# 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 replaced with a two-phase process:

• First, individuals get exposed to the virus, but are not yet become infectious. Then, the virus has just begun to develop with the host. This is called the latency period.
• Then later, exposed individuals become contagious. Note: they may or may not become symptomatic.

To model this, the compartment Infected in SIR gets split into two compartments Exposed and Infectious in SEIR. Exposed is the container for people in the latency period. Once they become contagious, they get moved to container Infectious.

Here are the reactions:

$$\mathrm{Susceptible} + \mathrm{Infectious} \xrightarrow{\mathit{exposure}} \mathrm{Exposed} + \mathrm{Infectious}$$

$$\mathrm{Exposed} \xrightarrow{\mathit{outbreak}} \mathrm{Infectious}$$

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

Exercise: draw the diagram for this reaction network.

#### Epilogue

We’ve reach the end of this introductory series. Hopefully, it has added some relevant concepts to your worldview.

But where one ends, another begins.

By way of anticipation for the next series, observe something that is missing from our description of the reaction networks: the rates at which the reactions take place in time. Using the metaphor of the pumps for the reactions, this becomes the question of how fast the pumps are running. Not surprisingly, these rates have a direct impact on how the epidemic evolves over time. Furthermore, as we will see, the relative rates of the reactions within the network leads to a qualitative impact on the dynamics of the epidemic.

Until next time…