My primary research focuses on the mathematical modeling of infectious diseases, ecological interactions, and climate-driven environmental changes. I work on enhancing mathematical models to improve the predictions of host-pathogen dynamics, zoonotic spillovers, and the impact of extreme weather on ecosystems. By integrating Bayesian inference, evolutionary dynamics, and other advanced tools, I aim to develop more accurate frameworks for epidemic forecasting, public health preparedness, and ecological resilience. I've shared more information about my submitted and ongoing research projects below.
Ongoing
Barsha Saha, Majid Bani Yaghoub. Zeeman’s Classifications of Competitive Species Dynamics in A Climate-Influenced Reaction-Diffusion Lotka-Volterra Model
Objective: This study integrates climate variables into a reaction-diffusion Competitive Lotka-Volterra model to analyze species dynamics. Using Zeeman’s classification, we examine how environmental factors shape population distribution, survival, extinction, and coexistence patterns.
Key-Highlights:
Incorporated temperature, precipitation, and extreme weather events into species interaction dynamics.
Applied Zeeman’s classification to identify species survival, extinction, and coexistence shifts.
Used reaction-diffusion modeling to capture the spatial effects of climate-driven competition.
Examined the long-term impact of climate change on species distributions and community stability.
Provided a mathematical framework for predicting climate-driven ecological transitions.
Barsha Saha, Majid Bani Yaghoub. Environmental and Weather Factors in the Competitive Lotka-Volterra Mode to predict the zoonotic spillover risk.
Objective: This study extends the three-species Competitive Lotka-Volterra (CLV) model with diffusion to evaluate zoonotic spillover risk under extreme weather events. We assess how environmental fluctuations impact species interactions and pathogen transmission by incorporating climate-driven factors.
Key-Highlights:
Integrated temperature, precipitation, drought, and habitat changes into species growth rates, carrying capacities, and competition coefficients.
Examined how climate-driven shifts in species interactions influence spillover dynamics.
Developed a mathematical framework to assess zoonotic spillover risk under climate change.
Applied diffusion-based modeling to capture spatial and ecological variations in pathogen transmission.
Provided insights into the ecological and epidemiological consequences of environmental fluctuations.
Majid Bani Yaghoub, Barsha Saha. Network-Based Analysis of Five Rodent Species Interactions Using AIC-Optimized Lotka-Volterra Models
Objective: This study employs AIC-optimized Lotka-Volterra models to analyze competition dynamics among five rodent species in Kansas (1973–2003). By constructing Weighted Adjacency Matrices (WAMs), we quantify species interactions and examine long-term ecological trends.
Key-Highlights:
Applied Akaike Information Criterion (AIC) optimization to identify the best-fitting species interaction models annually.
Constructed Weighted Adjacency Matrices (WAMs) to quantify competition strengths among species.
Reshaped WAMs into structured 25-element vectors for systematic temporal analysis.
Used boxplot visualizations and statistical summaries to reveal long-term trends in interspecies competition.
Provided a data-driven framework for assessing ecological stability and species coexistence over time.
Majid Bani Yaghoub, Barsha Saha, Survival-Extinction Dynamics of the Invasive Emerald Ash Borer Under Extreme Cold Events and Predation
Objective: This study introduces a novel analytical approach for deriving exact traveling wave solutions in a prey-predator model and extends the framework to incorporate the effects of extreme cold events on species interactions. The extended model is applied to the Emerald Ash Borer and its biological predators to investigate the impact of severe climate conditions on their survival-extinction dynamics.
Key-Highlights:
Developed a new method for obtaining exact traveling wave solutions in a reduced prey-predator model.
Extended the model to assess the influence of extreme cold events on interacting species.
Validated numerical solutions by comparing them with exact analytical solutions.
Conducted bifurcation analysis to identify unstable periodic solutions and assess system stability.
Submitted
Barsha Saha, Majid Bani Yaghoub, and C.N. Podder. UTILITY OF COMPARTMENTAL MODELS TO TEST THE COMPETING HYPOTHESES OF PATHOGEN EVOLUTION AND HUMAN INTERVENTION. Mathematic Bioscience Journal.
Objective: This study establishes a model-based hypothesis testing (MBHT) framework within compartmental models to evaluate competing hypotheses of pathogen evolution and human intervention. Using SARS-CoV-2 as a case study, we examine how viral mutations respond to changes in transmissibility, virulence, and vaccination effects over multiple epidemic waves.
Key-Highlights:
Proposed a disease model with six compartments, analyzed stability, and identified a backward bifurcation.
Estimated key parameter distributions across seven epidemic waves using U.S. COVID-19 data.
Applied Bayesian inference to compute posterior probabilities of competing mutation hypotheses.
Found that short-sighted evolution drove early mutations, while immune selection, vaccination-induced virulence, and transmission-virulence correlation shaped later-stage
Publication
Barsha Saha, Majid Bani Yaghoub, and C.N. Podder. UTILITY OF COMPARTMENTAL MODELS TO TEST THE COMPETING HYPOTHESES OF PATHOGEN EVOLUTION AND HUMAN INTERVENTION. Mathematic Bioscience, https://ssrn.com/author=7400686.(preprint)