Simple SIR (susceptible-infectious-recovered) compartmental model for an infectious disease outbreak.
This package is open source software.
It is licensed under the Apache License, Version 2.0 (the "License"); you may not use it except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0.
To build, use:
To run, use:
birch sample --config config/sir.json
The model on which this is based is described in Murray et. al. (2018).
The parameter model is given by:
where \lambda is a rate of interaction in the population, \delta the probability of infection when a susceptible individual interacts with an infectious individual, and \gamma the daily recovery probability.
The initial model for time t = 0 is:
The transition model for time t is:
where \tau_t is the number of interactions between infectious and susceptible individuals, \Delta i_t the number of newly infected individuals, and \Delta r_t the number of newly recovered individuals.
Population counts are then updated:
This package contains an influenza data set from Anonymous (1978), prepared in JSON format for Birch.
Anonymous (1978). Influenza in a boarding school. British Medical Journal. 1:587.
L.M. Murray, D. Lundén, J. Kudlicka, D. Broman, and T.B. Schön (2018). Delayed Sampling and Automatic Rao--Blackwellization of Probabilistic Programs.