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On parameter identifiability in network-based epidemic models
journal contribution
posted on 2023-06-10, 05:55 authored by Istvan KissModelling epidemics on networks represents an important departure from classical compartmental models which assume random mixing. However, the resulting models are highdimensional and their analysis is often out of reach. It turns out that mean-field models, low dimensional systems of differential equations, whose variables are carefully chosen expected quantities from the exact model provide a good approximation and incorporate explicitly some network properties. Despite the emergence of such mean-field models, there has been limited work on investigating whether these can be used for inference purposes. In this paper we consider network-based mean-field models and explore the problem of parameter identifiability when observations about an epidemic are available. Making use of the analytical tractability of most network-based mean-field models, e.g., explicit analytical expressions for leading eigenvalue and final epidemic size, we set up the parameter identifiability problem as finding the solution or solutions of a system of coupled equations. More precisely, subject to observing/measuring growth rate and final epidemic size, we seek to identify parameter values leading to these measurements. We are particularly concerned with disentangling transmission rate from the network density. To do this, we give a condition for practical identifiability and we find that except for the simplest model, parameters cannot be uniquely determined, that is they are practically unidentifiable. This means that there exists multiple solutions (a manifold of infinite measure) which give rise to model output that is close to the data. Identifying, formalising and analytically describing this problem should lead to a better appreciation of the complexity involved in fitting models with many parameters to data.
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Publication status
- Published
File Version
- Published version
Journal
Bulletin of Mathematical BiologyISSN
0092-8240Publisher
Springer NatureExternal DOI
Issue
18Volume
86Page range
1-17Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Mathematics Applied to Biology Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2023-01-10First Open Access (FOA) Date
2023-02-22First Compliant Deposit (FCD) Date
2023-01-10Usage metrics
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