Research
Mathematical Modeling of Ecological and Epidemiological Systems
Research Overview
My research efforts mainly focus on dealing with different aspects of ecological and epidemiological problems by using various modelling methodologies and analyzing them with the help of qualitative analysis tools such as stability and bifurcation theory, center manifold theory etc. As a young researcher, I want to expand my knowledge of analytical tools to connect the real world ecological, medical and environmental challenges with different modelling approaches.
My current research focuses on the emergence of drug resistance in HIV treatment, particularly in cases where patients exhibit sub-optimal or poor adherence to prescribed medications. My work aims to develop strategies across various scenarios with available treatment options to reduce the prevalence of drug-resistant HIV infections within affected communities. I employ dynamical systems as a primary tool to model these complex problems and conduct qualitative analysis using stability theory, bifurcation theory, and center manifold theory. Earlier, I worked on ecological problems, where the goal was to understand how the dynamic interplay between two or more species affects their population structure within natural food web systems.
For my future work, I aim to explore advanced modelling techniques that offer greater reliability in addressing emerging epidemiological and ecological challenges, given the growing availability of relevant data. Specifically, I am interested in applying tools such as stochastic modelling, network theory, machine learning, and optimization methods to these problems.
Research Areas
- Mathematical Biology
- Epidemiological Processes
- Ecological Processes
- Evolutionary Processes
- Deterministic and Stochastic Modeling
- Network Theory
Selected Publications
Dynamics of a multi-strain HIV/AIDS epidemic model with treatment and its adherence
Mathematical analysis of HIV transmission dynamics considering multiple strains and treatment adherence factors in community transmission scenarios.
Published in: The European Physical Journal Plus, 139(8), 1-22, 2024
Two strains and drug adherence: An HIV model in the paradigm of community transmission
Investigation of two-strain HIV dynamics with drug adherence considerations and their impact on community-level transmission patterns.
Published in: Nonlinear Dynamics, 108(3), 2767-2792, 2022
A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect
Analysis of ecological interactions in food webs focusing on intraguild predation and Allee effects in predator-prey systems.
Published in: Applied Mathematical Modelling, 89, 105-135, 2021
For a complete list of my published work, including detailed abstracts and citation information, please visit my publications page.
Future Research Directions
Moving forward, I aim to broaden my research by exploring new modeling tools that can better handle complex systems and real-world data. While my current work focuses on deterministic models in epidemiology and ecology, I'm interested in extending this to other fields and techniques that offer both flexibility and depth. Here are three areas I'm particularly keen to explore:
1. Network-Based Models
Many real-world systems — like disease spread, ecological interactions, or social behavior — operate over networks. I want to study how network structure influences system dynamics, especially in the context of disease transmission and species interaction. The goal is to build models where individuals or species are represented as nodes, and interactions happen over network connections. This can help capture heterogeneity in contact patterns and reveal important thresholds for outbreak control or ecosystem stability.
2. Machine Learning Tools
I'm interested in using machine learning to improve the modeling process — particularly in parameter estimation, model fitting, and decision-making. I'd like to explore tools like neural differential equations, Bayesian inference, and regularized regression for tuning model parameters using real-world data. Combining machine learning with traditional dynamical systems can help make the models more adaptive, data-informed, and predictive in nature.
3. Mathematical Modeling in Finance
Besides biology and ecology, I'm also curious about the application of mathematical modeling in financial systems. I'm interested in exploring areas like portfolio optimization, asset pricing models, and risk analysis using tools from differential equations, control theory, and probability. This direction allows me to apply my mathematical skills in a different but equally dynamic real-world domain.