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Discontinuity, Nonlinearity, and Complexity 15(2) (2026) 169--185 | DOI:10.5890/DNC.2026.06.003

Sapna Devi, Reda Fatma

Department of Mathematics, University of Allahabad, Prayagraj 211002, Uttar Pradesh, India

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Abstract

To understand the impacts of awareness program run by social media on the dynamics of wildlife species, a non-linear mathematical model is proposed and analysed. The mathematical model involves three dynamical variables namely: the density of human population, the density of wildlife species and awareness program run by social media. Existence and stability of equilibrium points are discussed. We further extend our mathematical model by introducing diffusion and analyse the reaction-diffusion model. Numerical simulations are performed to verify and validate our analytical results. By this study, we observe that the density of wildlife species increases as implementation rate of awareness program increases. It is also found that the introduction of diffusion destabilises the system which was stable in the absence of diffusion.

Acknowledgments

The second author gratefully acknowledges the financial support provided by the University Grant Commission (UGC), New Delhi, India through the Combined Research Entrance Test (CRET).

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