grace84 / bdsss-seir

Beta-Dirichlet Switching State-Space SEIR Model (BDSSS-SEIR)

Authors: Jingxue Feng ([email protected]), Liangliang Wang ([email protected])

Goal

We propose a Beta-Dirichlet switching state-space transmission model to track underlying dynamics of disease and evaluate the effectiveness of interventions simultaneously. Bayesian inference are performed using a particle MCMC algorithm.

Model Description

$$\boldsymbol{\theta}_t | \boldsymbol{\theta}_{t-1},x_t \sim \text{Dirichlet}(\kappa r(\boldsymbol{\theta}_{t-1}; \alpha, \beta, \gamma, f_{x_t})) \\$$ $$y_t |\boldsymbol{\theta}_t \sim \text{Beta}(\lambda p I_t, \lambda (1- p I_t))$$

• $y_t$ is the observed infectious proportion at time $t$ ;
• $x_t$ is a discrete latent variable describing the regime of model at time $t$;
• $p$ is the identification rate representing the fraction of infectious population identified by diagnosis;
• $\boldsymbol{\theta}_t = [S_t, E_t, I_t, R_t]^\top$ is the vector of the underlying proportion of the susceptible, exposed, infectious, and recovered population, where $S_t+E_t+I_t+R_t=1 \ \forall t$;
• $\alpha$, $\beta$ and $\gamma$ are the latency rate, transmission rate and recovery rate in the SEIR system respectively;
• $\lambda$ and $\kappa$ are the precision parameters controlling the variances (or randomness) for the observation and transition process;
• $f_{x_t}$ is the transmission rate modifier that changes with respect to the state variable $x_t$.
• $\psi$ represents the set of model parameters to be estimated.
• $r(.)$ is the solution of the modified SEIR system starting at $\boldsymbol{\theta}_{t-1}$.

Features

This repository contains R code for simulation studies and real data analysis of BDSSS-SEIR model, described as follows:

• "Code" contains source R code for particle Gibbs samplers in simulation study and real data analysis.
  • In "Simulation Study", the two-regime and three-regime cases are simulated and estimated.
  • In "Real Data", the particle Gibbs sampler is implemented for K=1,2,3 and 4
• "Data" contains simulated data in two-regime and three-regime settings, as well as the real data retreived from here.