Turing Patterns in Biology
Pattern formation in epidemic models with media coverage, cancer networks with sub-diffusion, and reaction–diffusion systems under stochastic forcing.
\[ \partial_t u = D\,\nabla^2 u + f(u) + \sigma\,\xi(x,t) \]
Assistant Professor · Mathematics & Statistics · BUBT
Mathematics for the living world.
I study how spatial patterns emerge in biological systems — Turing patterns in epidemic models and cancer networks, super- and sub-diffusion, stochastic forcing and neural field models of the brain — and build fast spectral methods to simulate them.
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- 0 since 2012
\[ \frac{\partial u}{\partial t} = d\,\nabla^2 u + f(u,v) \]
Reaction–diffusion · Turing patterns
Latest paper
Biological Cybernetics · 2026
Published in
- Biological Cybernetics
- International Journal of Bifurcation and Chaos
- Differential Equations and Dynamical Systems
- Nonlinear Science
- MethodsX
- AppliedMath
About
Applied mathematician, teacher and modeller
I am an Assistant Professor in the Department of Mathematics and Statistics at Bangladesh University of Business and Technology (BUBT), Dhaka. I earned my Ph.D. in Mathematics from South Asian University, New Delhi, supported by the SAARC India Silver Jubilee Scholarship, and my B.Sc. and M.Sc. in Mathematics from Jahangirnagar University.
My research uses reaction–diffusion theory, weakly nonlinear analysis and spectral methods to understand pattern formation in epidemics, cancer networks and neural fields. Alongside research I have taught university mathematics since 2012 and build interactive tools for my students.
2024 – present
Assistant Professor, Mathematics
Bangladesh University of Business and Technology (BUBT), Dhaka
2015 – 2023
Ph.D. in Mathematics
South Asian University, New Delhi, India · SAARC India Silver Jubilee Scholarship
2012 – 2015 · 2023
Lecturer in Mathematics
Bangladesh University of Business and Technology (BUBT)
2008 · 2009
B.Sc. & M.Sc. in Mathematics
Jahangirnagar University, Savar, Bangladesh
Research
Where mathematics meets biology and computation
My work sits at the intersection of dynamical systems, spatial pattern formation, scientific computing and nature-inspired optimization.
Anomalous Diffusion & Population Dynamics
Super-diffusive SI epidemic and Leslie–Gower predator–prey models, stability analysis and the spatial spread of interacting populations.
\[ \partial_t N = -d\,(-\Delta)^{\alpha/2} N + rN\!\left(1-\frac{N}{K}\right) - g(N,P) \]
Neural Field Models
Corticothalamic neural field theory and spatial spectral signatures across states of consciousness.
Spectral Methods for PDEs
Chebyshev collocation and exponential time-differencing (ETDRK4) schemes for stiff, nonlinear and stochastic PDEs with machine-precision benchmarks.
\[ u_{n+1} = e^{Lh}u_n + h\,\varphi_1(Lh)\,\mathcal{N}(u_n) \]
Swarm Intelligence & Optimization
Generic set-based Artificial Bee Colony and Whale Optimization algorithms for combinatorial problems.
\[ x^{*} = \arg\min_{x \in \mathcal{S}} f(x), \quad \mathcal{S} \subset 2^{U} \]
Data Analysis & Machine Learning
Bayesian model calibration, causal inference on technology adoption, and data-driven models of environmental systems such as CO2 emissions in Dhaka.
\[ p(\theta \mid y) \propto p(y \mid \theta)\,p(\theta) \]
Publications
Papers & preprints
This list updates itself: whenever a new paper with a DOI appears in the scholarly indexes, it shows up here automatically.
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Teaching
Interactive learning tools
Hands-on visualisers and practice pages I build for my students. Open one and play with the parameters.
Linear Algebra
Gaussian Elimination
Step through row operations and watch a system reduce to row-echelon form.
\[ A\mathbf{x} = \mathbf{b} \;\longrightarrow\; \left[\,U \mid \mathbf{c}\,\right] \]
Open tool
Linear Algebra
Vector Practice
Interactive drills on vector addition, scaling, dot products and projections.
\[ \mathbf{u}\cdot\mathbf{v} = \|\mathbf{u}\|\,\|\mathbf{v}\|\cos\theta \]
Open tool
Linear Algebra
p-Norm Unit Ball Visualizer
See how the unit ball changes shape as p moves from 1 to ∞.
\[ \|\mathbf{x}\|_p = \Big(\sum_i |x_i|^p\Big)^{1/p} \]
Open tool
Calculus
Integration Learning Hub
Techniques of integration with worked examples and practice problems.
\[ \int u\,dv = uv - \int v\,du \]
Open hub
Geometry
Conic Sections
Explore ellipses, parabolas and hyperbolas by adjusting their parameters live.
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
Open tool
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Contact
Let's collaborate
Open to research collaborations, student supervision and invited talks.
Email
ronobir.sarker@gmail.com
Affiliation
Department of Mathematics and Statistics, Bangladesh University of Business and Technology (BUBT)
Location
Mirpur, Dhaka, Bangladesh