Prof. Dr. Niel Hens: Health economics and
mathematical models of infectious diseases
MAIN QUESTION: GIVES YOU THE RULES ON A PATHOGEN & YOU CREATE A SCHEMATIC REPRESENTATION OF
HOW YOU WOULD MAKE A MATHEMATICAL METHOD .
PROLOGUE
BACKGROUND INFORMATION
- There are countless infectious agents infecting human, animal and plant hosts
- Infectious diseases are caused by pathogens, which are transmissible between hosts:
o Transmitted directly between hosts (resp. air or bodily fluids)
o Transmitted indirectly through intermediary source
E.g. mosquitos, tickets, rodents, environmental particles or blood products
- Infectious agents evolve & transform while new agents emerge regularly
o Their supply can be considered infinite
- Microscopically small infectious agents with relatively short life spans, which replicate within
their hosts called microparasites such as viruses, bacteria and fungi.
- Larger infectious agents w/ relatively longer life spans: macroparasites (e.g. parasitic worms)
o Parasitic worms are more complicated to model. Neglected tropical diseases have
been neglected for a long while because they are so complicated to study.
- Infectious agents causing disease in their hosts are often referred to as pathogens.
o Many infectious agents live inside/on their hosts’ bodies without causing illness or
discomfort. Hosts can depend for survival on infectious agents (e.g. bacteria in gut)
AN INFECTIOUS DISEASE IS OFTEN CHARACTERIZED BY ITS:
1. Transmission route 4. Acquired immunity
2. Transmission potential 5. Symptomatic/asymptomatic
3. Natural history: incubation time, latent or pre-infectious period, infectious period
TRANSMISSION ROUTE
The essential underestimation of SARS-COV2 was because it was compared to SARS-COV1: contained
quickly because it only spread when there were symptoms. Also the case for MERS-COV, Ebola. To
some extend this is the case for monkeypox: you can have symptoms but you could not notice them.
However, Ebola outbreaks still occur because the symptoms are not always distinguishable. The first
symptoms of Ebola are very flu-like and malaria-like. Ebola is fairly easy to contain but the big
outbreak could occur because of the civil war that destroyed the health-care system.
We need to know the transmission (route) to characterize an infection. For example the sexual
transmission route is a very infective route. We want to test the hypothesises of transmission
because it tells us what to expect in the future, who to vaccinate, who to treat,… The transmission
route is critical: whether SARS-cov-2 is aerosolized or are it thick droplets or both? Depends on the
pathogen and it can be very difficult to determine the true infective route. You also just need to
know the most important transmission route: malaria can also be transmitted faecal-orally, but you
don’t need to focus on this as it doesn’t happen as much: focus on the mosquito.
,TRANSMISSION POTENTIAL
There is often the mention of the R0. This is however not completely correct. It tells you how many
secondary case one infectious case would induce in a completely susceptible population but you
don’t know how fast it occurs! You also need to look at the speed. You have to look at the number of
people you can infect but also the time it takes for this infection.
NATURAL HISTORY
- Incubation time: between time of infection & time of onset of symptoms
o Short for flu: can be ignored, longer for SARS-COV2: cannot be ignored
o When it overlaps with the infectious period: interesting for the pathogen because
you will still have more contacts with others, facilitating spread
- Latent or pre-infectious period: period between infection and the onset of communicability
- Infectious period: not known for SARS-cov2 because we took measures quickly, destroying
actual observations.
ACQUIRED IMMUNITY
How much immunity did we gain in the previous waves? Are new variants still true concerns? These
questions are posed often again and we need answers but the data can be lacking or lagging.
ASYMPTOMATIC / SYMPTOMATIC
Asymptomatic transmission: you need to take this into account in modelling too. Symptomatic cases
are often more ‘transmissionable’. You need to include this in the models. However which symptoms
are included? However symptomatic individuals can change their behaviour: stay away from people…
However asymptomatic people don’t know they carry the virus: more contacts etc. Therefore both S
and A people could be the ones driving the transmission.
EXAMPLE OF THE INFECTIOUS DISEASE PROCESS
This is a good model for eg measles. if you experience a natural infection with measles you are
protected for life. In BE there is a high vaccination coverage for measles.
1. Infection: pathogen starts replicating and mounting
2. At a certain point you are infectious
3. This drops (hopefully) after a while & you recover
4. After recovery you are either recovered or ‘removed’ because you can also be dead
, We don’t model it like this anymore, we split recovery & death. If you die, for example of covid, this
happens faster than people recovering: these differences need to be taken into account in the
models.
- Infection status: can be extended too with more compartments.
