I am Dr. Arun Kumar, currently working as a Research Associate in the School of Mathematical and Statistical Sciences, Indian Institute of Technology (IIT) Mandi, India, under the supervision of Dr. Nitu Kumari in a CSIR-sponsored project. My research lies at the intersection of mathematical biology, epidemiology, and complex systems, where I develop and analyze mathematical models to understand nonlinear biological and ecological dynamics.

At IIT Mandi, my work extends toward computational and theoretical studies involving partial differential equations (PDEs), delay differential equations (DDEs), and ordinary differential equations (ODEs). I aim to integrate machine learning and deep learning frameworks - particularly Physics-Informed Neural Networks (PINNs)- with mechanistic models to achieve data-driven prediction and parameter estimation in complex biological systems. My ongoing research also explores how climate change influences infectious disease dynamics through changes in environmental and host factors.

Beyond my research, I contribute actively to academic writing and peer review in applied mathematics and theoretical biology. I have co-authored and published several papers in reputed journals, including works on bifurcation analysis, nonlinear dynamics, and hydra effects in predator-prey models. My publications collectively advance understanding of how mathematical abstractions can reveal real-world biological complexities such as stability shifts, oscillations, and pattern formation.