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Developing the SIR Model

Nimalan Arinaminpathy

Compartmental modelling is a cornerstone of mathematical modelling of infectious diseases and this course will introduce some of the basic concepts in building compartmental models, including how to interpret and represent rates, durations and proportions. You'll learn to place the mathematics to one side and concentrate on gaining intuition into the behaviour of a simple epidemic, and be introduced to further basic concepts of infectious disease epidemiology, such as the basic reproduction number (R0) and its implications for infectious disease dynamics. To express the mathematical underpinnings of the basic drivers that you study, you'll use the simple SIR model, which, in turn, will help you examine different scenarios for reproduction numbers. Susceptibility to infection is the fuel for an infectious disease, so understanding the dynamics of susceptibility can offer important insights into epidemic dynamics, as well as priorities for control.

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What's inside

Syllabus

Modelling the Basics
Compartmental modelling is a cornerstone of mathematical modelling of infectious diseases. You will be introduced to some of the basic concepts in building compartmental models, including how to interpret and represent rates, durations and proportions in such models. This work lays the foundations for modelling the dynamics of infectious disease transmission.
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Anatomy of an Epidemic
You will be placing the mathematics to one side and concentrating on gaining intuition into the behaviour of a simple epidemic of a perfectly immunising infection in a stable population. You will also study further basic concepts of infectious disease epidemiology, including the basic reproduction number (R0), and its implications for infectious disease dynamics.
Combining Modelling and Insights
You will now consolidate the insights that you have gained over the past two modules to express the mathematical underpinnings of the basic drivers that have been examined. You will use the simple SIR model that you already developed in module 1 to examine different scenarios for reproduction numbers.
Dynamics of Susceptibles
Susceptibility to infection is the fuel for an infectious disease; understanding the dynamics of susceptibility can offer important insights into epidemic dynamics, as well as priorities for control. In this module, building on the basic SIR model that you have coded so far, you will cover three important mechanisms by which susceptibility can change over the course of an epidemic: (i) population turnover, (ii) vaccination, (iii) immunity waning over time. For simplicity, you will learn very simple approaches to modelling vaccination. In our subsequent courses in the Infectious Disease Modelling specialisation, you have the opportunity to cover more detailed approaches for capturing this important intervention.

Good to know

Know what's good
, what to watch for
, and possible dealbreakers
Introduces compartmental models, fundamental for infectious disease modeling, helping students build a solid foundation in disease transmission dynamics
Provides insights into the behavior of epidemics without delving deeply into mathematics, making the concepts accessible to those new to infectious disease epidemiology
Emphasizes understanding the basic reproduction number (R0) and its implications for infectious disease dynamics, building a solid understanding of key epidemiological concepts
Utilizes the simple SIR model to express mathematical underpinnings, enabling students to grasp the fundamental principles driving disease transmission
Explores the dynamics of susceptibility, a crucial aspect of understanding epidemic dynamics and control priorities, providing a comprehensive view of infection susceptibility
Integrates concepts covered throughout the course, solidifying understanding of the interplay between model parameters and disease dynamics

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Reviews summary

Confidently model infectious disease with sir

Learners say this course largely positive is engaging and informative if you're interested in learning how to code SIR models. It starts from the very basics and you'll need just a foundational knowledge of R programming. You'll learn how to adjust parameters in order to make predictions and how to find out where the epidemic projection curves that you see on the news come from.
You'll learn how to use SIR models to make predictions.
"learnt three extension of SIR Model; Population Turnover, Vaccination and Waning Immunity."
"As well as the basics of mathematical modeling of infectious disease epidemics, the course also includes some generic skills around logical thinking and R programming."
You'll learn R programming in this course.
"Programming exercises are useful."
"I am a MSc Biotech graduate of IIT Bombay. I have taken this course towards my project on COVID-19 epidemiology modelling."
"In particular, the accessible introduction to solving systems of differential equations in R feels like a really valuable skill."
This course teaches you all about SIR models.
"This is a great course to learn about the SIR model."
"One way of calculating this is dividing the number in each compartment by the total initial population size. The SIR model could be REPLICATED..."
"If you are a novice R programmer like I am, you will need to grow your R knowledge."
The content of this course is considered informative and valuable.
"learnt so much!"
"If anyone want to learn about infectious disease modeling from scratch, using R programming language, This is the best course ever."
"This course content was challenging enough to feel worth the time, but not so technical that it was a barrier."
This course starts with the basics.
"This course introduces us to the very basics of epidemiological modeling but builds a solid foundation from which to build models in the real world"
"It starts with simple states of infectious disease and can develop in many way. Required just foundation of R programming."
"This course will teach anyone not only the very basic, but will made everyone self sufficient to make and code their own model."
Some shortcomings with this course include unresponsive forums, lack of slides, and ambiguous questions.
"The material is really well presented and the exercises are great. The only downside is that the forums are not very active and responses are slow or in some cases - questions are not answered at all."
"One thing that would be a nice addition would be course slides to go with the videos."
"The structure and flow in the notebooks were somewhat disordered; the questions were some ambiguous, perhaps a revision in sentences required?"

