The **key difference** between SIR and SEIR model is that **SIR is one of the simplest models of epidemiology which has three compartments as susceptible, infected, and recovered, while SEIR is a derivative of SIR which has four compartments as susceptible, exposed, infected and recovered. **

Epidemiology studies how often diseases occur in different groups of people and why. In other words, epidemiology analyses the distribution, patterns and determinants of health and disease conditions in defined populations. It has compartmental models which are mathematical modelling of infectious diseases. In these models, the population is divided into compartments and used to predict how a disease spreads. SIR and SEIR are two models used in epidemiology. In fact, SIR is one of the simplest and basic models, and SEIR is an elaboration of it. In SIR model, there are three compartments as S, I and R while in SEIR model, there are four compartments as S, E, I and R.

### CONTENTS

1. Overview and Key Difference

2. What are the Compartments in SIR and SEIR Model

3. What is SIR Model

4. What is SEIR Model

5. Similarities Between SIR and SEIR Model

6. Side by Side Comparison – SIR vs SEIR Model in Tabular Form

7. Summary

## What are the Compartments in SIR and SEIR Model?

- Susceptible (S) compartment consists of individuals that are prone to become infected.
- Infectious (I) compartment consists of individuals that are infected with a pathogen and capable of disease transmission.
- Recovered (R) compartment has individuals that are no longer infectious or deceased individuals.
- Exposed (E) group has individuals that have been infected, but not infectious due to the pathogen’s incubation period.

## What is SIR Model?

SIR model or susceptible-infectious-recovered model is one of the simplest epidemiological models. It is a basic type of model. There are many derivatives of this model. In this model, there are three compartments as susceptible (represents the number of susceptible individuals), infectious (represents the number of infected individuals) and recovered (represent s the number of recovered or deceased individuals). Therefore, the total population N = S + I + R. The members of compartments generally progresses from susceptible to infectious to recovered.

SIR model is basically applicable to a variety of diseases, especially measles, mumps and rubella, which are airborne childhood diseases with lifelong immunity upon recovery. Therefore, this model is reasonably predictive for infectious diseases which are transmitted from human to human.

## What is SEIR Model?

SEIR model or susceptible-exposed-infectious-recovered model is a derivative of the basic SIR model. It has four compartments: S, E, I and R. S represent the number of susceptible individuals while E represents individuals who experience a long incubation duration; I represents the number of infectious individuals, and R represents the number of recovered or deceased individuals. Therefore, SEIR model differs from the SIR basically by the incorporation of a latency period.

During the latent or incubation period, individuals are infected but are not infectious due to the incubation period of the pathogen. In this model, total population N = S + E + I + R. Similar to SIR model, SEIR model is also applicable for measles, mumps and rubella.

## What are the Similarities Between SIR and SEIR Model?

- SIR and SEIR are two epidemiological models.
- Both models are applicable to measles, mumps and rubella.
- These models have the same value as the reproductive number.
- SEIR model can be modified into SIR model by turning off the incubation period.

## What is the Difference Between SIR and SEIR Model?

SIR is a simplest and the most basic compartmental model used in epidemiological studies. Meanwhile, SEIR model is a derivative of basic SIR model which has an additional compartment called exposed, including the individuals who are infected, but not yet infectious. So, this is the key difference between SIR and SEIR. SIR model has three variables/compartments as S, I and R while SEIR model has four as S, E, I, and R.

Moreover, SEIR model differs from the SIR model by the addition of latency period. Therefore, the progress of individuals occurs from susceptible to infectious to recovered in the SIR model while the progress occurs from susceptible to exposed to infectious to recovered in the SEIR model. Besides, in SIR model, N = S + I + R is the total population while in SEIR model, N = S + E + I + R is the total population.

The below infographic summarizes the difference between SIR and SEIR.

## Summary – SIR vs SEIR Model

SIR and SEIR are two compartmental models used in epidemiology. SIR is a basic model while SEIR is a derivative of SIR model. The key difference between SIR and SEIR is that SIR model has only three compartments as S, I and R while SEIR model has four compartments as S, E, I and R. Therefore, SEIR model has a compartment that consists of individuals who are infected but not infectious due to the incubation period of the pathogen. In SIR model, total population is represented by N = S + I + R while in the SEIR model, total population is represented by N = S + E + I + R.

##### Reference:

1. “SEIR And SEIRS Models — HIV Model Documentation”. Idmod.Org, 2020, Available here.

2. “Compartmental Models In Epidemiology”. En.Wikipedia.Org, 2020, Available here.

##### Image Courtesy:

1. “SIR Flow Diagram” By Viki Male – File:SIR.PNG (CC BY-SA 3.0) via Commons Wikimedia

2. “SEIR” By The original uploader was Imoen at English Wikipedia. – Transferred from en.wikipedia to Commons by Kafuffle using CommonsHelper (CC BY-SA 3.0) via Commons Wikimedia

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