IIT Mandi | India
Dr. Arun Kumar is a Research Associate (Postdoctoral) at the Indian Institute of Technology Mandi, specializing in mathematical and computational modeling of complex biological, ecological, and epidemiological systems. He earned his Ph.D. in Mathematics from Banaras Hindu University in 2023, following an M.Sc. in Mathematics from the same institution and a B.Sc. from CCS University, Meerut. His research focuses on nonlinear dynamics, bifurcation theory, delay differential equations, reaction–diffusion systems, Turing patterns, and the integration of deep learning and physics-informed neural networks (PINNs) for solving partial differential equations. Dr. Kumar has published extensively in high-impact journals on topics including SIR/SIRS epidemic models, cross-diffusion models, predator–prey dynamics, and pattern formation in spatial ecological systems. His work bridges theoretical mathematics and practical applications in disease modeling and ecology, offering insights into complex population interactions, control strategies, and spatio-temporal dynamics. Currently, he is developing deep learning algorithms to solve PDEs with applications in ecological and epidemiological systems. His ongoing research explores predator-prey interactions, learning in ecological models, and the forecasting of infectious diseases such as monkeypox. Dr. Kumar’s contributions have advanced the understanding of nonlinear systems, providing both analytical and computational tools for studying complex biological and ecological phenomena.
Featured Publications
Gupta, R. P., & Kumar, A. (2022). “Endemic bubble and multiple cusps generated by saturated treatment of an SIR model through Hopf and Bogdanov–Takens bifurcations.” Mathematics and Computers in Simulation, 197, 1–21.
Gupta, R. P., Kumar, A., & Yadav, D. K. (2024). “The complex dynamical study of a UAI epidemic model in non-spatial and spatial environments.” The European Physical Journal Plus, 139(2), 117.
Yadav, D. K., Gupta, R. P., & Kumar, A. (2022). “Nonlinear dynamics of a three species prey-predator system incorporating fear effect and harvesting.” Journal of Mathematical Control Science and Applications.
Kumar, A., Gupta, R. P., & Tiwari, S. (2022). “Influences of nonlinear cross-diffusion on a reduced SI epidemic model with saturated treatment.”
Kumar, A., Kumari, N., Mandal, S., & Tiwari, P. K. (2025). “Autonomous and non-autonomous dynamics of an SIRS model with convex incidence rate.” Journal of the Franklin Institute, 108236.