- IR: first cellular immunity then humoral that’s more targeted. After a while the IR also drops
again, but here it is higher at the end than at the start = memory cells.
- Overlap of incubation period & infectious period : good for pathogen. Diseased & recovered
also overlap: when you had a cold it’s possible to still have a little cough when recovered.
The key challenge is that your mathematical models line up with your data. This is difficult because
you need the medical status of people, but you only get this when it’s bad enough that people go to
the GP. You miss out on asymptomatic people & people that are not sick enough.
TAXONOMY
- Generation interval: the interval defined by the times of infection of two consecutive
cases in a transmission chain
o The ‘timing’ next to the reproduction number. You cannot measure this: you typically
don’t really know when you’re infected. You know when the symptoms started
- Serial interval: the interval defined by the times of symptom onset of two consecutive
cases in a transmission chain
o Time between your first symptoms and the person you infected’s first symptoms.
Often used as a proxy for the generation interval
TRANSMISSION ROUTES
1. Close Contacts Transmission (Chickenpox, Influenza, Mumps, Tuberculosis, Measles, ...)
2. Sexual Transmission (Hepatitis B, HIV, HPV, ...)
3. Parenteral Transmission (Hepatitis B and C, HIV, ...)
4. Orofecal Transmission (Hepatitis A, Cholera, Rotavirus, ...)
5. Vertical Transmission (Hepatitis B and C, HIV, Syphilis, ...)
6. Vector-borne Transmission (Malaria, Dengue, Leishmaniasis, ...)
Close contacts transmissions can be aerosol, droplets,.. because you often don’t really know what’s
at play. Transmission routes can change depending on the setting you’re in. HIV in sub-Saharan
Africa: sexual transmission, in EU: more needle drug use & sex workers. Sometimes you take all
infectious routes into account in the model but sometimes you only need the most important ones.
MATHEMATIC MODELLING OF INFECTIOUS DISEASES
PURPOSES: You cannot experiment in real life so you need models. You need to check the impact of
interventions before you launch them. However you cannot treat them as the holy grail. We need to
be clear about what mathematical models can and cannot do. 1. Prediction: You try to forecast
what will happen under certain conditions: if we would close schools. Forecasting requires inclusion
of the known complexities, structures and population-level heterogeneity. Then you come up with
scenarios such as vaccines, boosters,… 2. Understanding: to investigate factors that drive
mathematical models of infectious diseases
MAIN QUESTION: GIVES YOU THE RULES ON A PATHOGEN & YOU CREATE A SCHEMATIC REPRESENTATION OF
HOW YOU WOULD MAKE A MATHEMATICAL METHOD .
PROLOGUE
BACKGROUND INFORMATION
- There are countless infectious agents infecting human, animal and plant hosts
- Infectious diseases are caused by pathogens, which are transmissible between hosts:
o Transmitted directly between hosts (resp. air or bodily fluids)
o Transmitted indirectly through intermediary source
E.g. mosquitos, tickets, rodents, environmental particles or blood products
- Infectious agents evolve & transform while new agents emerge regularly
o Their supply can be considered infinite
- Microscopically small infectious agents with relatively short life spans, which replicate within
their hosts called microparasites such as viruses, bacteria and fungi.
- Larger infectious agents w/ relatively longer life spans: macroparasites (e.g. parasitic worms)
o Parasitic worms are more complicated to model. Neglected tropical diseases have
been neglected for a long while because they are so complicated to study.
- Infectious agents causing disease in their hosts are often referred to as pathogens.
o Many infectious agents live inside/on their hosts’ bodies without causing illness or
discomfort. Hosts can depend for survival on infectious agents (e.g. bacteria in gut)
AN INFECTIOUS DISEASE IS OFTEN CHARACTERIZED BY ITS:
1. Transmission route 4. Acquired immunity
2. Transmission potential 5. Symptomatic/asymptomatic
3. Natural history: incubation time, latent or pre-infectious period, infectious period
TRANSMISSION ROUTE
The essential underestimation of SARS-COV2 was because it was compared to SARS-COV1: contained
quickly because it only spread when there were symptoms. Also the case for MERS-COV, Ebola. To
some extend this is the case for monkeypox: you can have symptoms but you could not notice them.
However, Ebola outbreaks still occur because the symptoms are not always distinguishable. The first
symptoms of Ebola are very flu-like and malaria-like. Ebola is fairly easy to contain but the big
outbreak could occur because of the civil war that destroyed the health-care system.
