Welcome to My Research

Exploring the intersection of mathematics and biology through innovative research and teaching.

\[ \frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right) \]

Logistic growth equation in population dynamics

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Dr. Ronobir Chandra Sarker

Research Areas

Mathematical Biology

Developing mathematical models to understand biological processes and systems.

\[ \frac{\partial u}{\partial t} = D\frac{\partial^2 u}{\partial x^2} + f(u) \]

Population Dynamics

Studying the mathematical principles behind population growth and interactions.

\[ \frac{dN_1}{dt} = r_1N_1\left(1 - \frac{N_1 + \alpha_{12}N_2}{K_1}\right) \]

Neural Networks

Modeling neural systems and brain function using mathematical approaches.

Neural Network Diagram
\[ \tau\frac{dv}{dt} = -v + \sum_{j=1}^n w_{ij}s(v_j) + I_i \]

Recent Publications

Mathematical Modeling of Disease Spread in Heterogeneous Populations

Sarker, R.C., Smith, J., & Johnson, A.

Journal of Mathematical Biology, 2023

This paper presents a novel mathematical framework for modeling disease transmission in populations with varying susceptibility levels. We introduce a system of differential equations that accounts for heterogeneity in contact rates and immune responses.

\[ \frac{dS}{dt} = -\beta SI, \quad \frac{dI}{dt} = \beta SI - \gamma I \]
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Stability Analysis of Predator-Prey Systems with Time Delays

Sarker, R.C., & Williams, B.

Theoretical Population Biology, 2022

We investigate the stability properties of predator-prey systems incorporating time delays in the functional response. Our analysis reveals new stability criteria that depend on the delay parameters and system coefficients.

\[ \frac{dP}{dt} = rP\left(1 - \frac{P}{K}\right) - \frac{aP}{1 + bP}Q, \quad \frac{dQ}{dt} = -mQ + c\frac{aP(t-\tau)}{1 + bP(t-\tau)}Q \]
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Teaching Materials

Mathematical Modeling

Introduction to mathematical modeling techniques for biological systems.

\[ \frac{dx}{dt} = f(x, y), \quad \frac{dy}{dt} = g(x, y) \]
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Population Dynamics

Mathematical approaches to understanding population growth and interactions.

\[ N(t) = N_0e^{rt} \]
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Network Theory

Mathematical foundations of network theory and its applications in biology.

\[ A_{ij} = \begin{cases} 1 & \text{if nodes } i \text{ and } j \text{ are connected} \\ 0 & \text{otherwise} \end{cases} \]
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Contact Me

Email

ronobir.sarker@university.edu

Location

Department of Mathematics
University of Science
123 Academic Street
City, Country

Phone

+1 (123) 456-7890