Topics in Mathematical Science II (Graphs and epidemiology)

Course Purpose

The motivation for studying and teaching this subject has been triggered by the pandemic which started in 2020. Graphs, and in particular random graphs, are used for studying the propagation of epidemics on them. During this course, we shall study the necessary notions for understanding the current researches on this hot topic.

Goals of the Course

Understand the basic notions of epidemics on graphs.

Course Prerequisites

Knowledge on standard undergraduate linear algebra, calculus and advanced calculus.

Related Courses

Any course on graph theory or on probability. This course will complement such courses, but they are not considered as prerequisite.

Recommended Reading

Free reference books will be provided during the lectures, but first part of the course is mainly based on
J.L. Gross, J. Yellen, M. Anderson, Graph theory and its applications, CRC press, 2019.
M. Newman, Networks, second edition, Oxford University Press, 2018.
I. Kiss, J. Miller, P. Simon, Mathematics of epidemics on networks, Springer, 2017.

Course Content

1. Basic definitions
2. Random graphs (additional information available in Chapters 10 and 11 of these lecture notes)
3. Ergodic systems on graphs: top-down
4. Bottom-up approach, closure
5. Mean-field (Appendix on one application of SEIR model)
6. SIR and percolation
7. Dynamic networks
8. Miscellaneous

Lecture Notes

The cumulative notes

Grading

Grades based on attendance and on written reports. An active participation of the students is expected.

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