Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation

Individual-level models of disease transmission incorporating piecewise spatial risk functions

Modelling epidemics is crucial for understanding the emergence, transmission, impact and control of diseases. Spatial individual-level models (ILMs) that account for population heterogeneity are a useful tool, accounting for factors such as location, vaccination status and genetic information. Parametric forms for spatial risk functions, or kernels, are often used, but rely on strong assumptions about underlying transmission mechanisms. Here, we propose a class of non-parametric spatial disease transmission model, fitted within a Bayesian Markov chain Monte Carlo (MCMC) framework, allowing for more flexible assumptions when estimating the effect on spatial distance and infection risk. We focus upon two specific forms of non-parametric spatial infection kernel: piecewise constant and piecewise linear. Although these are relatively simple forms, we find them to produce results in line with, or superior to, parametric spatial ILMs. The performance of these models is examined using simulated data, including under circumstances of model misspecification, and then applied to data from the UK 2001 foot-and-mouth disease.

Ensemble learning methods of inference for spatially stratified infectious disease systems

Individual level models are a class of mechanistic models that are widely used to infer infectious disease transmission dynamics. These models incorporate individual level covariate information accounting for population heterogeneity and are generally fitted in a Bayesian Markov chain Monte Carlo (MCMC) framework. However, Bayesian MCMC methods of inference are computationally expensive for large data sets. This issue becomes more severe when applied to infectious disease data collected from spatially heterogeneous populations, as the number of covariates increases. In addition, summary statistics over the global population may not capture the true spatio-temporal dynamics of disease transmission. In this study we propose to use ensemble learning methods to predict epidemic generating models instead of time consuming Bayesian MCMC method. We apply these methods to infer disease transmission dynamics over spatially clustered populations, considering the clusters as natural strata instead of a global population. We compare the performance of two tree-based ensemble learning techniques: random forest and gradient boosting. These methods are applied to the 2001 foot-and-mouth disease epidemic in the U.K. and evaluated using simulated data from a clustered population. It is shown that the spatially clustered data can help to predict epidemic generating models more accurately than the global data.

Flexible Bayesian inference on partially observed epidemics

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and heterogeneity of realistic contact dynamics. In this article, we consider Bayesian inference on the spreading parameters of an SIR contagion on a known, static network, where information regarding individual disease status is known only from a series of tests (positive or negative disease status). When the contagion model is complex or information such as infection and removal times is missing, the posterior distribution can be difficult to sample from. Previous work has considered the use of Approximate Bayesian Computation (ABC), which allows for simulation-based Bayesian inference on complex models. However, ABC methods usually require the user to select reasonable summary statistics. Here, we consider an inference scheme based on the Mixture Density Network compressed ABC, which minimizes the expected posterior entropy in order to learn informative summary statistics. This allows us to conduct Bayesian inference on the parameters of a partially observed contagious process while also circumventing the need for manual summary statistic selection. This methodology can be extended to incorporate additional simulation complexities, including behavioural change after positive tests or false test results.

Geographically dependent individual-level models for infectious diseases transmission

Infectious disease models can be of great use for understanding the underlying mechanisms that influence the spread of diseases and predicting future disease progression. Modeling has been increasingly used to evaluate the potential impact of different control measures and to guide public health policy decisions. In recent years, there has been rapid progress in developing spatio-temporal modeling of infectious diseases and an example of such recent developments is the discrete-time individual-level models (ILMs). These models are well developed and provide a common framework for modeling many disease systems; however, they assume the probability of disease transmission between two individuals depends only on their spatial separation and not on their spatial locations. In cases where spatial location itself is important for understanding the spread of emerging infectious diseases and identifying their causes, it would be beneficial to incorporate the effect of spatial location in the model. In this study, we thus generalize the ILMs to a new class of geographically dependent ILMs, to allow for the evaluation of the effect of spatially varying risk factors (e.g., education, social deprivation, environmental), as well as unobserved spatial structure, upon the transmission of infectious disease. Specifically, we consider a conditional autoregressive (CAR) model to capture the effects of unobserved spatially structured latent covariates or measurement error. This results in flexible infectious disease models that can be used for formulating etiological hypotheses and identifying geographical regions of unusually high risk to formulate preventive action. The reliability of these models is investigated on a combination of simulated epidemic data and Alberta seasonal influenza outbreak data ($2009$). This new class of models is fitted to data within a Bayesian statistical framework using Markov chain Monte Carlo methods.