Activities

Coming soon We're preparing activities for Developing the SIR Model. These are activities you can do either before, during, or after a course.

Career center

Learners who complete Developing the SIR Model will develop knowledge and skills that may be useful to these careers:
Epidemic Intelligence Service Officer
An Epidemic Intelligence Service Officer is a public health professional who works to prevent and control the spread of infectious diseases. This course may be useful for an Epidemic Intelligence Service Officer, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Infectious Disease Physician
An Infectious Disease Physician is a doctor who specializes in the diagnosis and treatment of infectious diseases. This course may be useful for an Infectious Disease Physician, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Mathematical Modeler
A Mathematical Modeler is a mathematician who develops and uses mathematical models to solve problems in a variety of fields. This course may be useful for a Mathematical Modeler, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Public Health Scientist
A Public Health Scientist is a scientist who works to improve the health of populations. This course may be useful for a Public Health Scientist, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Data Scientist
A Data Scientist is a professional who uses data to solve problems. This course may be useful for a Data Scientist, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Health Educator
A Health Educator is a professional who works to promote health and prevent disease. This course may be useful for a Health Educator, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Epidemiologist
An Epidemiologist is a research scientist who studies the causes and patterns of health and disease in populations. This course may be useful for an Epidemiologist, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Biostatistician
A Biostatistician is a statistician who applies statistical methods to the analysis of biological data. This course may be useful for a Biostatistician, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Health Policy Analyst
A Health Policy Analyst is a professional who analyzes health policies and programs. This course may be useful for a Health Policy Analyst, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Immunologist
An Immunologist is a scientist who studies the immune system. This course may be useful for an Immunologist, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Virologist
A Virologist is a scientist who studies viruses. This course may be useful for a Virologist, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Operations Research Analyst
An Operations Research Analyst is a professional who uses mathematical and analytical methods to improve the efficiency of organizations. This course may be useful for an Operations Research Analyst, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Software Engineer
A Software Engineer is a computer scientist who designs, develops, and maintains software systems. This course may be useful for a Software Engineer, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Actuary
An Actuary is a professional who uses mathematical and statistical methods to assess risk. This course may be useful for an Actuary, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.
Biomedical Engineer
A Biomedical Engineer is an engineer who applies engineering principles to the study of medicine and biology. This course may be useful for a Biomedical Engineer, as it provides a foundation in compartmental modeling, a cornerstone of mathematical modeling of infectious diseases. Compartmental modeling can be used to study the spread of infectious diseases in populations, and to develop strategies to prevent and control them.

Reading list

We've selected ten books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Developing the SIR Model.
Provides a graduate-level introduction to mathematical epidemiology, with a focus on the analysis of deterministic and stochastic models. It covers topics such as compartmental models, stability analysis, and bifurcation theory.
Provides an introduction to mathematical demography, with a focus on the application of mathematical models to the study of human populations. It covers topics such as population growth, age structure, and mortality.
Provides an introduction to dynamical systems theory, with a focus on applications in biology. It covers topics such as phase portraits, stability analysis, and bifurcation theory.
Provides an introduction to probability and stochastic processes, with a focus on applications in science and engineering. It covers topics such as probability distributions, random variables, and Markov chains.
Provides an introduction to linear algebra, with a focus on applications in science and engineering. It covers topics such as vectors, matrices, and linear transformations.
Provides an introduction to calculus, with a focus on applications in science and engineering. It covers topics such as limits, derivatives, and integrals.
Provides an introduction to algebra and trigonometry, with a focus on applications in science and engineering. It covers topics such as polynomials, trigonometric functions, and conic sections.
Provides an introduction to arithmetic, with a focus on basic operations and number theory. It covers topics such as addition, subtraction, multiplication, and division.
Provides an introduction to fractions, decimals, and percents, with a focus on basic operations and applications. It covers topics such as converting fractions to decimals and percents, and solving problems involving fractions, decimals, and percents.

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