COVID-19/Mathematical Modelling/Compartment Models

SIR Model - Animation

Compartment Models in Epidemiology

With Compartmental Models one of the available techniques to simplify the mathematical modelling of infectious disease. The population is divided into compartments, with the assumption that every individual in the same compartment has the same characteristics. The characteristic is e.g. the epidemiological status of a person in the considered total population. The people having a specific epidemiological status can change their status

• susceptible person for a disease can be infected,
• an infected person in the population can be immune and recover from a disease,
• an infected person could keep the status of being infected and can be regarded at a patient with a chronic disease (immune system does not create anti-bodies against the virus).

Blue=Susceptible, Red=Infected, and Green=Recovered

Each member of the population typically progresses from susceptible to infectious to recovered. This can be shown as a flow diagram in which the boxes represent the different compartments and the arrows the transition between compartments, i.e.

The number of infected patients, the number of recoverd (includes immune) patients and the number of susceptible people in the community determine the spread of disease, because the spread of the disease is dependent on the contact between people in the disease and especially, when infected people meet susceptible people. If the probability that infected people meet susceptible people is decreasing, that the epidemiological spread slows down. The probability that infected people infect susceptible people in the community is dependent on the risk literacy of the population, due to the fact the knowledge about the disease and governmental interventions can have a impact on the contact of infected and susceptible people in the total population.

Its origin is in the early 20th century, with an important early work being that of Kermack and McKendrick in 1927.