250168 VO The Population Dynamics of Infectious Diseases (2005W)

A. Introduction to population dynamics

B. Deterministic Models

1. (Bi)linear models (The mass-action law)

1.1. One population models
1.1.1. SIR models
1.1.2. SIS models
1.1.3. The general structure of bilinear models

1.2. Epidemic models with two or more interacting populations
1.2.1. Gonorrhea
1.2.2. Host-vector-host systems
1.2.2.1.Malaria
1.2.2.2. Schistosomiasis

1.2. Nonconstant population models
1.2.2. Epidemic models with vital dynamics
1.2.3. HIV/AIDS modelling

1.3. Multigroup models
1.3.2. Gonorrhea
1.3.3. HIV/AIDS

2. Strongly nonlinear models (generalization of the mass-action law)
2.1. Equilbria and their stability
2.2. HIV/AIDS in structured populations

3. Cooperative systems
3.1. Epidemic models with positive feedback
3.2. Quasimonotone systems
3.3. Gonorrhea
3.4. Malaria
3.5. Schistosomiasis

4. Spatially structured epidemics
4.1. Quasimonotone systems
4.2. Lyapunov methods
4.3. Nonlocal forces of infection
4.3.1. Man-environment-man epidemics
4.3. Front propagation in rabies epidemics
4.4. Saddle-point behaviour

5. Age structured epidemics

6. Optimal control problems
6.1. Boundary feedback control problems
6.2. Stabilizability by local control

C. Stochastic Models

7. The simple stochastic epidemic

8. The general stochastic epidemic

9. Spatially structured models
9.1. The Neyman-Scott model for spatial epidemics
9.2. Percolation models

10. Problems of inference for stochastic models

11. Continuous approximation of stochastic models

12. Hybrid models for epidemic models

12.1. A model for HIV/AIDS in structured populations of drug addicts
12.2. A model for HIV/AIDS with sexual transmission