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I am currently developing an individual-based (or agent-based) mathematical model (IBM) of an epidemic. I want to calibrate the transmission parameters in my IBM to match empirical data (epidemic curve time series) using least-squares. Suppose I have an epidemic curve that looks like this Epidemic Curve and this epidemic curve is based on a population of 60,000,000 (roughly the population of England). The peak incidence of the epidemic from this graph are in week 8: 9,600 cases. This gives 0.016% of the total population.

In my IBM I am only looking to simulate a population of 10,000. If I were to calibrate my transmission parameters so that my IBM output matches the epidemic curve in the attached figure, I am looking at a peak incidence of 0.016% in week 8 which, in a population of 10,000 people is just 1.6 people. This proportion is far too small to sustain an epidemic in a population of 10,000.

I presume there is something wrong with my approach. What would be the best way to calibrate an IBM to check that model output matches empirical data?

Alexis
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crabcanon
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  • You may want to indicate if they are incidence cases or total cases. If they are incidence cases you will have more than 1.6 people to work with? – Penguin_Knight Jul 19 '18 at 18:39
  • These are incidence cases i.e. they are the total number of new cases each week. How would I have >1.6? Could you elaborate please? Thanks. – crabcanon Jul 19 '18 at 18:46

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Technically, if your IBM treats individuals as discrete units, you won't even have 1.6 individual - you will have 2, maybe 1, individual.

A couple notes about your problem:

  1. It's not self-evident that 1.6 individuals per week is too few to sustain an epidemic.
  2. This is the problem with scaling down large population incidence estimates. If possible, you should look for smaller district/county/etc. level data to get an idea of what the dynamics are in smaller populations.
  3. This is why, if you look at epidemic curves on those scales, they're often much noisier.

Fundamentally, smaller populations have noisier dynamics governed more by stochasticity than any underlying epidemic dynamics. This doesn't mean your approach is wrong. Just that the outcome of your approach isn't clean. Those are two very different things.

Fomite
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