Instructor Profile
Duration:
05 Weeks
Mode of Delivery:
Online Weekend Program
Schedule:
Enrollment Opening Soon
This course introduces the fundamental concepts and techniques of mathematical modeling in biological systems, with an emphasis on applications in epidemiology and cancer dynamics. Participants will learn how differential equations and dynamical systems can be used to describe, analyze, and predict biological processes such as population growth, infectious disease transmission, and tumor progression. The course begins with the foundations of mathematical modeling, including ordinary differential equations and biological growth models. It then explores compartmental models used in infectious disease modeling, such as SIR and SEIR models, along with stability analysis and sensitivity analysis to understand the behavior of biological systems.
In the later weeks, the course focuses on dynamic modeling of cancer growth, including tumor–immune system interactions and treatment strategies. Participants will also learn how to critically read and analyze research articles in mathematical biology. The final part of the course introduces modern research tools, including artificial intelligence (AI) and computational methods, to assist in model development, parameter estimation, and research exploration. Students will develop a mini research project, allowing them to apply mathematical modeling techniques to real biological problems. This course is designed for students and researchers from mathematics, biology, engineering, data science, and related fields who are interested in learning how mathematical and computational tools can be used to study complex biological systems.
By the end of this course, participants will be able to:
I. Understand the fundamental principles of mathematical modeling and their applications in biological systems, and develop differential equation models for biological processes such as population growth and disease transmission.
II. Apply compartmental modeling approaches (e.g., SIR and SEIR models) to study infectious disease dynamics.
III. Perform stability analysis, sensitivity analysis, and interpret model parameters for dynamical systems arising in biological modeling.
IV. Construct and simulate mathematical models of cancer growth, including tumor–immune interactions and treatment effects.
V. Understand the use of computational tools such as MATLAB and Python in implementing and analyzing mathematical models.
VI. Gain awareness of modern computational and AI-assisted approaches that can support tasks in mathematical and biological modeling.
VII. Design and present a small research project demonstrating the application of mathematical modeling to a biological problem.
Week 1 – Module 1: Foundations of Mathematical Modeling and Dynamical Systems
Week 2 – Module 2: Compartmental Modeling and Stability Analysis
Week 3 – Module 3: Dynamic Modeling in Cancer Biology
Week 4 – Module 4: Research Paper Analysis
Week 5 – Module 5: Research Training, AI Tools, and Project Development
Course Weekly Plan
Week 1 – Foundations of Mathematical Modeling and Dynamical Systems
• Course introduction and objectives
• Importance of mathematical modeling in biological sciences
• Overview of biological systems and complexity
• Definition and classification of differential equations (ODEs & PDEs)
• Examples of differential equations in biology
• Concept and steps of mathematical model development
• Types of mathematical models in biology (deterministic vs stochastic, continuous vs discrete)
• Basic mathematical model of bacterial growth
• Logistic growth model and interpretation of parameters
• Introduction to dynamical systems
• Analytical solution of basic ODE models
• Concept of doubling time
• Parameter interpretation and biological meaning
• Introduction to numerical simulations using computational tools (MATLAB / Python)
Week 2 – Compartmental Modeling and Stability Analysis
• Introduction to infectious disease modeling
• Compartmental modeling framework
• SIR epidemic model
• SEIR model and model extensions
• Model assumptions and limitations
• Case study: Ebola virus disease model
• Case study: Dengue disease model
• Vaccination and intervention strategies in epidemic models
• Dimensional analysis and scaling
• Non-dimensionalization of models
• Boundedness and invariant regions
• Equilibrium points (steady states)
• Linearization of nonlinear systems
• Local stability analysis using Jacobian matrix
• Global stability concepts
• Basic reproduction number
• Sensitivity analysis of model parameters
• Brief introduction to optimal control in epidemic models
Week 3 – Dynamic Modeling in Cancer Biology
• Introduction to cancer biology and tumor dynamics
• Importance of mathematical modeling in cancer research
• Tumor growth models
• Exponential tumor growth model
• Logistic tumor growth model
• Gompertz tumor growth model
• Interaction between tumor and immune system
• Tumor–immune system mathematical models (Show equation)
• Modeling tumor treatment strategies (chemotherapy / immunotherapy)
• Parameter interpretation in tumor models
• Numerical simulation of cancer growth models
• Visualization of tumor dynamics
• Discussion of limitations and challenges in cancer modelling
• Sensitivity analysis of the cancer model
• Stability analysis
•Parameter optimization
Week 4 – Research Paper Analysis
• Introduction to scientific literature in mathematical biology
• How to read and analyze a research article
• Structure of a scientific research paper
• Understanding modeling assumptions and methodologies
• Review of a compartmental modeling paper (example: COVID-19 epidemic model)
• Review of a dynamical biological model (example: cancer growth model)
• Identification of model components (variables, parameters, equations)
• Discussion of modeling results and interpretation
• Critical evaluation of published research
• Discussion on possible model improvements and extensions
Week 5 – Research Training, AI Tools, and Project Development
• Introduction to research methodology in mathematical biology
• How to design a mathematical modeling research project
• Formulating research questions and hypotheses
• Model formulation and development process
• Introduction to Artificial Intelligence in scientific research
• Using AI tools for literature review and idea generation
• AI-assisted parameter exploration and data analysis
• Visualization and interpretation of modeling results
• Writing a short research report
• Guidelines for preparing a scientific presentation
• Student research project development
• Presentation and discussion of project ideas
