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Further infectious disease modelling Flashcards

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1
Q

Why do we model infectious disease transmission?

A

So that we can determine the population-level effect of fundamental infection and transmission processes occurring at the individual level

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2
Q

What does modelling infectious disease transmission allow us to do?

A

Simplify a complex system so it is suitable for analysis

Capture essential behaviour by incorporating key processes

Clarify thinking about what is known and what needs further research

Help to understand transmission dynamics and the impact of control interventions

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3
Q

Modelling infectious disease transmission is used to answer numerous questions of veterinary and human public health importance. What are some of these questions?

A

How large will an epidemic be?

How quickly will an epidemic rise, peak and fall?

How can we control an epidemic?

How prepared are we for an epidemic?

How do we control or eliminate endemic diseases?

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4
Q

What does an uninfected individual’s risk of becoming infected depend on?

A

Prevalence of infectious individuals, their rate of contact, infectiousness, etc

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5
Q

What is the process of transmission?

A

A dynamic one. An individual’s risk of infection changes with time

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6
Q

What models are required for transmission?

A

Dynamic models for analysis and prediction

(think rates of change)

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7
Q

What are some modelling considerations?

A

Population structure, demography; age- and sex-specific patterns of infection; contact patterns

Natural history of infection
- Latency; infectious period; portective acquired immunity, asymptomatics, other hosts, vectors or reservoirs of infection

Transmission of infection
- Direct or indirect?
- Horizontal or vertical?
- What affects contact rates?

Interventions
- What parts of the transmission process can be targeted?
- How can they be effectively targeted?

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8
Q

What do we need to think about when modelling disease with regards to natural history of infection?

A

Latency

Infectious period

Protective acquired immunity

Asymptomatics

Other hosts, vectors or reservoirs of infection

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9
Q

What do we need to think about when modelling disease with regards to transmission of infection?

A

Direct or indirect?

Horizontal or vertical?

What affects contact rates?

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10
Q

What do we need to think about when modelling disease with regards to interventions?

A

What parts of the transmission process can be targeted?

How can they be effectively targeted?

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11
Q

What are the three main steps to building a transmission model?

A
  1. Draw a flow diagram representing the natural history of infection
  2. Write a set of equations - usually ordinary differential equations - and parameterize
  3. Solve the equations, algebraically or more often numerically, using algorithms implemented in a variety of softward packages (e.g. R)
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12
Q

What are the 5 other steps when building a transmission model?

A
  1. Fitting: Estimate parameters by fitting to data
  2. Validation: Compare model output with data not used to fit the model
  3. Projection/forecasting/ prediction: Use the model (cautiously and carefully) to predict the future!
  4. Improve/refine: An iterative process capable of incorporating new knowledge/biology/treatments/interventions
  5. Documentation: Formal mathematical description of the model, code and user guide
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13
Q

How do you draw a flow diagram for disease modelling?

A

Divide population of interest into compartments/categories according to biological properties of different states (e.g. stages of infection in host populations)

  • In a population-based model, all those individuals have the same properties
  • These correspond to the average properties of those in the ‘real world’

Susceptible (naiive) –> Infectious –> Recovered (immune)

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14
Q

What are the 2 basic elements that compartmental models (e.g. the SIR model) are constructed from?

A
  1. (Sub-)Population sizes
  2. Rates of change of (sub-) population sizes
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15
Q

What do we mean by (sub-) population sizes?

A

E.g. the number of susceptible, infectious or immune individuals in a population

These values are stored in state variables which describe the state of the system

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16
Q

What do we mean by rates of change of (sub-) population sizes?

A

E.g. incidence of infection, recovery rate

These values usually depend on one or more of the values of the state variables, so they change dynamically as the system changes (i.e. there is feedback)

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17
Q

What is the compartmental model?

A

The model itself is a set of differential equations that descrive the system and its dynamics

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18
Q

What are the solutions in compartmental modelling?

A

The solutions to the equations are the predictions of the model.

Solutions are normally found using numerical integration implemented in computer software

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19
Q

What happens in deterministic models?

A

Each set of parameters gives a unique solution, which can include fractions of individuals

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20
Q

What are the equations in the SIR model?

A

dS/dt = transmission events

dI/dt = transmission events - recoveries

dR/dt = recoveries

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21
Q

What is a ‘flow rate’?

A

Each flow rate is the number of individuals entering or leaving a compartment per unit time.

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22
Q

What does the flow rate depend on?

A

The per capita rate

The number of individuals subject to that per capita rate

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23
Q

What is the flow rate equation?

A

Flow rate = per capita rate x number of individuals

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24
Q

What is the average duration spent in a compartment?

