Pathogen.jl: Infectious Disease Transmission Network Modelling with Julia

We introduce Pathogen.jl for simulation and inference of transmission network individual level models (TN-ILMs) of infectious disease spread. TN-ILMs can be used to jointly infer transmission networks, event times, and model parameters within a Bayesian framework via Markov chain Monte Carlow (MCMC). We detail our specific strategies for conducting MCMC for TN-ILMs, and our implementation of these strategies in the Julia package, Pathogen.jl, which leverages key features of the Julia language. We provide an example using Pathogen.jl to simulate an epidemic following a susceptible-infectious-removed (SIR) TN-ILM, and then perform inference using observations that were generated from that epidemic. We also demonstrate the functionality of Pathogen.jl with an application of TN-ILMs to data from a measles outbreak that occurred in Hagelloch, Germany in 1861 (Pfeilsticker 1863; Oesterle 1992).

[1]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[2]  David Welch,et al.  epinet: An R Package to Analyze Epidemics Spread across Contact Networks , 2018 .

[3]  Glenn F. Webb Individual based models and differential equations models of nosocomial epidemics in hospital intensive care units , 2017 .

[4]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[5]  D. Hunter,et al.  Bayesian Inference for Contact Networks Given Epidemic Data , 2010 .

[6]  Qing Nie,et al.  DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia , 2017, Journal of Open Research Software.

[7]  Christopher Rackauckas,et al.  ADAPTIVE METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS VIA NATURAL EMBEDDINGS AND REJECTION SAMPLING WITH MEMORY. , 2017, Discrete and continuous dynamical systems. Series B.

[8]  Hiroshi Nishiura,et al.  The correlation between infectivity and incubation period of measles, estimated from households with two cases. , 2011, Journal of theoretical biology.

[9]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[10]  David Welch,et al.  A Network‐based Analysis of the 1861 Hagelloch Measles Data , 2012, Biometrics.

[11]  D. Gillespie Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[12]  J. Rosenthal,et al.  Coupling and Ergodicity of Adaptive Markov Chain Monte Carlo Algorithms , 2007, Journal of Applied Probability.

[13]  Rob Deardon,et al.  INFERENCE FOR INDIVIDUAL-LEVEL MODELS OF INFECTIOUS DISEASES IN LARGE POPULATIONS. , 2010, Statistica Sinica.

[14]  Seyed M. Moghadas,et al.  Projecting demand for critical care beds during COVID-19 outbreaks in Canada , 2020, Canadian Medical Association Journal.

[15]  Kenneth Lange,et al.  BioSimulator.jl: Stochastic simulation in Julia , 2018, Comput. Methods Programs Biomed..

[16]  Andrew Parker,et al.  Using approximate Bayesian computation to quantify cell–cell adhesion parameters in a cell migratory process , 2016, npj Systems Biology and Applications.

[17]  Leonhard Held,et al.  Spatio-Temporal Analysis of Epidemic Phenomena Using the R Package surveillance , 2014, ArXiv.

[18]  Vaibhav Dixit,et al.  DiffEqFlux.jl - A Julia Library for Neural Differential Equations , 2019, ArXiv.

[19]  Martina Morris,et al.  EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks , 2017, bioRxiv.

[20]  Zoubin Ghahramani,et al.  Turing: A Language for Flexible Probabilistic Inference , 2018 .