# 198008 – Mathematical models of infectious disease

This course is given in the spring semester of 2021.

See information sheet for details.

This course is taught in a “flipped” format. What that means is that you will learn the course material from recorded lectures or other resources, and answer the assignment questions at times convenient to you.  Every week we will meet for an active session in which the assignment solutions will be presented and discussed by the students.

Generally speaking, course materials are available to the public, but attendance in the active sessions is restricted to registered students.  If you are a Technion student and are not yet sure you’d like to register you are welcome to join the first active meeting, given that you have completed assignment I and are enrolled as a free listener.  Students from other universities may follow intra-university procedures to enroll.

 Week Lecture Lecture notes Additional reference Assignment Active class meeting Introduction and fundamental concepts 1a Introduction by Guest lecturer: Amit Huppert Slides – The first week of the Coursera course Developing the SIR Model partially overlaps with this week’s material.  Note that you can access the course material in audit’ mode. – The beginning of Chapter 2 in Brauer’s book discusses compartmental models and the SIS model, but please do note that beta is defined a bit differently than in my lecture. Assignment 1 Assignments are restricted to registered students.  The worksheet is available here. Active class meeting #1 Zoom meeting Active meetings are restricted to registered students. If you are not yet sure you’d like to register you are welcome to join the first meeting, given that you have completed the assignment and are enrolled as a free listener. 1b First examples – the SIS mode Notes 1c First code in R Code – Installing an R environment 2a Model extension – SIDS Notes – Chapter 2 in the book by Keeling and Rohani provides an excellent reference for lectures 2a and 2b. – The first week of the Coursera course Developing the SIR Model partially overlaps with this week’s material.  Note that you can access the course material in audit’ mode. – Here is a link to the Insightmaker demonstration presented in the lecture Assignment 2 pdf Active class meeting #2 Active meetings are restricted to registered students. 2b Model extension – SEIS Notes 2c The basic reproduction number and the next generation matrix Notes – Chapter 5.2 in Brauer’s book. Systematic derivation of the SIR model 3a Intro: The Kermack-McKendric paper – The paper from 1927 is available here (or here for registered students) Assignment 3 pdf Details are published in the course website 3b The basic stochastic age-of-infection model Notes – The lecture is based on section 2 in Guy Katriel’s paper available here (or here for registered students) 3c A stochastic simulation in R R code #1 R code #2 3d A deterministic version of the model Notes – The lecture is based on section 3 in Guy Katriel’s paper available here (or here for registered students) 3e Model approximations and reduction to the SIR model Notes – The lecture is based on section 4 in Guy Katriel’s paper available here (or here for registered students) Analysis of ODE epidemic models 4a Outline of an epidemic as described by the SIR model Notes – Chapter 2 in the book by Keeling and Rohani provides a basis for lectures 4a and 4b. – Chapters 3 and 7 in the book by Martcheva provides a good overview of the analysis of autonomous dynamical systems – If you are new to dynamical systems, you may want to refer to Strogatz’s well-known book on this subject Details are published in the course website 4b Analysis of an SIR model with natural birth/death Notes 4c Analysis of an SEI model for tuberculosis (TB) Notes – Chapter 7.5 in the book by Martcheva 5 Oscillations in Epidemic models Notes – Chapter 3.6 in the book by Martcheva – For Background on limit cycles, see, e.g., chapter 7 in Strogatz’s well-known book on this subject. Details are published in the course website 6 Epidemic final size Notes – This paper presents the derivation of final size equations in a rather general case, together with examples. – Guy Katriel’s paper available here (or here for registered students) presents the derivation of final size equations for discrete-time age-of-infection models. – An R code for solving the nonlinear algebraic final size equation is available here. Subpopulations 7 Subpopulations Notes – Here is an excellent short description of the subject.  It also includes reference to an R code for the system presented in the lecture.