INDIVIDUAL-BASED TRANSMISSION MODELS PROF. WILLEM
INTRODUCTION
COURSE OBJECTIVES:
1. Infectious diseases
2. Transmission models : Population level Individual-based
3. Model exploration
1. INFECTIOUS DISEASES
- Epidemic: a disease that affects a large number of people within a community, population or
region local
o Example: Ebola: mostly in Western Africa
- Pandemic: an epidemic that’s spread over multiple countries or continents
o Example: SARS-CoV2
2. TRANSMISSION MODELS
Models are useful for scenario analysis: when people are ill, they stay home instead of going to the
office. Other scenario: what would have happened if I was in class being symptomatic for covid-19.
To go into the machinery: in this virtual reality we can track 1 individual through his day / life, count
the number of social encounters… Much less trivial in the real world.
A model is always an abstraction, it will never catch all aspects
of reality but they can be useful is used properly
EXAMPLE OF A SCENARIO ANALYSIS:
HOUSEHOLD BUBBLES
We did scenario analysis without and with bubbles: closed
network vs open network (same number of contacts as closed
but other people instead of the same people).
1. DETERMINISTIC MODELS
STATIC MODEL
- Abstract
- E.g. economic analyses
- “Spreadsheet”
Number of cases / incidence over time & average cost per case -> calculate the
cost. There is no feedback loop: the number of cases today have no impact on
the cases of tomorrow.
, DYNAMIC COMPARTMENT MODEL
- Population = { compartments }
- (At least) based on health state
- Population averages
- Deterministic
SIR model for example. The number of infected today will have an impact on the number of new
infections in the next time step.
FORCE OF INFECTION (λ)
- Transmission rate β
- Proportionality factor q
- Contact rate cij
- Number of contacts mij
- Population size N
Differential equations -> model is fully characterized and will always have the same outcome for the
same conditions.
EXAMPLE: FITTING SIR
Fit the data by using a solver & the
differential equations find a parameter
combinations which matches this outcome
of the number of infected over time.
BASIC REPRODUCTION NUMBER R0
“Number of secondary cases of a typical individual in a completely susceptible population.”
“~= the average number of secondary cases from an index case during their infectious period (=1/v)”
- When at the start of the epidemic we talk about R0:
o If R0 = 1 -> epidemic is stable
o If R0 < 1 -> epidemic fades out
o If R0 > 1 -> epidemic is growing
2. INDIVIDUAL-BASED MODELLING
SIR model but they are not homogeneously spread
in the population. Some people stay at home, others
go to work/school, in the night all people go home.
Clustering: people in workplaces. In 1 school you can
have a lot of infected people while in another one
you don’t -> clustering, no random allocation.
Individual based modelling for infectious diseases: characterize unique individuals that interact and
include an infectious disease
INTRODUCTION
COURSE OBJECTIVES:
1. Infectious diseases
2. Transmission models : Population level Individual-based
3. Model exploration
1. INFECTIOUS DISEASES
- Epidemic: a disease that affects a large number of people within a community, population or
region local
o Example: Ebola: mostly in Western Africa
- Pandemic: an epidemic that’s spread over multiple countries or continents
o Example: SARS-CoV2
2. TRANSMISSION MODELS
Models are useful for scenario analysis: when people are ill, they stay home instead of going to the
office. Other scenario: what would have happened if I was in class being symptomatic for covid-19.
To go into the machinery: in this virtual reality we can track 1 individual through his day / life, count
the number of social encounters… Much less trivial in the real world.
A model is always an abstraction, it will never catch all aspects
of reality but they can be useful is used properly
EXAMPLE OF A SCENARIO ANALYSIS:
HOUSEHOLD BUBBLES
We did scenario analysis without and with bubbles: closed
network vs open network (same number of contacts as closed
but other people instead of the same people).
1. DETERMINISTIC MODELS
STATIC MODEL
- Abstract
- E.g. economic analyses
- “Spreadsheet”
Number of cases / incidence over time & average cost per case -> calculate the
cost. There is no feedback loop: the number of cases today have no impact on
the cases of tomorrow.
, DYNAMIC COMPARTMENT MODEL
- Population = { compartments }
- (At least) based on health state
- Population averages
- Deterministic
SIR model for example. The number of infected today will have an impact on the number of new
infections in the next time step.
FORCE OF INFECTION (λ)
- Transmission rate β
- Proportionality factor q
- Contact rate cij
- Number of contacts mij
- Population size N
Differential equations -> model is fully characterized and will always have the same outcome for the
same conditions.
EXAMPLE: FITTING SIR
Fit the data by using a solver & the
differential equations find a parameter
combinations which matches this outcome
of the number of infected over time.
BASIC REPRODUCTION NUMBER R0
“Number of secondary cases of a typical individual in a completely susceptible population.”
“~= the average number of secondary cases from an index case during their infectious period (=1/v)”
- When at the start of the epidemic we talk about R0:
o If R0 = 1 -> epidemic is stable
o If R0 < 1 -> epidemic fades out
o If R0 > 1 -> epidemic is growing
2. INDIVIDUAL-BASED MODELLING
SIR model but they are not homogeneously spread
in the population. Some people stay at home, others
go to work/school, in the night all people go home.
Clustering: people in workplaces. In 1 school you can
have a lot of infected people while in another one
you don’t -> clustering, no random allocation.
Individual based modelling for infectious diseases: characterize unique individuals that interact and
include an infectious disease
