4  Basic DCMs with EpiModelWeb

4.1 EpiModelWeb Introduction

EpiModel includes a web-based interface for simulating basic epidemic models using the R Shiny platform. This is currently available for all three model classes in EpiModel (deterministic compartmental models, individual contact models, and network model). Today we are going to use the apps for the first two classes.

4.2 Getting Started

Open Rstudio and load EpiModel:

library(EpiModel)

Launch the Shiny app for EpiModel’s Deterministic Compartmental Model class:

epiweb("dcm")

4.3 Deterministic SIR Model

  • Use the following parameters for your first model
    • Model type = SIR
    • S = 1000; I = 1; R = 0
    • Transmission probability per act = 0.2; act rate = 1.4; recovery rate = 0.1
    • Press “Run Model” button

4.3.1 Questions

  • What is \(R_0\) for this infectious disease system? Does the epidemic “take off”?
  • What is the time step of peak incidence? Eyeball it with the Plot Selection set to Disease Incidence. Look up the exact value in the Data tab. Hint: you can sort the columns, and si.flow is disease incidence.
  • Now do the same for disease prevalence (i.num). Why is the peak prevalence later than the peak time of disease incidence?
  • The net reproduction number, \(R_n\), is the natural reproduction number of the epidemic under conditions of I > 1. It tells us how close the epidemic is to the persistence threshold over the course of the epidemic. It is calculated as: \(R_n = R_0 * (S_t/N_t)\)
  • Calculate that \(R_n\) for this epidemic at time steps 1, 20, the time of peak prevalence, and 60.

4.4 Changing the SIR Model Parameters

  • Change the model parameters
    • Model type = SIR
    • S = 1000; I = 1; R = 0
    • Transmission probability per act = 0.2; act rate = 1.4; recovery rate = 0.4
    • Press “Run Model” button

4.4.1 Questions

  • What is \(R_0\) for this infectious disease system? Does the epidemic “take off”?
  • What is the time of peak prevalence and incidence now?
  • Explain the logic (in words) why the epidemic trajectory changed related to parameter that you changed.

4.5 Deterministic SIS Model

  • Change the model parameters
    • Model type = SIS
    • S = 1000; I = 1
    • Transmission probability per act = 0.2; act rate = 1.4; recovery rate = 0.1
    • Press “Run Model” button

4.5.1 Questions

  • What is \(R_0\) for this infectious disease system? (Use the same calculation as for an SIR for simplicity, but consider why this may be mathematically ambiguous too). Does the epidemic “take off”? How does this epidemic signature look vs an SIR?
  • Pick a time when the prevalence has reached an “equilibrium state” (i.e., the slope of the prevalence curve is flat).
  • Under the Summary tab, enter this time step. Looking at the summary statistics in the table, and the flow diagram, explain why an equilibrium state for an SIS is occurring (hint: look at the flows!)

4.6 Changing the SIS Model Parameters

  • Change the model parameters
    • Model type = SIS
    • S = 1; I = 0.001
    • Transmission probability per act = 0.2; act rate = 1.4; recovery rate = 0.1
    • Press “Run Model” button

4.6.1 Questions

  • What did we just do? How did scaling the population size down by a factor of 1000 substantively change your evaluations about the epidemic?
  • What would happen if we scaled up by a factor of 1000 (S = 1 mil, I = 1000)?
  • In general, for this model, how do the model results (absolute compartment sizes versus fractions/frequencies) depend upon the choice of population size?