SmallCouplingDynamicCavity

Small Coupling expansion of the Dynamic Cavity method for epidemic inference

The purpose of SmallCouplingDynamicCavity.jl is to provide a general and computationally efficient solution for Bayesian epidemic inference and risk assessment. The package offers an efficient structure implementation for the most used epidemic models, such as Susceptible-Infected (SI), Susceptible-Infected-Recovered (SIR), Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered-Susceptible (SIRS).

For all these models, the package provides:

• a simulation tool, which allows to sample an epidemic outbreak with specified parameters
• a statistical inference tool, which allows to obtain fully bayesian estimates of the epidemic uotbreak

The package can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add SmallCouplingDynamicCavity

Or, equivalently, via the Pkg API:

julia> import Pkg; Pkg.add("SmallCouplingDynamicCavity")

Define an infection model through the available structures.

# SI model with 0.0 self-infection rate, 4 individuals and 5 epidemic timesteps
julia> infection_model = SI(0.0, 4, 5)
SI([0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0; 0.0 0.0 … 0.0 0.0])

Define an epidemic model

# SI epidemic model on a graph G with infection probability encoded by the matrix λ 
julia> model = EpidemicModel(infection_model, G, 5, log.(1 .- λ))

• Sampling

  # Sample the epidemic cascade specifying the patient zero as individual 1
  julia> config = sim_epidemics(model, patient_zero=[1])
  4×6 Matrix{Int8}:
  1  1  1  1  1  1
  0  1  1  1  1  1
  0  1  1  1  1  1
  0  0  0  1  1  1

• Inference

  # Insert the observations as a matrix (-1 = unobserved, 0 = observed S, 1 = observed I)
  julia> model.obsmat .= [-1 -1 1 -1 -1 -1; 0 -1 -1 -1 1 -1; -1 -1 -1 -1 -1 -1;  -1 -1 -1 -1 -1 1]
  4×6 Matrix{Int8}:
  -1  -1   1  -1  -1  -1
   0  -1  -1  -1   1  -1
  -1  -1  -1  -1  -1  -1
  -1  -1  -1  -1  -1   1
  
  # Run the inference algorithm with maximum 10 iterations, a convergence threshold of 0.1, and a damping factor of 0.0. The prior probability of being infected at time 0 is 1/4, and the observation probability obsprob is user-specified
  julia> nodes = run_SCDC(model, obsprob, 1/4, 10, 0.1, 0.0)
  Converged after 4 iterations
  4-element Vector{SmallCouplingDynamicCavity.Node{SI}}

A more detailed use of the package is presented in the Tutorial.