The course presents the following areas of Mathematical Biology:

1. Ecology

• Exponential Model

• Logistic Model

• Lotka-Volterra Model

• Lotka-Volterra Model with Logistic Growth

• Lotka-Volterra Model with Allee Effect

2. Epidemiology

• Compartmental Model

• Classical SIR

• SIR with Demographic Terms

• Structured Models by Age and by Time of Disease

3. Biochemical Kinetics

• Multi-Time Scales Models

• Michaelis-Menten Equation

• Hodgkin-Huxley Equation

• Classical Model of Enzyme Kinetics

• Models of Autocatalysis

4. Diffusion

• Diffusion Equation and Systems

• Turing Instability and Pattern Formation

• Belousov-Zhabotinsky Chemical Reaction

• Diffusion in Ecology, Epidemiology and Biochemistry Kinetics

5. Wave phenomena

• Fisher equation

• Traveling and plane waves in Ecology, Epidemiology and Physiology

For the above biological applications, the necessary mathematical notions and results will be presented from the following areas of Analysis:

1. Ordinary Differential Equations, Discrete Differential Equations and Delay Differential Equations

2. Applied Mathematics Methods

3. Partial Differential Equations

4. Dynamical Systems