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The SEIR Model

An important application of the mathematical models in epidemiology is the study of the spread of infectious diseases. Compartmental models provide a simple and elegant way of modelling the infectious diseases. 

The SEIR model labels each individual in the given population as either Susceptible, Exposed, Infectious, or Recovered. Typically the entire population starts from the Susceptible state and then moves from Exposed to Infectious to Recovered. This transition of state is governed by differential equations which in turn are dependent on many parameters, ranging from virus transmission dynamics to clinical to environmental to local behavioural dynamics. The order of the labels usually shows the flow patterns between the compartments. While typically the transition is from S to E to I, but if Susceptible population starts to get a vaccine for example, they will be out of the system directly without going through the other model states. Similarly, when these model states are used at a state or district level, the migration patterns of people may change the overall population of the model system. As mentioned, the dynamics of this model are characterised by a set of four ordinary differential equations that correspond to the stages of the disease’s progression as shown below:

Figure 1: SEIR Model | Reference

For many important infections, there is a significant incubation period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment E (for exposed). The SEIR model considers this compartment.

The clinical dynamics in this model are an elaboration on SEIR that simulates the disease’s progression at a higher resolution, subdividing R into mild (patients who recover without the need for hospitalization), moderate (patients who require hospitalization but survive) and fatal (patients who require hospitalization and do not survive). Each of these variables follows its own trajectory to the final outcome, and the sum of these compartments add up to the values predicted by SEIR.

Modifications to the SEIR Model

  • The SEIR approach assumes a starting base transmission rate (R) and key parameters as the initial conditions.
  • Fits the Transmission Rate (Rt) to real-time data on a daily basis (model predictions are updated daily). This allows the model to be more flexible to on-ground interventions, like the India Lockdown 1.0 (25 Mar, 2020), Lockdown 2.0, Lockdown 3.0, Lockdown 4.0, Unlock 1.0+, and the creation of containment zones.
  • Categorises the population by age groups in the S, E, I, R compartments to increase granularity and therefore allow defining the key parameters like hospitalisation rate, mortality rate by age groups as opposed to a flat rate for the entire population.
  • Defines model configurations on a global and nodal level. This allows node-specific parameters to override global configurations.
  • India Model and state-level models were obtained as an aggregation of many district-level models which are connected in a network. Connected district-level models allow for the migration of population from one model system to another model system and thereby simulating the migration patterns. People from one model system can migrate from any model state (S,E,I,R) to another model system in any of its states.

Key Features

  • Modified SEIR-Model
  • Runs at granular levels, e.g. district (Separate node-specific zones can also be created)
  • Optimizes the prediction to match the actual reported infections daily
  • State model is not an aggregation of all district models
  • National model is an aggregation of all state models
  • Provides 15-30 day district-wise (or zone-wise) predictions
  • Provides the latest “Mortality Rate” and “Test Positivity Rate” for each zone i.e. districts, states, and India.
    (Please refer to Model Assumptions for the definition)

Model Approach- An Aggregation of Many Granular Models

The iSPIRT India COVID-19 SEIR Model can be used to approach multiple scenarios, including Country-State | State-District. These approaches are configurable; for more information visit the Model Configurations

Figure: India District Model | Data Source for Tracking –

Other Popular COVID-19 Models*

ModelModel TypeLink
Centre for Disease Dynamics, Economics and Policy (CDDEP)IndiaSimlink
IHMESIR | CurveFitlink
Adaptive Lockdown – MIT | Univ. of ChicagoSIRlink
WUSTL – Washington University St LouisSIRlink

*This is an indicative list of popular COVID-19 Models in use today, and is by no means exhaustive.


Source Code (now open-sourced on GitHub):

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