IONISE - Inference Of Non-markovIan SEIR Model

Overview

IONISE is a user-friendly computational package developed for the gamma model approach, specifically targeting the SEIR (Susceptible-Exposed-Infectious-Removed) model. The package is implemented in R software version 4.3.2 and aims to estimate epidemiological parameters from sole confirmed case data using gamma-distributed latent and infectious periods.

Getting Started

Prerequisites

• R software version 4.3.2 or higher
• Additional R packages:
  • deSolve
  • MASS
  • mvtnorm
  • dplyr
  • invgamma
  • ramcmc

Modules

Source functions are modularized with four modules below:

• IONISE_module_basic_computing.R: This module contains basic functions for the packages, such as calculating probability density functions and convolutions between density functions.
• IONISE_module_diff_eqs.R: This module contains numerical solvers for differential equations describing the SEIR and extended SEIR models with delays.
• IONISE_module_MH.R: This module contains functions for the Metropolis-Hastings (MH) algorithm used in Markov chain Monte Carlo (MCMC) sampling.
• IONISE_module_MCMC.R: This module contains functions performing MCMC sampling.

Installation

1. Download the IONISE package and example CSV files from the GitHub repository (link will be activated after acceptance).
2. Save confirmed case data as a CSV file with the name input_data.csv in the folder containing the R code of the main function, IONISE_main.R.

Usage

1. Open IONISE_main.R in your R environment.
2. Set the folder containing the R code as the working directory using the function setwd().
3. Install and load the required packages:

   install.packages(c("deSolve", "MASS", "mvtnorm", "dplyr", "invgamma", "ramcmc"))
   library(deSolve)
   library(MASS)
   library(mvtnorm)
   library(dplyr)
   library(invgamma)
   library(ramcmc)

4. Compile the necessary function libraries using the line source("IONISE_source.R").
5. Import the input data CSV file using the line read.csv("input_data.csv").

Simple Manual

For more details, refer to a step-by-step manual provided in the relevant reference (Supplementary Note 2).

1. Set the variable initial_phase to TRUE if the data comes from the initial phase of disease spread; otherwise, set it to FALSE.
2. Specify whether to estimate the infectious period distribution (estim_infect).
   • If TRUE, the code will estimate shape and scale parameters (k_(τ_I), s_(τ_I)).
   • If FALSE, specify the mean and variance of the infectious period distribution (infect_mean, infect_var).
3. Specify the parameters for the MCMC procedure. The variable nrepeat represents the number of MCMC iterations, and the variable tun_beta represents the proposal variance for the Metropolis-Hastings algorithm for sampling the β. The default values for nrepeat and tun_beta are 10,000 and 0.1, respectively.
4. Specify the distribution type for the delays (i.e., latent and infectious periods) in the model using the variable dist_type. The variable is one of exp, gamma, invgamma, lognormal, and weibull.
5. Specify the type of the likelihood function for the inference using the variable lik_type. The variable is one of poisson and gaussian.
6. Set up hyperparameters for prior distributions:
   • Transmission rate (prior_mean_beta, prior_var_beta).
   • Infectious period (prior_mean_infect_shape, prior_mean_infect_scale, prior_var_infect_shape, prior_var_infect_scale).
   • Default values are non-informative priors (mean=1, variance=1,000,000).
7. Specify the type of a model used for the inference using the variable “model_type.” If the variable is SEIR, the SEIR model is used for the inference. If the variable is Extended_SEIR, the extended model is used for the inference. See the relevant reference to see descriptions of the SEIR model and the extended model.
8. In the code section PART 2-1 or PART 2-2, specify the initial values of the compartment and the values of the parameters in the chosen model.
9. Run the code section named PART 3: Perform MCMC.

Output

Once IONISE_main.R is properly executed, a CSV file named post_samples.csv is created. This file contains posterior samples of β, k_(τ_I), s_(τ_I), μ_(τ_I), and R in the first, second, third, fourth, and fifth columns, respectively. Note that the burn-in period and thinning for the MCMC iterations are not automatically applied in the code. To obtain independent posterior samples from the MCMC iterations, users may need to apply the burn-in period and thinning.

Expected Runtimes

• Installation: Less than 10 seconds.
• Execution: Approximately 1 hour per 10,000 MCMC iterations for the example data when it the code tested with MacBook Air (2023) running macOS Sonoma (14.4.1) with processor M2 8-Core with R version 4.3.2 (2023-10-31).

Reference

1. To be updated.