We need to know the transmission (route) to characterize an infection. For example the sexual
transmission route is a very infective route. We want to test the hypothesises of transmission
because it tells us what to expect in the future, who to vaccinate, who to treat,… The transmission
route is critical: whether SARS-cov-2 is aerosolized or are it thick droplets or both? Depends on the
pathogen and it can be very difficult to determine the true infective route. You also just need to
know the most important transmission route: malaria can also be transmitted faecal-orally, but you
don’t need to focus on this as it doesn’t happen as much: focus on the mosquito.
,TRANSMISSION POTENTIAL
There is often the mention of the R0. This is however not completely correct. It tells you how many
secondary case one infectious case would induce in a completely susceptible population but you
don’t know how fast it occurs! You also need to look at the speed. You have to look at the number of
people you can infect but also the time it takes for this infection.
NATURAL HISTORY
- Incubation time: between time of infection & time of onset of symptoms
o Short for flu: can be ignored, longer for SARS-COV2: cannot be ignored
o When it overlaps with the infectious period: interesting for the pathogen because
you will still have more contacts with others, facilitating spread
- Latent or pre-infectious period: period between infection and the onset of communicability
- Infectious period: not known for SARS-cov2 because we took measures quickly, destroying
actual observations.
ACQUIRED IMMUNITY
How much immunity did we gain in the previous waves? Are new variants still true concerns? These
questions are posed often again and we need answers but the data can be lacking or lagging.
ASYMPTOMATIC / SYMPTOMATIC
Asymptomatic transmission: you need to take this into account in modelling too. Symptomatic cases
are often more ‘transmissionable’. You need to include this in the models. However which symptoms
are included? However symptomatic individuals can change their behaviour: stay away from people…
However asymptomatic people don’t know they carry the virus: more contacts etc. Therefore both S
and A people could be the ones driving the transmission.
EXAMPLE OF THE INFECTIOUS DISEASE PROCESS
This is a good model for eg measles. if you experience a natural infection with measles you are
protected for life. In BE there is a high vaccination coverage for measles.
1. Infection: pathogen starts replicating and mounting
2. At a certain point you are infectious
3. This drops (hopefully) after a while & you recover
4. After recovery you are either recovered or ‘removed’ because you can also be dead
, We don’t model it like this anymore, we split recovery & death. If you die, for example of covid, this
happens faster than people recovering: these differences need to be taken into account in the
models.
- Infection status: can be extended too with more compartments.
- IR: first cellular immunity then humoral that’s more targeted. After a while the IR also drops
again, but here it is higher at the end than at the start = memory cells.
- Overlap of incubation period & infectious period : good for pathogen. Diseased & recovered
also overlap: when you had a cold it’s possible to still have a little cough when recovered.
The key challenge is that your mathematical models line up with your data. This is difficult because
you need the medical status of people, but you only get this when it’s bad enough that people go to
the GP. You miss out on asymptomatic people & people that are not sick enough.
TAXONOMY
- Generation interval: the interval defined by the times of infection of two consecutive
cases in a transmission chain
o The ‘timing’ next to the reproduction number. You cannot measure this: you typically
don’t really know when you’re infected. You know when the symptoms started
- Serial interval: the interval defined by the times of symptom onset of two consecutive
cases in a transmission chain
o Time between your first symptoms and the person you infected’s first symptoms.
Often used as a proxy for the generation interval
TRANSMISSION ROUTES
1. Close Contacts Transmission (Chickenpox, Influenza, Mumps, Tuberculosis, Measles, ...)
2. Sexual Transmission (Hepatitis B, HIV, HPV, ...)
3. Parenteral Transmission (Hepatitis B and C, HIV, ...)
4. Orofecal Transmission (Hepatitis A, Cholera, Rotavirus, ...)
5. Vertical Transmission (Hepatitis B and C, HIV, Syphilis, ...)
6. Vector-borne Transmission (Malaria, Dengue, Leishmaniasis, ...)
Close contacts transmissions can be aerosol, droplets,.. because you often don’t really know what’s
at play. Transmission routes can change depending on the setting you’re in. HIV in sub-Saharan
Africa: sexual transmission, in EU: more needle drug use & sex workers. Sometimes you take all
infectious routes into account in the model but sometimes you only need the most important ones.
MATHEMATIC MODELLING OF INFECTIOUS DISEASES
PURPOSES: You cannot experiment in real life so you need models. You need to check the impact of
interventions before you launch them. However you cannot treat them as the holy grail. We need to
be clear about what mathematical models can and cannot do. 1. Prediction: You try to forecast
what will happen under certain conditions: if we would close schools. Forecasting requires inclusion
of the known complexities, structures and population-level heterogeneity. Then you come up with
scenarios such as vaccines, boosters,… 2. Understanding: to investigate factors that drive
