Intro to modelling infectious diseases

Question 1

What is a model?

Answer 1

model - a formalised way of thinking about a process

Question 2

What does the risk of becoming infected dependent on?

Answer 2

an uninfected individual’s risk of becoming infected (remember this is called force of infectiion) depends upon the prevelance of infectious individuals (a population level of measure) - how likely somebody is to develop AIDS is dependent on the HIV prevalence of the part of the world they are living in

Question 3

Can transmission change over time?

Answer 3

transmission of infection in a population is a dynamic process and the individual risk of infection can change over time - poplations aren’t static and their composition can change over the course of an outbreak - a 2 year old doesn’t have the same immunity as an adult or an old person

Question 4

What is a deterministic model?

Answer 4

deterministic - describe what happens on average in the population. The input parameters are fixed and therefore the models predictions such as the number of cases which will be seen over time will be “predetermined”

Question 5

What is a stochastic model?

Answer 5

stochastic - allow the number of individuals who move between compartments to vary through chance. They provide a chance in which an outcome such as the number of cases over time will occur

Question 6

What are model types based on?

Answer 6

models vary based on how much of the process description they have in them

Question 7

What is a static model?

Answer 7

static- model does not explicitly describe contact. The risk of force of infection therefore takes predetermined values;

Question 8

What is a micro-simulation model?

Answer 8

individual-based or micro-simulation model: the model tracks the infection process for every individual in thee computationally generated population. Many individual based models are stochastic; bases of COVID-19 models from Imperial

Question 9

What is a transmission dynamic model?

Answer 9

transmission dynamic models - model incorporates contact between individuals. The risk or force of infection depends on number of infectious individuals in the population and so the risk shifts in time as the number of infectious individuals change. Determining that the risk of infection is strictly dependant on thee number of infected individuals

Question 9

What is a transmission dynamic model?

Answer 9

transmission dynamic models - model incorporates contact between individuals. The risk or force of infection depends on number of infectious individuals in the population and so the risk shifts in time as the number of infectious individuals change. Determining that the risk of infection is strictly dependant on thee number of infected individuals

Question 10

What is a compartment model?

Answer 10

compartment models - individuals in thee population are subdivided into subgroups and thee model tracks the infection process for these individuals collectively (can be deterministic or stochastic, but primarily deterministic)

Question 11

What is a network model?

Answer 11

network - model in which the network of contacts between individuals is explicitly modelled (like STIs A had sex with B) The risk of infections for an individual in the model depends on their network contacts

Question 12

What is the most common compartment model?

Answer 12

• most common is SIR - susceptible, infected , recovered
  
  • individuals are subdivided into those categories and that’s how you track the process of disease

Question 13

When can you get an SI model?

Answer 13

f you have an infection that doesn’t create any immunity to it in the host you might only have an SI model - the host never really recovers from the infection but they are all still susceptible to it

Question 14

What other models can you get depending on the immunity gained by the host?

Answer 14

You can also have cases where the host only gets it once and develops lifelong immunity against the disease (becomes solidly immune) or you can have a case where the host clears the infection temporarily but that doesn’t mean that after some time they won’t get it again.

Question 15

What is a SEIR model?

Answer 15

We need to remember about the period where the individual has been exposed to the pathogen, they have been exposed to the infection but are not yet infectious and can spread the disease so for that we would have an SEIR model in which we would add an “exposed box”.

Question 16

Why are the accuracy and time period important for the model?

Answer 16

1. daily estimates from and SIR model are less reliable than SEIR (both will give the same total number of infections at the end but on the daily level some Es will still look like an S so the next day Is will differ
2. Long term models might need to incorporate important changes to demography (schools out!) or if variation in birth and death rates. Longer term might also need to consider changes to the strain infectivity

Question 17

What model is best for solving research questions?

Answer 17

ideally we want the simplest model possible - it is a simplification of reality that allows us too explore patterns

Question 18

How to calculate how many people will get infected between t and t+1

Answer 18

the number of individuals who are newly infected between t and t+1 is the product of risk of susceptible individual becoming infected between t and t+1 (which we sue lambda to abbreviate) and the number of susceptible individuals at the time t
example 5% of susceptible individuals are newly infected between today and tomorrow and 200 susceptible individuals are present today, then the number of individuals who are newly infected between today and tomorrow equals 0.05*200=10

Question 19

What is a differential equation?

Answer 19

used to represent rates of exchange or time-varying phenomenon

Question 20

How do you check if your differential equations are good?

Answer 20

• # of equations = # of compartments in the model
• in the model the populations are treated as closed populations - no ine is leaving or entering so if you sum up the equations they should be equal to zero!

Question 21

How do you check if your differential equations are good?

Answer 21

• # of equations = # of compartments in the model
• in the model the populations are treated as closed populations - no ine is leaving or entering so if you sum up the equations they should be equal to zero!

Question 22

Why should we use differential equations?

Answer 22

• working with single time steps in the difference equations rapidly becomes cumbersome (GIANT EXCEL SHEET!)
• allows us to describe current transmission dynamics but also gain insights into dynamics of infections and factors influencing incidence and course of epidemic

Question 23

What is ß?

Answer 23

ß is a rate at which two specific individuals come into effective contact per unit time and I(t) is the number of infectious individuals at time t

Question 24

What is R0?

Answer 24

• basic reproductive number - reproductive number when an infectious person is introduced to a completely susceptible population
  
  • average number of secondary infections resulting from a typical infectious person following their introduction into a totally susceptible population

Question 25

What does R>1 mean?

Answer 25

R>1 for most infections is the point at which the disease can spread

Question 26

What is the relationship between, population size, duration of infectoiusness and R0?

Answer 26

The higher the contact rate, population size and infectious period the greater the R0

R0 = ßND

Question 27

Write difference the equations for S I and R at time t+1

Answer 27

see notes

Question 28

What does the reliability of difference equations depend on?

Answer 28

The reliability of difference equations depends on the tilmestep used - if your tilmestep is three days then your model will be less reliable than if it was one day as you will be overestimating/ underestimating some compartments

Question 29

write out the differential equations for the SIR model

Answer 29

see notes

Question 30

write the difference equations for the SEIR model

Answer 30

see notes