Introduction to Mathematical Epidemiology: the SIS and Kermack and McKendrick epidemiological models

Item: Introduction to Mathematical Epidemiology: the SIS and Kermack and McKendrick epidemiological models
Rating: 4
Author: PostSingularity Institute

by Julien A

Formal & Physical Sciences Mathematics PBWApplied mathematics PBWHMathematical modelling

🎙 Julien A 👥 618 📅 October 9, 2022 ⏱ 94 min 👁 1K 📄 lecture 🧭 2026-08-17

Available in: English (current) Français

Keywords

SIR modelSIS modelcompartmental modelsbasic reproduction numberherd immunity

Summary

This lecture provides an introduction to mathematical epidemiology, focusing on two classical models: the Kermack-McKendrick SIR epidemic model and the endemic SIS model. The instructor begins by explaining compartmental models, which are a general framework for modeling the flow of individuals between disease states. He then details the SIR model, deriving the differential equations, discussing equilibria, and introducing the basic reproduction number R0. The lecture also covers incidence functions, which describe the rate of new infections, and concludes with a discussion of herd immunity. The presentation is mathematically rigorous, with derivations and phase-plane analysis, and is suitable for students with a background in differential equations.

105 words

Critical Evaluation

Value of the Information & Strength of the Argument

The lecture provides a solid foundation in mathematical epidemiology, with clear derivations and explanations of key concepts such as R0 and herd immunity. The argumentation is logical and well-structured, building from compartmental models to specific examples. The instructor emphasizes the assumptions and limitations of the models, which is valuable for understanding their applicability. The use of phase-plane analysis to illustrate epidemic dynamics is particularly instructive.

Scientific Rigor, Source Quality, Title Accuracy

The lecture is based on the seminal work of Kermack and McKendrick, and the instructor references their original papers. The mathematical derivations are rigorous and the presentation is accurate. The title accurately reflects the content, which is an introduction to the SIS and SIR models. The lecture is part of a university course, and the slides are available online, providing additional resources.

142 words

Title / Content Match

The title accurately reflects the content, which introduces the SIS and SIR models in mathematical epidemiology.

Quality & Reliability

8/10

The lecture is based on the classical Kermack-McKendrick model and provides a rigorous mathematical derivation, with references to the original papers. The presentation is clear and technically sound, though it is an introductory lecture and does not cover recent developments.

Chapters

Cited Sources

Course slides — Slides used in the lecture, containing the models and derivations.

Concurring Sources

Kermack-McKendrick model — General reference on compartmental models, consistent with the lecture's content.

Contribution & Novelties

The lecture provides a clear and rigorous introduction to classical epidemic models, emphasizing the mathematical foundations. It is particularly useful for students new to the field. The discussion of incidence functions and herd immunity adds practical relevance.

Pour aller plus loin :

Kermack-McKendrick model — Wikipedia article on compartmental models, including the SIR model.
Basic reproduction number — Wikipedia article on R0, a key concept in epidemiology.
Herd immunity — Wikipedia article on herd immunity, explaining the concept and its implications.

81 words

Radar Profile

The radar profile shows high scores in information quantity, quality, and reliability, with a slightly lower technical level, indicating a well-balanced introductory lecture that is both informative and accessible.

Reliability 8/10