Bayesian inference of spreading processes on networks

Abstract

Infectious diseases are studied to understand their spreading mechanisms, to evaluate control strategies and to predict the risk and course of future outbreaks. Because people only interact with few other individuals, and the structure of these interactions influence spreading processes, the pairwise relationships between individuals can be usefully represented by a network. Although the underlying transmission processes are different, the network approach can be used to study the spread of pathogens in a contact network or the spread of rumours in a social network. We study simulated simple and complex epidemics on synthetic networks and on two empirical networks, a social/contact network in an Indian village and an online social network. Our goal is to learn simultaneously the spreading process parameters and the first infected node, given a fixed network structure and the observed state of nodes at several time points. Our inference scheme is based on approximate Bayesian computation, a likelihood-free inference technique. Our method is agnostic about the network topology and the spreading process. It generally performs well and, somewhat counter-intuitively, the inference problem appears to be easier on more heterogeneous network topologies, which enhances its future applicability to real-world settings where few networks have homogeneous topologies.

Modelling microbial infection to address global health challenges

“…Sources for network parameterization may include surveys, partner notification services or phylogenetic tracing 23,24 . As with individual-based models, network models tend to require significant amounts of data to fully parameterize, but various computational and statistical methods have been developed to analyse the impact of uncertain parameter values on model predictions 25 . Network models are applied to discern the influence of contact structure on disease transmission and on the effectiveness of targeted intervention strategies.…”

Estimating a novel stochastic model for within-field disease dynamics of banana bunchy top virus via approximate Bayesian computation

“…Given the intractability of the likelihood function for this model, we employ approximate Bayesian computation (ABC) [7] for estimating model parameters and their uncertainty. Our methodology is inspired by Dutta et al [8], who demonstrate that ABC may be effectively used to estimate the spreading parameters of a disease by applying a simple Susceptible-Infected (SI) model over a known network structure. This paper adapts and extends this approach to further understand the spreading characteristics of BBTV, evaluate various disease management strategies at the plantation level, and predict the spread of future outbreaks.…”

“…We propose to model the spread of BBTV in a banana plantation by modifying the 'simple contagion' model developed by Dutta et al [8]. The 'simple contagion' model simulates a standard SI process on a fixed network structure.…”

“…Dutta et al [8] denote this model by M s and parameterise it in terms of the spreading rate θ and the seed node n sn . For given values of these two parameters, n sn = n sn * and θ = θ *, they forward simulate the evolving epidemic over time using the model M s .…”

“…We adapt the model M s in several ways for our application. Dutta et al [8] determine a node to be an individual person, with edges representing each person's contacts. Modelling the individual status of every plant as a node would be impractical and computationally expensive, due to the varying contact points between plants, and the complex plant-pathogen-vector relationships as described in the previous section.…”