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

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

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:

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

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.

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

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

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

The SEIR model

Last time, we started a tour of extensions to the SIR model. Now we conclude the tour and this series by describing an extension SEIR, which can cover basic facts on the ground for pandemics like covid. It stands for stands for Susceptible, Exposed, Infectious, Recovered.

In SEIR, the infection… Read more