This app allows you to explore a very basic infectious disease simulation. The main goal is to provide familiarity with the overall setup and ideas behind using these simulations, and how to run them. Read about the model in the “Model” tab. Make sure to read the ‘general notes’ section. Then do the tasks described in the “What to do” tab. Finally, check out the “Further Information” tab to learn where you can find some background information on this (and many of the other) apps.
This model is a compartmental SIR (susceptible-infected-recovered) model. Compartmental means that we place individuals into distinct compartments, according to some characteristics. We then only track the total number of individuals in each of these compartments. In the simplest model, the only characteristic we track is a person’s infection status. We allow for 3 different stages/compartments:
The SIR model is very basic. It could be extended by introducing further compartments. For instance, we could stratify according to gender, which would give us 2 sets of SIR compartments, one for males and one for females. Some of these extensions are implemented in other apps.
In addition to specifying the compartments of a model, we need to specify the processes/mechanisms determining the changes for each compartment. Broadly speaking, there are processes that increase the number of individuals in a given compartment/stage, and processes that lead to a reduction. Those processes are sometimes called inflows and outflows.
For our system, we specify only 2 processes/flows:
As with the compartments, we could extend the model and allow other processes to occur. For instance, we could allow for natural births and deaths, waning immunity, deaths due to disease, etc. Some of that will be included in other apps.
For compartmental models (and also often other types of models), it is useful to show a graphical schematic representation of the compartments and processes included in the model. For compartmental models, such a diagram/figure is usually called a flow diagram. Such a diagram consists of a box for each compartment, and arrows pointing in and out of boxes to describe flows and interactions. For the simple SIR model, the flow diagram looks as follows:
Flow diagram for simple SIR model.
To allow us to simulate this model, we need to implement it on the computer. For that purpose, it is often useful to write the model as mathematical equations (this is not strictly needed, some computer simulation models are never formulated as mathematical models). A very common way (but not the only one) to implement compartmental models such as the simple SIR model is a set of ordinary differential equations. Each compartment/variable gets an equation. The right side of each equation specifies the processes going on in the system and how they change the numbers in each compartment via inflows and outflows. For the model described above, the equations look like this:
S:\[\dot S = -bSI\] I:\[\dot I = bSI - gI\] R:\[\dot R = gI\]
Note: If you don’t see equations but instead gibberish, try opening the app with a different browser. I have found that occasionally, on some computers, the built-in RStudio viewer does not process the equations correctly. Firefox and Chrome seem to work.
Some of the tasks below (and in future apps) are fairly open-ended. The idea is that these tasks give you something to get started, but you should feel free to explore the simulations any way you want. Play with them, query them, go through iterations of thinking what you expect, observing it, and if discrepancies occur, figure out why. Essentially, the best way to use these apps is to do your own science/research with them.
This and most other simulations/apps in DSAIDE do not have natural time units (unless specifically stated). You could, therefore, assume that your model runs in units of days or weeks/months/years, based on what’s most suitable for the disease you want to study. You have to make sure that all your parameters are in the right time units. Always make sure to check if a given simulation can handle different time units or assumes specific ones.
The tasks below are described in a way that assumes everything is in units of days (rate parameters, therefore, have units of inverse days). If any quantity is not given in those units, you need to convert it first (e.g. if it says a week, you need to convert it to 7 days).
simulate_introduction.R
. You can call this function directly, without going through the shiny app. Type ?simulate_introduction
into the R console for more information (you need to exit the graphical interface first or start a new R session). If you go that route, you need to use the results returned from this function and produce useful output (such as a plot) yourself.vignette('DSAIDE')
into the R console).Keeling, Matt J, and Pejman Rohani. 2008. Modeling Infectious Diseases in Humans and Animals. Princeton University Press.
Vynnycky, Emilia, and Richard White. 2010. An Introduction to Infectious Disease Modelling. Oxford University Press.