## Epidemic Models 2, Part 2

David A. Tanzer, August 17, 2020

# What is meant by the rate of a reaction?

Let’s take a simple model, with just one reaction:

$$\mathrm{Sick} \xrightarrow{\mathit{Recovery}} \mathrm{Healthy}$$

Suppose that everyone starts out ill, and eventually recovers.

Suppose that, on any given day, there is a 10% chance that a sick person will recover. So, viewing the process of recovery as a whole, it will be like a popcorn process, where … Read more

## Epidemic Models 2, Part 1

David A. Tanzer, August 17, 2020

# The rates matter

In the last series, we introduced the idea of a reaction network, which is a collection of processes that are moving individuals between the compartments. What was missing there, though, was any kind of description of how fast the reactions run. This has a significant impact on the overall behavior of the network.

Let’s make this point concrete with an example. … Read more

## Epidemic Models 1, Part 7

David A. Tanzer, July 27, 2020

# 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 gives accurate description of the facts on the ground for pandemics like covid. It stands for stands for Susceptible, Exposed, Infectious, Recovered.

In SEIR, the infection process from SIR gets … Read more

## Epidemic Models 1, Part 6

David A. Tanzer, July 27, 2020

# 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 low-hanging fruits to comprehend.

## Epidemic Models 1, Part 5

David A. Tanzer, July 26, 2020

# 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 it to the compartments than the … Read more

## Epidemic Models 1, Part 4

David A. Tanzer, July 18, 2020

# 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 that the three compartments are represented … Read more

## Epidemic Models 1, Part 3

David A. Tanzer, July 18, 2020

# 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 reaction proceeds in small steps. In … Read more

## Epidemic Models 1, Part 2

David A. Tanzer, July 10, 2020

# 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 introducing more compartments.