SEIR Model vs. SIS Model

Attribute	SEIR Model	SIS Model
Population compartments	4 compartments: Susceptible, Exposed, Infected, Recovered	2 compartments: Susceptible, Infected
Recovery rate	Individuals move from Infected to Recovered compartment at a certain rate	Individuals move back to Susceptible compartment after infection
Immunity	Individuals gain immunity after recovery	No immunity gained after infection
Transmission rate	Depends on contact rate and probability of transmission	Depends on contact rate and probability of transmission
Equilibrium state	Stable equilibrium with all compartments having non-zero values	Equilibrium may have only Infected compartment with non-zero value

Introduction

The SEIR (Susceptible-Exposed-Infectious-Recovered) model and the SIS (Susceptible-Infectious-Susceptible) model are two commonly used mathematical models in epidemiology to study the spread of infectious diseases. Both models have their own set of attributes and are used to understand different aspects of disease transmission dynamics.

SEIR Model

The SEIR model divides the population into four compartments: susceptible individuals (S), exposed individuals (E), infectious individuals (I), and recovered individuals (R). In this model, individuals move through these compartments based on certain transition rates. Susceptible individuals can become exposed to the disease, then progress to being infectious, and finally recover from the disease. The SEIR model is particularly useful for diseases where there is an incubation period between exposure and becoming infectious, such as COVID-19.

• Divides population into four compartments
• Includes an incubation period
• Individuals progress through compartments based on transition rates
• Useful for diseases with distinct stages of infection

SIS Model

The SIS model, on the other hand, divides the population into two compartments: susceptible individuals (S) and infectious individuals (I). In this model, individuals can become infected with the disease and then recover, only to become susceptible again. The SIS model is often used to study diseases where individuals do not develop immunity after recovering, such as the common cold. This model is useful for understanding the cyclical nature of infections within a population.

• Divides population into two compartments
• Individuals can become infected and recover
• Individuals can become susceptible again after recovering
• Useful for diseases without lasting immunity

Comparison of Attributes

While both the SEIR and SIS models are used to study disease transmission dynamics, they have distinct attributes that make them suitable for different types of infectious diseases. The SEIR model is more appropriate for diseases with distinct stages of infection and an incubation period, while the SIS model is better suited for diseases where individuals can become infected multiple times without developing lasting immunity.

One key difference between the two models is the number of compartments used to divide the population. The SEIR model has four compartments, allowing for a more detailed analysis of disease progression through different stages. In contrast, the SIS model has only two compartments, simplifying the model but limiting the ability to capture complex disease dynamics.

Another important distinction is the concept of immunity in the two models. In the SEIR model, individuals move from the infectious compartment to the recovered compartment, indicating that they have developed immunity and cannot be infected again. This assumption is crucial for diseases where immunity plays a significant role in controlling the spread. On the other hand, the SIS model does not include a recovered compartment, allowing individuals to become infected multiple times.

Furthermore, the SEIR model incorporates an incubation period, which is not present in the SIS model. This feature is essential for diseases where individuals can be infected but not yet infectious, affecting the timing and intensity of disease transmission. By including an exposed compartment, the SEIR model can capture the delay between exposure and becoming infectious, providing a more accurate representation of disease spread.

Both models rely on certain parameters and assumptions to describe disease transmission dynamics, such as transmission rates, recovery rates, and population size. These parameters can be adjusted to simulate different scenarios and study the impact of interventions, such as vaccination or social distancing measures. Understanding the differences between the SEIR and SIS models can help researchers choose the most appropriate model for studying specific infectious diseases and designing effective control strategies.