This course provides an introduction to the use of ordinary differential equations in modeling biological and biomedical systems. Topics include population dynamics, epidemic models, immune and cancer dynamics, gene regulatory networks, and pharmacokinetics. Emphasis is placed on model formulation, analytical techniques, and interpretation of results in biological contexts.

I. Course Exit Outcomes

By the end of the semester, students will

1. Develop and analyze mathematical models for biological systems using ODEs.

2. Interpret biological implications of analytical and numerical results.

3. Use computational tools for simulating biological models.

4. Communicate modeling results effectively in oral and written formats.

II. Course Objectives

1. Cognitive Domain:

a) Understand key biological processes that can be modeled mathematically.

b) Derive and solve ODE-based models for population dynamics, disease spread, and cellular interactions.

c) Analyze the stability and behavior of nonlinear systems.

2. Affective Domain:

a) Appreciate the role of mathematical models in biology and medicine.

b) Foster interdisciplinary thinking by integrating biological knowledge with mathematical tools.

3. Psychomotor Domain:

a. Utilize software (e.g., Python, R) for simulating biological systems.

b. Sketch phase portraits and interpret bifurcation diagrams.