MA801 Mathematical management of renewable resources and infectious diseases


Instructor: Nikolay S. Strigul
E-mails: nstrigul@stevens.edu, nstrigul@princeton.edu
Office Hours: by appointment

Lectures: E.A. Stevens 230, Tuesday 6:15 pm -8:45 pm
Homeworks: There will be weekly homework assignments.
Exams: There will be Midterm and Final Exams.

Grading:

Course program Course program (PDF)

General comments:

This course is designed for graduate students in applied mathematics who are interested in natural resources management. The goal of this course is to study mathematical methods in bioeconomics, using examples in fisheries and forestry management, marine reserve design, and infectious disease and public heath management. The math of natural resources management is very similar to that of disease progression, and diseases are frequently a worry in natural resources management. Biological systems are introduced as complex adaptive systems operating at different temporal and spatial scales, and the course emphasizes management problems which emerge from biological complexity. Mathematical concepts include analysis of deterministic and stochastic dynamical systems, nonlinear optimization and optimal control theory, and game-theory approaches. Applied topics include: fishery models based on the logistic equation (the Schaefer model), stock-recruitment models, models incorporating life-history and age-structured models (in particular, the Beverton-Holt model), the Faustmann forestry management model, harvesting of interacting populations, spatially-distributed models and optimal design of marine reserves. For disease management, we will examine both compartmental (SIR, SEIR, and MSIR) and demographic models. We will consider numerous research papers and actively use the Mathematica program to perform computer simulations.

Textbooks:

1) C. Clark. Mathematical Bioeconomics: Optimal Management of Renewable Resources. 2005 ISBN: 0471751529
2) R.M. Anderson, R.M. May. Infectious diseases of humans, dynamics and control. 1991 ISBN: 019854040X
3) F. Hoppensteadt. Mathematical Theories of Populations: Demographics, Genetics and Epidemics. 1997 ISBN: 0898710170
4) A. Okubo, S.A. Levin. Diffusion and Ecological Problems. 2002 ISBN: 0387986766
5) J.D. Murray. Mathematical Biology II. 2004 ISBN: 0387952284


Course program:

Lecture 1. - Introduction. Mathematics of Renewable Resource Management.

Lecture 2. - The Schaefer model.

Lecture 3. - Optimal control problems in fisheries. The Maximum Principle.

Lecture 4. - Supply and demand models in fisheries.

Lecture 5. - Discrete and continuous life-history models. Optimal harvest policies.

Lecture 6. - Age- and size- structured models in fisheries.

Lecture 7. - Spatial models: metapopulation and reaction-diffusion models.

Lecture 8. - Theories of marine reserves.

Lecture 9. - Forestry management.

Lecture 10. - Stochastic population dynamics and resource management.

Lecture 11. - Ecology and evolution of host-parasite interactions.

Lecture 12. - Theories of epidemics. Compartmental models.

Lecture 13. - Demographic models of epidemics.

Lecture 14. - Scaling in epidemiology: foot and mouth disease in the UK (Keeling et al., 2001-2005).

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