Category: Unit – Epidemic Models 1

Unit Overview – Epidemic Models 1 – Intro to Compartmental Models and SEIR

David A. Tanzer, July 2020, in unit Epidemic Models 1. Next unit: Epidemic Models 2.

This is an introduction to compartmental models, which are basic to understanding how epidemics move through populations. We start with the simplest models, and then build towards the SEIR model, which is a starting point for understanding epidemics like Covid.… Read more

Epidemic Models 1, Part 1

David A. Tanzer, July 10, 2020, in unit Epidemic Models 1.

A first look at compartmental models

The grim curves that we see in the papers show things like the number of daily infections, and the number of daily deaths. Epidemic models aim to predict these curves. The models depend both on natural parameters such as infectiousness and the duration of the infectious period, as well as on social … Read more

Epidemic Models 1, Part 2

David A. Tanzer, July 10, 2020, in unit Epidemic Models 1.

A menu of compartmental models

Last time, we talked about the idea of compartmental models, where the population is divided into compartments like Susceptible and Infected. If these are the only compartments, the model is called SI. But SI is very simplistic, and cannot express things like recovery, immunity or death.

Richer models are obtained by … Read more

Epidemic Models 1, Part 3

David A. Tanzer, July 18, 2020, in unit Epidemic Models 1.

General idea of reactions

Last time we surveyed some compartmental models in epidemiology. Now it’s time to look deeper, as the compartments are only part of a model.

The models also contain reactions, which connect the compartments and cause them to change over time; they are processes which ‘stir’ and transform the contents of the compartments. A … Read more

Epidemic Models 1, Part 4

David A. Tanzer, July 18, 2020, in unit Epidemic Models 1.

The SIR model

Last time, we introduced the general idea of reactions. Now we turn to the SIR reaction network, which is a fundamental model:

SIR-network

Footnote: such diagrams are called ‘Petri nets’, after Carl Petri, who invented them in 1939, at age 13, to describe chemical reactions. They are now more widely applied.

Here we see … Read more

Epidemic Models 1, Part 5

David A. Tanzer, July 26, 2020, in unit Epidemic Models 1.

The SIR model (cont’d)

Last time, we introduced the SIR model, and looked at the formula for one of its reactions, recovery. Here we complete the effort, by looking into the more complex reaction, infection.

SIR-network

The infection reaction

Recall that the recovery reaction has the formula:

$$\mathrm{Infected} \xrightarrow{\mathit{recovery}} \mathrm{Recovered}$$

The infection reaction has more arrows connecting … Read more

Epidemic Models 1, Part 6

David A. Tanzer, July 27, 2020, in unit Epidemic Models 1.

A diversity of compartmental models

Last time, we finished our pilot study of the SIR model. By taking variations on this theme, we are now in a position to grasp the structure of a diverse range of compartmental models. So we begin a small tour. Having absorbed the general ideas through SIR, these other models will be … Read more

Epidemic Models 1, Part 7