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Skip to 0 minutes and 45 seconds JOHN EDMUNDS: So we try and estimate and measure how people move between these different classes. And the critical component of a transmission model is that the rate at which individuals go from the susceptible to the exposed class is dependent on the number of infectious people in the population at a given point in time. So if there’s more infectious people in the population then the risk to susceptibles is correspondingly greater. The idea of the model is that it summarises the epidemiology in a simple form that is in some way tractable, maybe mathematically. So it could be summarised mathematically, or it could be put on a computer. It doesn’t include everything, so it’s only got the key points.

Skip to 1 minute and 27 seconds It’s a bit like a cartoon of the epidemic. And you can use it then to both gain an understanding of what’s going on, and then also, you can use it for making predictions about what might happen. The approach tends to be to make some simple assumptions about the contact behaviour. Because more complicated assumptions would require data that is just not there. And so the simplest assumption is homogeneous mixing, that means people mix randomly within the population, clearly, they don’t. If mixing is much more clustered, then the infection would spread less quickly in the population as a whole. And less people, in the end, are likely to be infected.

Skip to 2 minutes and 21 seconds When we’re looking at the numbers of cases, we know that we’re not capturing all of the cases. There are other cases of infections that are occurring. And if a large number of infections are not reported, or a large number of infections are subclinical, so don’t have very overt symptoms, then it could be that the numbers of cases that we see is only a very small fraction of the total number of infections occurring in the community. And this matters a lot. The reason why those epidemics stop, so the reason why an epidemic peaks, and then comes down, an epidemic such as that peaks and then starts to decline is because you start to run out of susceptible individuals.

Skip to 3 minutes and 3 seconds So it’s susceptibles that are– in some sense they’re like the fuel to the fire. And if you remove the fuel, then the fire starts to dampen out. And that’s the same for a big epidemic. And the problem in terms of predictions is that if you’re not observing many of these cases, and not observing many of these infections because they’re subclinical, then the predictions over a long time course of the epidemic are going to be out by perhaps orders of magnitude. One of the key problems with modelling over a long time course, over the course of an epidemic, is that people may well change their behaviour. So embedded within the transmission model is some assumption about how people contact each other.

Skip to 3 minutes and 52 seconds So how susceptibles come into contact with cases and transmission occurs. There’s reasonably good evidence that behaviour has changed. But exactly what has occurred, and whether we can make any predictions about behavioural change, is very difficult. The mathematical models tend to assume that the behaviour is not changing, and that’s almost certainly not the case. Interpreting model predictions, I think you need to be careful, particularly over the longer term. Models may be useful for giving a sketch of what might occur if the assumptions that have been put in are reasonable. But in terms of accurate predictions over the longer term, I think we’re not at that stage where we can do that. We don’t have the biological knowledge.

Skip to 4 minutes and 47 seconds The reproduction number for Ebola is not much above one, particularly now, in each of the– in all of the settings– it’s not a lot of above one. And into those circumstances, chance also plays quite a major role in driving the epidemic. I think there are a couple of areas where the models have been useful in this epidemic. First of all, in predicting the numbers of beds that might be required. So earlier in the epidemic in particular, we were working with colleagues to try and estimate how many cases may occur over the next few weeks and take into account the length of stay in hospitals by an average Ebola patient.

Skip to 5 minutes and 33 seconds And in fact, the variance in that, as well, to say how many beds may be required. We can make predictions about the potential impact of different interventions. Either interventions that have occurred, like expanding hospital bed capacity, and we can see whether that might have had an impact on the epidemiology, or interventions that are planned such as the potential role of new vaccines. There’s lots of different ways you can deliver a vaccine. You can deliver it to everybody in the population, but that requires a lot of vaccine, of course. You can target certain age groups. You can target geographical areas that are most at risk, or have most cases recently, and so on.

Skip to 6 minutes and 14 seconds And you can use mathematical models to run through these different scenarios before you actually have to do them. And so you can see which ones are likely to bear most fruit, in terms of being able to prevent the epidemic in the most efficient way. We’ve been looking at what the impact of expanding the numbers of beds available. So for instance, there’s been a recent decline in the reproduction number in Western area in Sierra Leone. The models have been used to suggest that the expansion of bed capacity that is planned, might just be sufficient to be able to help turn the epidemic around. And that means drive the reproduction number to below one.

Modelling the outbreak and making projections

The purpose of infectious disease transmission models is to improve our understanding of the key drivers of disease spread and to make predictions about what might happen next. Although models giving long-term predictions tend to make headlines they can be very inaccurate. In this video Professor John Edmunds describes the basic principles, how models can be helpful, and how we should be cautious when interpreting their predictions.

The basic model splits the population into different groups:

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People in the removed group do not contribute further to transmission. For Ebola, the ‘removed’ group would be those who have either died (and are safely buried) or have recovered, and thus are immune.

The way people move between these groups can be described mathematically. This makes many simplifying assumptions. A common assumption is that people mix randomly (homogeneously) in the population, which is not the case. If mixing is more clustered, then the infection will spread less quickly and affect fewer people.

A model tries to reproduce the key features of the epidemic. To do this accurately, the model must be adapted to match the observed data, and this process must be repeated as more data become available. This is one reason why it is important to have an accurate count of cases. As discussed in previous steps, the data from the current outbreak are very inaccurate. If many cases are not reported, or if many infections are sub-clinical (i.e.they have no noticeable symptoms), the number of infections occurring will be underestimated. If cases are not reported the number of infectious individuals will be undercounted. Sub-clinical cases (if they occur) are unlikely to be infectious, but they would probably become immune and would therefore be in the removed group, so there would be fewer susceptible people.

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Remember that the average number of secondary cases per case (the reproduction number, R) depends on the number of susceptible people and decreases as an increasing percentage of the population becomes immune. If many sub-clinical cases occur and models do not allow for this, the predictions will greatly over-estimate the numbers of cases. This is a particular worry for longer term predictions.

As the epidemic has progressed, the reproduction number, R, has decreased to just above 1, due to control measures, behaviour change and people moving to the ‘removed’ group. It is difficult to measure these changes in behaviour and to allow for them in models. Also, when R is close to 1, chance plays an important role in whether outbreaks occur in different places, and again, long term predictions become very inaccurate.

Examples of where models have been useful are:

  • Predicting the number of beds that will be required over the next few weeks

  • Predicting the potential impact of new interventions

  • Working out the best way of delivering potential new interventions (e.g. vaccines)

  • Estimating the impact that control measures have had on the epidemic.

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Ebola in Context: Understanding Transmission, Response and Control

London School of Hygiene & Tropical Medicine