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Register a new userEfficient Uncertainty Quantification and Sensitivity Analysis in Epidemic Modelling using Polynomial Chaos
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Added by
Bj{\\o}rn Jensen
Publication date
2021
fields
Mathematical Statistics
and research's language is
English
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In the political decision process and control of COVID-19 (and other epidemic diseases), mathematical models play an important role. It is crucial to understand and quantify the uncertainty in models and their predictions in order to take the right decisions and trustfully communicate results and limitations. We propose to do uncertainty quantification in SIR-type models using the efficient framework of generalized Polynomial Chaos. Through two particular case studies based on Danish data for the spread of Covid-19 we demonstrate the applicability of the technique. The test cases are related to peak time estimation and superspeading and illustrate how very few model evaluations can provide insightful statistics.
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This study presents a Bayesian spectral density approach for identification and uncertainty quantification of flutter derivatives of bridge sections utilizing buffeting displacement responses, where the wind tunnel test is conducted in turbulent flow. Different from traditional time-domain approaches (e.g., least square method and stochastic subspace identification), the newly-proposed approach is operated in frequency domain. Based on the affine invariant ensemble sampler algorithm, Markov chain Monte-Carlo sampling is employed to accomplish the Bayesian inference. The probability density function of flutter derivatives is modeled based on complex Wishart distribution, where probability serves as the measure. By the Bayesian spectral density approach, the most probable values and corresponding posterior distributions (namely identification uncertainty here) of each flutter derivative can be obtained at the same time. Firstly, numerical simulations are conducted and the identified results are accurate. Secondly, thin plate model, flutter derivatives of which have theoretical solutions, is chosen to be tested in turbulent flow for the sake of verification. The identified results of thin plate model are consistent with the theoretical solutions. Thirdly, the center-slotted girder model, which is widely-utilized long-span bridge sections in current engineering practice, is employed to investigate the applicability of the proposed approach on a general bridge section. For the center-slotted girder model, the flutter derivatives are also extracted by least square method in uniform flow to cross validate the newly-proposed approach. The identified results by two different approaches are compatible.
The celebrated Abakaliki smallpox data have appeared numerous times in the epidemic modelling literature, but in almost all cases only a specific subset of the data is considered. There is one previous analysis of the full data set, but this relies on approximation methods to derive a likelihood. The data themselves continue to be of interest due to concerns about the possible re-emergence of smallpox as a bioterrorism weapon. We present the first full Bayesian analysis using data-augmentation Markov chain Monte Carlo methods which avoid the need for likelihood approximations. Results include estimates of basic model parameters as well as reproduction numbers and the likely path of infection. Model assessment is carried out using simulation-based methods.
The surrogate model-based uncertainty quantification method has drawn a lot of attention in recent years. Both the polynomial chaos expansion (PCE) and the deep learning (DL) are powerful methods for building a surrogate model. However, the PCE needs to increase the expansion order to improve the accuracy of the surrogate model, which causes more labeled data to solve the expansion coefficients, and the DL also needs a lot of labeled data to train the neural network model. This paper proposes a deep arbitrary polynomial chaos expansion (Deep aPCE) method to improve the balance between surrogate model accuracy and training data cost. On the one hand, the multilayer perceptron (MLP) model is used to solve the adaptive expansion coefficients of arbitrary polynomial chaos expansion, which can improve the Deep aPCE model accuracy with lower expansion order. On the other hand, the adaptive arbitrary polynomial chaos expansions properties are used to construct the MLP training cost function based on only a small amount of labeled data and a large scale of non-labeled data, which can significantly reduce the training data cost. Four numerical examples and an actual engineering problem are used to verify the effectiveness of the Deep aPCE method.
Network-based interventions against epidemic spread are most powerful when the full network structure is known. However, in practice, resource constraints require decisions to be made based on partial network information. We investigated how the accuracy of network data available at individual and village levels affected network-based vaccination effectiveness. We simulated a Susceptible-Infected-Recovered process on empirical social networks from 75 villages. First, we used regression to predict the percentage of individuals ever infected based on village-level network. Second, we simulated vaccinating 10 percent of each of the 75 empirical village networks at baseline, selecting vaccinees through one of five network-based approaches: random individuals; random contacts of random individuals; random high-degree individuals; highest degree individuals; or most central individuals. The first three approaches require only sample data; the latter two require full network data. We also simulated imposing a limit on how many contacts an individual can nominate (Fixed Choice Design, FCD), which reduces the data collection burden but generates only partially observed networks. We found mean and standard deviation of the degree distribution to strongly predict cumulative incidence. In simulations, the Nomination method reduced cumulative incidence by one-sixth compared to Random vaccination; full network methods reduced infection by two-thirds. The High Degree approach had intermediate effectiveness. Surprisingly, FCD truncating individuals degrees at three was as effective as using complete networks. Using even partial network information to prioritize vaccines at either the village or individual level substantially improved epidemic outcomes. Such approaches may be feasible and effective in outbreak settings, and full ascertainment of network structure may not be required.
We consider the problem of selecting deterministic or stochastic models for a biological, ecological, or environmental dynamical process. In most cases, one prefers either deterministic or stochastic models as candidate models based on experience or subjective judgment. Due to the complex or intractable likelihood in most dynamical models, likelihood-based approaches for model selection are not suitable. We use approximate Bayesian computation for parameter estimation and model selection to gain further understanding of the dynamics of two epidemics of chronic wasting disease in mule deer. The main novel contribution of this work is that under a hierarchical model framework we compare three types of dynamical models: ordinary differential equation, continuous time Markov chain, and stochastic differential equation models. To our knowledge model selection between these types of models has not appeared previously. Since the practice of incorporating dynamical models into data models is becoming more common, the proposed approach may be very useful in a variety of applications.
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