A

1 / per capita rate

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25
What is the rate of recovery from infection?
Let the per capita rate of recovery be p The population recovery or 'flow rate' is p x I
26
What is the transmission rate?
Flow between susceptible and infectious compartments The transmission rate depends on the proportion of infected infectious individuals 'I/N' at each time and the rate of infectious contacts with susceptible individuals, ß Population transmission rate = ßSI/N
27
How do we solve the equations for compartmental model?
We are interested in plotting how the numbers in each compartment change over time The model differential equation specify derivative or rates of change in state variables (i.e. number of S, I and R) at any time. To get the numbers, we solve the equations by integration. Usually we do this numerically using computers Numerical integration requires specification of initial values (i.e. starting numbers of individuals in each state)
28
What should the compartmental models be?
Simple, while capturing the essential details (principle of parsimony). Important details include: - Latent period - Incubation period Other examples inc. compartments for additional hosts (such as vector-borne diseases) or exogenous infections (e.g. zoonotic infections or infections imported into susceptible populations) We can include these essential features by incorporating additional compartments or rate parameters
29
What is the latent period?
The period between an individual being infected and becoming infectious
30
What is the incubation period?
The time between an individual being infected and becoming symptomatic
31
What do we assume in the SIR model?
That individuals are infectious as soon as they become infected.
32
What do we do in a compartmental model when there is a significant delay between infection and infectiousness?
Add an additional 'exposed' compartment ie. SEIR To capture the latent period
33
What do we know about the incubation period and SIR models?
Infections are often treated when a person becomes symptomatic and so becomes aware that they are infected For some diseases, symptoms and infectiousness coincide (e.g. SARS-CoV-1) while for others, symptoms begin after the person is infectious (e.g. Influenza, HIV, SARS-CoV-2) This disease-specific feature has a very important consequences for the identification of cases and implementation of effective control
34
What is the basic reproduction number, R0?
R0 is the average number of secondary infections caused by one primary case/infection in a totally susceptible population
35
What does it mean if R0>1?
Disease WILL spread
36
What does it mean if R0≤1?
The disease WILL NOT spread
37
What can occur if R0≤1?
Small outbreaks can occur, but they will die out eventually Think small zoonotic outbreaks
38
What does R0 describe?
How effectively an infection spreads and how hard it is to control!
39
What is the R0 number for Measles?
12-18
40
What is the R0 number for Smallpox (eradicated)?
5-7
41
What is the R0 number for Chicken Pox?
7-8
42
What is the R0 number for Mumps?
4-7
43
What is the R0 number for HIV/AIDS?
2-5
44
What is the R0 number for Malaria?
1-55
45
What is the R0 number for H1N1 influenza (1918 Pandemic)?
2-3
46
What is the R0 number for Ebola (2014 outbreak)?
1.5-2.5
47
What is the R0 number for SARS-CoV-1?
~ 2.5
48
What is the R0 number for MERS-CoV?
~ 0.5
49
What is the R0 number for SARS-CoV-2?
~ 2.5
50
What is the reproduction number, Rt?
Rt is the average number of secondary infections caused by one primary case/infection in a totally susceptible population
51
What does Rt describe?
Rt describes whether an epidemic is currently increasing or declining
52
What is Rt useful for?
Monitoring the progress of an epidemic and evaluating the impact of interventions
53
What does it mean when Rt>1?
The outbreak is growing Each person infects more than one other person
54
What does it mean when Rt = 1?
The outbreak is stable - the number of new cases is not increasing or decreasing (without intervention) Herd immunity has been reached
55
What does Rt<1 mean?
The outbreak is shrinking - each person infects fewer than one other person
56
What is the epidemic overshoot beyond the point Rt=1?
Total number of infections increases for a time beyond this point
57
How do we estimate R0 and Rt?
There is no single way to estimate R0/R but we can broadly divide the methods into data-driven ('top down') and model-driven ('bottom up') approaches
58
What are 'bottom up' methods?
Bottom up methods are derived from models and are related to the fundamental transmission and infection processes considered by the model
59
What are 'top down' methods?
Methods which rely on combining estimates of the growth rate of an epidemic, r, with knowledge about the generation time, Tg, which is the time between the infection of an individual and the infections that follow
60
How do we estimate R0 and Rt from the SIR model using the 'bottom up' method?
Consider one primary individual infected. He or she is infected for a duration 1/p during which time they infect people at a rate ß So... R0 = ß/p Rt = ßIpS/N (the re-parameterisation ß=R0p is often used to avoid having to specify a contact rate)
61
How do we estimate R0 and Rt from the SEIR model using the 'bottom up' method?
So again... R0 = ßIp Rt = ßIp*S/N (Assuming everyone survives the 'exposed state' and becomes infectious)
62
How are parameters estimated using the 'bottom-up' method?
Some parameters we can estimate directly, others we have to estimate from epidemiological data - Average duration of infection (quite easy, but does not necessarily correspond to duration of infectiousness) - Incubation period (harder, but possible with contact tracing) - Latent period (harder still but possible with very detailed contact information but more likely estimated from model - Contact rate (nearly always impossible to measure, except for STIs so estimated as part of model fitting)
63
How do we fit a model to data?
Typically models fitted to data and often during the early phase of an epidemic E.g. we may fit an SIR model (or another structure) to incidence data to estimate R0 (assuming we know p, in this example 1/10 per day)
64
What do we know about exponential growth and generation time?
1 person infected 2 more infected (1st gen) 4 more infected (2nd gen) Generation time, Tg = 1 day New cases (incidence) = exp(rt)
65
What is the general R0 formula regarding epidemic growth rate and generation time?
R0 = exp (rTg) A simple formula can be used to estimate R0 at the start of an outbreak to give an early indication of the likely course of the epidemic and how difficult the disease might be to contain
66
What is incidence derived from when estimating Rt during epidemics?
Incidence of new infections now, It, is derived from infections in the past, It-1, It-2, It-3 etc The contribution of infections from the past occurring now is defined by the distribution of Tg

Epidemiology (11 decks)

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