Mathematical model on the effect of primary and secondary toxicants on a biological species: occurrence of deformity

Document Type : Research Article

Authors

Anuj Kumar Agarwal ¹

Alok Agrawal ²

¹ Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki, 225003, Uttar Pradesh, India.

² Department of Mathematics, Amity University, Lucknow, 226028, Uttar Pradesh, India

10.22067/ijnao.2026.97893.1848

Abstract

In this paper, a mathematical model is proposed and analyzed to study the effect of primary and secondary toxicants on a biological species. Here, we consider a situation that after-effect of the primary and secondary toxicants a subclass of biological species shows deformity as stagnating the reproduction capability. we analyzed the model using stability analysis and Hopf-bifurcation theory. The analysis of model shows, primary and secondary toxicants badly affects the biological species. These toxicants decrease the growth rate of species as well as causing deformity in a subclass. For high emission of primary toxicant, system become unstable, total density and deformed subclass density of species start oscillating around their equilibrium levels. This study helps us to plan best courses of action to make a healthier environment for living things such as plant trees, properly dispose the wastes, use pesticides and insecticides sparingly, use eco-friendly vehicles, etc.

Keywords

Biological species

Primary and secondary toxicants

Deformity

Hopf-bifurcation

Subjects

• Modeling and Simulation

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