4: The SIR model and its Variants (pt 1)

Question 1

key feature of the SIR model

Answer 1

divide the population into several classes or compartments to then model the transition between them
- compartmental models

Question 2

what are the 3 models of the SIR model?

Answer 2

susceptibles - infected - recovered

susceptible include people who have not yet been infected but can be once exposed to the virus

infected/infectious where we assume everyone infected is infectious immediately

recovered as the people who have recovered and are no longer infectious with the assumption that once recovered, you are totally free from infectious again

Question 3

unrealistic assumptions of the SIR model

Answer 3

no one dies
- not that important with SARS-CoV-2 since the fatality rate is not so high

no demography (no one is born or dies from other causes)

• total population remains constant
• even if the disease didn’t kill anyone, people would die and a realistic model would take that into account
• not a big deal for a short period of time

transition only goes from one direction
- from S to I to R but you don’t go the other way

everyone in the population falls into one of the 3 categories (N = S + I + R)
- not everyone is susceptible, some might have recovered but still be susceptible, might be infected but not infectious, etc.

immunity doesn’t wane

• you can never be infected again according to the model
• immunity is not only perfect and 100% effective but never goes away
• level of antibodies goes down with time, virus mutates with natural selection, etc.

homogenous population mixing: assumption that people have contact which each other in the population at random
- effectively saying that if you are infectious, you have the same probability of infecting someone you will never meet as your best friend

infection and recovery processes take place at a constant rate

• infect other people at the same rate once infected in the model
• not realistic since you don’t infect anyone right after being infected (virus needs time to replicate)

no latency period between infection and infectiousness
- when someone is infected, they ar immediately infectious but obviously this is not true