Infectious Disease Modelling

Question 1

What is the SIR Model for Infectious Diseases

Answer 1

Susceptible –> Infected –> Recovered

Everyone is allocated to 1 box, can’t be in more than 1.

Question 2

What is R0

Answer 2

the average number of secondary infections caused by a single typical infectious individual over their lifetime when introduced to a completely susceptible population (depends on both pathogen and population)

Question 3

What is Re or Rt
(Net/Effective Reproduction Number)

Answer 3

Takes into account the current state of the population:
- not everyone is susceptible (some people are immune etc.)
- changes in contact rate
- If 1 infection is in reality causing <1 case: good.

Question 4

What is herd immunity

Answer 4

A population is protected when not everyone is immune
(most people are immune so Re (or Rt) is <1).

Question 5

What is a stochastic model?

Answer 5

Used when there are small numbers of cases - early phase. The outcome isn’t the same each time - can’t precisely predict outcome as get a different answer each time - need many runs to build up a picture of outcomes. Includes variability from chance.

If the population is small, stochastic effects may be of substantial importance and you may never get to a point where stochastic effects are negligible

Question 6

What is the deterministic model

Answer 6

if you start in the same place with the same parameters you get the same result each time (only applicable to big numbers).
Only 1 run needed for meaningful outcome.
No accounting for probability

Question 7

Compartmental Models

Answer 7

Population is divided into boxes and the count from each box is modelled.
Deterministic or Stochastic
Easier & less intensive (but can still be complex)

Question 8

Individual Based Models

Answer 8

aka: infectious disease models, microsimulations, agent based models
Every individual in the population is modelled
Necessarily stochastic (because not just small numbers but 1)

Question 9

What happens in the growth phase
What is generation time

Answer 9

Exponential Growth.
Generation Time = mean time interval between infection and the onwards infections they cause <– if known can give data about R0.
Need to know R0 and Generation Time because otherwise exponential growth can either be a big R0 and small generation time or a small R0 and big generation time
Contact tracing can help estimate

Question 10

Turnover

Answer 10

when stops being exponential and starts decreasing (reaches a peak)

Question 11

SI Model

Answer 11

Susceptible –> Infected

never stop being infected e.g. HIV

If R0 = 2: will stop infecting when 1/2 population is infected.
If R0 = 4 or 5: theoretically will only cause infection when 75-80% of population infected (but in HIV this doesn’t actually happen due to heterogeneity –> a core group e.g. those with lots of sexual partners will have high prevalence but this is usually a small fraction of the population

Question 12

SIS Model

Answer 12

Susceptible –> Infected –> Susceptible
e.g. Gonorrhoea, Rhinovirus

Question 13

SIRS Model

Answer 13

Susceptible –> Infected –> Recovered –> Susceptible

Stay immune for a while but it wanes e.g. pertusis

Question 14

SEIR Model

Answer 14

Susceptible –> Exposed –> Infected –> Recovered

Exposed = latent infection. Allows to build a delay in modelling between infection and infectiousness. Useful for contact tracing and quarantine

Question 15

What happens after infection spike is over (endgame)

Answer 15

Following a decline & reaching endemicity, children or immigration can increase numbers again. –> the higher the birth rate the smaller the interval between peaks