Infectious Disease Modelling

This GitHub repository contains the code and data for a simulation-based study comparing two infectious disease modelling techniques: Compartmental Models and Renewal Models.

Overview

The study aims to analyze and compare the effectiveness of these two techniques using a simple SIR case for Compartmental Models and various scenarios for Renewal Models.

Compartmental Models

SIR Model

• Description: The SIR (Susceptible-Infected-Recovered) model is a simple compartmental model used in epidemiology to simulate how a disease spreads through a population by means of Suscpetible, Infectious and Recovered compartments in population.
• Implementation:
  • The R code using deSolve is employed to simulate the data.
  • Subsequently, Stan code is utilized to back-calculate the transmission rate ((\beta)) and the basic reproduction number ((R_0)) from the simulated incidence data .

Renewal Models

Scenarios

1. Single (R_0)

   • Description: Maintains a constant (R_0) value over a specified time period.
   • Implementation: The simulated data is backtested using Stan to verify the results.

2. Changing (R_t) ((R_t1) and (R_t2))

   • Description: After 15 days, the (R_t) value changes.
   • Implementation: The change in (R_t) is modeled and the results are validated using Stan.

3. Dependent (R_t) Vector

   • Description: After 6 days, the (R_t) value changes, with the new (R_t) value correlated to the previous one.
   • Implementation: This scenario simulates a dependent change in (R_t) and the results are analyzed using Stan.

4. Independent (R_t) Vector

   • Description: After 6 days, the (R_t) value changes, with the (R_t) values in the vector are uncorrelated.
   • Implementation: This scenario models independent changes in (R_t) and the simulation data is backtested using Stan.

Repository Structure

Infectious-Disease-Modelling/
├── compartmental_models/
│   ├── SIR_Model/
│   │   ├── simulate_data.R
│   │   ├── back_calculate_stan.stan
│   │   └── results/
├── renewal_models/
│   ├── Single_R0/
│   │   ├── simulate_data.R
│   │   ├── back_calculate_stan.stan
│   │   └── results/
│   ├── Rt1_Rt2/
│   │   ├── simulate_data.R
│   │   ├── back_calculate_stan.stan
│   │   └── results/
│   ├── Dependent_Rt/
│   │   ├── simulate_data.R
│   │   ├── back_calculate_stan.stan
│   │   └── results/
│   └── Independent_Rt/
│       ├── simulate_data.R
│       ├── back_calculate_stan.stan
│       └── results/
└── README.md

Requirements

• R and RStudio
• deSolve and EpiEstim package for R
• Stan for R (rstan package)