM, Lungu EM. The plant-herbivore interaction with Allee effect. BIUST Research and

Innovation Symposium (RDAIS). Botswana International University of Science and Technology Palapye, Botswana; 2017.

Asfaw MD, Kassa SM, Lungu EM. Effects of temperature and rainfall in plant-herbivore interactions at different altitude. Ecological Modelling. 2019;460:50-59.

Crawley MS. The herbivore dynamics. In; Crawley M. S. ed. Plant Ecology. Second edition. Oxford; Blackwell Scientific; 1997.

Khan MS, Samreen M, et. al. On the qualitative study of a two-trophic plant-herbivore model. J. Math. Bio. 2022;85(34).

Cindy P, David W. Differentiated plant-defense strategies: Herbivore community dynamical affects plantherbivore interaction. 2022;13401.

Hauntly N. Herbivores and the dynamics of communities and ecosystems. Annual Review of Ecology and Systematic. 1991;22:477-503.

Asfaw MD, Kassa SM, Lungu EM. Coexistence of threshold in the dynamics of the plant-, L’Dherbivore

interaction with Allee effect and harvest. International journal of Biomathematics. 2018;11(4):1850057.

Vijayalakshmi S, Gunasekaran M. Complex dynamics behavior of disease spread in a plant-herbivore system with Allee effect. IJSR. 2015;11(6):74-83.

Arturo J, Nic-May, Eric JAV. Dynamics of tritrophic with volatile compounds in plants. Sociedad Matimatica. 2020;16(29):3-31.

Birkhoff G, Rota GC. Ordinary differential equation. Ginn and Co. Boston; 1982.