- Message-Passing strategies for epidemic tracing
- Epidemic Control
- Inference of epidemic parameters
- References
We show the effectiveness of strategies built on message-passing, Belief Propagation [1-7] and Mean-Field, and compare with a simple heuristic strategy for estimating infection risk consisting in ranking each individual by the number of contacts with other individuals that either showed symptoms of various degrees or have been tested positive:
- BP: we build a probability distribution over all possible histories of disease spreading [1]. The inference procedure consists in passing a set of so-called cavity messages along the edges of the network. At convergence, BP equations yield an approximation to the posterior distribution given the observations and the current estimate of transmission and recovery parameters. This method, which represents an exact Bayesian inference on networks without loops [1,2], has been shown to produce excellent results in a variety of partially observable settings on disease spreading;
- MF: Generalization of time-forward evolution equations for factorized (mean-field) probability marginals plus a backward propagation of the effects of evidences due to observations. See https://github.com/sphinxteam/sir_inference for more details;
- Tracing: at time t, individuals are ranked according to the number of contacts with individuals who tested positive in the time interval [t−τ, t].
ROC curves and precisions at differents epidemic sizes:
We employ realistic individual-based models to investigate a number of intervention strategies aiming at containing epidemic outbreaks, such as case-based measures (e.g. individual and household quarantine and mobility restrictions).
OpenABM-Covid19 is an agent-based model (ABM) developed by Oxford's Fraser group to simulate the spread of Covid-19 in a urban population.
An Intervention API that allows testing of risk assessment and quarantine strategies can be found at the following link: https://github.com/aleingrosso/OpenABM-Covid19.
Intervention results in a network of 50K nodes:
The population is seeded with 10 infected individuals at day 0. Intervention strategies start at day 10.
From the BP messages it is possible to compute an approximation of the log-likelihood of the data, the so-called Bethe free entropy. This quantity allows us to infer the hyper-parameters of the epidemic model such as the infection rate or the recovery rate thorugh a gradient ascent of the log-likelihood with respect to the target parameters.
As an example of the effectiness of this procedure, we report here a plot of the Bethe free entropy as a function of the shape and rate parameters (𝛼, 𝛽) of the Gamma distribution of the recovery time. The blue point in the 2D plot corresponds to the maximum log-likelihood point.
The temporal graph used here consists in 10K nodes and all contacts up to day T = 30. After 5 initial days, 10 % of the nodes are selected uniformly at random and observed on a daily basis. We also report the values of the AUC in the (𝛼, 𝛽) plane associated with the inference of the infected nodes at time T = 30.
