Simulating disease progress curves

Introduction

In epiffiter, opposite to the fit_ functions (estimate parameters from fitting models to the data), the sim_ family of functions allows to produce the DPC data given a set of parameters for a specific model. Currently, the same four population dynamic models that are fitted to the data can be simulated.

The functions use the ode() function of the devolve package (Soetaert,Petzoldt & Setzer 2010) to solve the differential equation form of the e epidemiological models.

Hands On

Packages

First, we need to load the packages we'll need for this tutorial.

library(epifitter)
library(magrittr)
library(ggplot2)
library(cowplot)

The basics of the simulation

The sim_ functions, regardless of the model, require the same set of six arguments. By default, at least two arguments are required (the others have default values)

When n is greater than one, replicated epidemics (e.g. replicated treatments) are produced and a level of noise (experimental error) should be set in the alpha argument. These two arguments combined set will generate random_y values, which will vary randomly across the defined number of replicates.

The other arguments are:

Exponential

Let's simulate a curve resembling the exponential growth.

exp_model <- sim_exponential(
  N = 100,    # total time units 
  y0 = 0.01,  # initial inoculum
  dt = 10,    #  interval between assessments in time units
  r = 0.045,  #  apparent infection rate
  alpha = 0.2,# level of noise
  n = 7       # number of replicates
)
head(exp_model)

A data.frame object is produced with four columns:

Use the ggplot2 package to build impressive graphics!

exp_plot = exp_model %>%
  ggplot(aes(time, y)) +
  geom_jitter(aes(time, random_y), size = 3,color = "gray", width = .1) +
  geom_line(size = 1) +
  theme_minimal_hgrid() +
  ylim(0,1)+
  labs(
    title = "Exponential",
    y = "Disease intensity",
    x = "Time"
  )
exp_plot

Monomolecular

The logic is exactly the same here.

mono_model <- sim_monomolecular(
  N = 100,
  y0 = 0.01,
  dt = 5,
  r = 0.05,
  alpha = 0.2,
  n = 7
)
head(mono_model)
mono_plot = mono_model %>%
  ggplot(aes(time, y)) +
  geom_jitter(aes(time, random_y), size = 3, color = "gray", width = .1) +
  geom_line(size = 1) +
  theme_minimal_hgrid() +
  labs(
    title = "Monomolecular",
    y = "Disease intensity",
    x = "Time"
  )
mono_plot

The Logistic model

logist_model <- sim_logistic(
  N = 100,
  y0 = 0.01,
  dt = 5,
  r = 0.1,
  alpha = 0.2,
  n = 7
)
head(logist_model)
logist_plot = logist_model %>%
  ggplot(aes(time, y)) +
  geom_jitter(aes(time, random_y), size = 3,color = "gray", width = .1) +
  geom_line(size = 1) +
  theme_minimal_hgrid() +
  labs(
    title = "Logistic",
    y = "Disease intensity",
    x = "Time"
  )
logist_plot

Gompertz

gomp_model <- sim_gompertz(
  N = 100,
  y0 = 0.01,
  dt = 5,
  r = 0.07,
  alpha = 0.2,
  n = 7
)
head(gomp_model)
gomp_plot = gomp_model %>%
  ggplot(aes(time, y)) +
  geom_jitter(aes(time, random_y), size = 3,color = "gray", width = .1) +
  geom_line(size = 1) +
  theme_minimal_hgrid() +
  labs(
    title = "Gompertz",
    y = "Disease intensity",
    x = "Time"
  )
gomp_plot

Combo

Use the function plot_grid() from the cowplot package to gather all plots into a grid

plot_grid(exp_plot,
          mono_plot,
          logist_plot,
          gomp_plot)

References

Karline Soetaert, Thomas Petzoldt, R. Woodrow Setzer (2010). Solving Differential Equations in R: Package deSolve. Journal of Statistical Software, 33(9), 1--25. DOI: 10.18637/jss.v033.i09



Try the epifitter package in your browser

Any scripts or data that you put into this service are public.

epifitter documentation built on June 14, 2021, 5:08 p.m.