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.
Publications
A. Poonia and S. P. Chakrabarty, “Dynamics of a multi-strain HIV/AIDS epidemic model with treatment and its adherence,” The European Physical Journal Plus, vol. 139, no. 8, p. 769, 2024.
A. Kumar and A. Poonia, “Dynamical analysis and optimal harvesting policy of a prey-predator model with holling type-iii functional response”, 2023.(Pre-print)
S. Satija, A. Saha, A. Poonia, and S. P. Chakrabarty, “Deterministic and stochastic models for Chronic Myelogenous Leukemia cellular populations in presence of immune response,” The Journal of Innovation Sciences and Sustainable Technologies, vol. 3, no. 2, pp. 79–98, 2023.
A. Poonia and S. P. Chakrabarty, “Two strains and drug adherence: An HIV model in the paradigm of community transmission,” Nonlinear Dynamics, vol. 108, no. 3, pp. 2767–2792, 2022.
J. P. Tripathi, P. S. Mandal, A. Poonia, and V. P. Bajiya, “A widespread interaction between generalist and specialist enemies: The role of intraguild predation and Allee effect,” Applied Mathematical Modelling, vol. 89, pp. 105–135, 2021.