*Dynamical Systems Approaches to Infectious Disease Epidemiology (DSAIDE)* is an R package that allows individuals to explore and study concepts of infectious disease epidemiology using dynamical systems models, without the need to read or write computer code. The idea behind the specific structure of the package is that it uses mathematical models to teach infectious disease epidemiology concepts, but does not require the user to write any computer code. Another idea is that if a user wants to continue on their journey of learning modeling and infectious disease epidemiology, they can do so relatively seamlessly with this package by directly accessing and modifying the underlying code. The different use cases for the package are described below.

The package consists of several simulations/apps that allow for the simulation and exploration of different topics in infectious disease epidemiology.

The underlying models are written as compartmental dynamical models, either deterministic using differential equations (deSolve package) or stochastic using a Gillespie-type approach (adaptivetau package). A graphical user interface is wrapped around each simulation/app. The graphical user interfaces are written using the functionality of the R Shiny package. This allows exploration of models and infectious disease epidemiology concepts without the need to write any code. At the same time, the package is structured in a modular way that should allow those interested in the actual models and learning R coding to easily move from one stage to another.

Each app is meant to be fully self-explanatory and contains a description of the model, a list of tasks the user could try, and information on further details and readings.

The following simulations/apps are currently available:

The following simulations/apps are currently available:

App_Name | Model | Topic_covered |
---|---|---|

ID Dynamics Intro | 3 compartment (SIR) ODE model | A first introduction to a simple compartmental SIR model. Allows simulation of a single outbreak for different parameter and initial condition settings. |

Characteristics of ID | 6 compartment ODE model | The potential role of different disease states (e.g. pre-symptomatic, asymptomatic, symptomatic) on ID dynamics. |

ID Patterns | 6 compartment ODE model. Includes births-deaths, waning immunity, seasonality. | Different ID patterns (single outbreak, osciallations, steady states). |

Direct Transmission | 3 compartment ODE model. Births, deaths and waning immunity are included. | The differences between density-dependent and frequency-dependent transmission and their impact on ID dynamics. |

Environmental Transmission | 4 compartment ODE model. Includes explicit environmental stage. Births-deaths and waning immunity are included. | The impact of environmental shedding, decay and transmission. |

Vector Transmission | 5 compartment ODE model. Includes susceptible and infected vectors and their dynamics. Births and deaths for vectors and waning immunity for hosts are included. | Exploration of a simple vector-borne transmission model. |

Reproductive Number | 3 compartment ODE model. Includes vaccination of population at the beginning of the simulation. Births, deaths and waning immunity are included. | The reproductive number concept and how to estimate it from (simulated) data. |

ID Control | 9 compartment ODE model. An environmental and 2 vector stages as well as 6 host stages. | The impact of different control measures for different types of ID. |

Host Heterogeneity | 6 compartment ODE model. 2x SIR for 2 different hosts. | The impact of host heterogeneity and core groups on ID dynamics and control. |

Stochastic dynamics | 4 compartment (SEIR) stochastic model. | The impact of stochasticity on dynamics, the phenomenon of ID extinction. |

Evolutionary dynamics | 5 compartment stochastic model. Untreated and treated hosts infected with wild-type, and hosts infected with a resistant strain. | Interaction between drug treatment and evolution/emergence of drug resistance. |

Multi-Pathogen Dynamics | 9 compartment ODE model with basic SIR dynamics. | Infection dynamics with 2 pathogens that act independently. |

The audience for this app is individuals interested in infectious disease epidemiology from a *systems/modeling perspective*. For instance the apps allow exploration of concepts such as *patterns of infectious disease incidence*, *reproductive number concept*, *extinctions and critical community size*, etc. All these concepts are not well described by applying classical epidemiology approaches (i.e. assuming independence between individulas) to infectious diseases, but can readily by understood using a systems/modeling approach.

The documentation for each app tries to be complete and self-contained. However, the information provided inside each app is unlikely sufficient for a complete novice to fully understand the modeling and infectious disease material.

A highly motivated user could likely learn the modeling and infectious disease material covered by the apps on their own by working through some of the references provided for each app and/or general infectious disease modeling textbooks (e.g. (Keeling and Rohani 2008,Vynnycky and White (2010))).

Another intended use is for this package to be part of a course on infectious disease epidemiology/modeling.

The following sections describe the main envisioned ways the content in this R package can be used and extended. The idea is that everyone starts at level 1, and then depending on individual needs and interests, can decide to move on to the next level.

The interactive exploration of the models and infectious disease concepts through the graphical user interface is the main intended use of this package. The steps to get there are simple.

From CRAN, the package can be installed via

`install.packages('DSAIDE')`

To get a more up-to-date version of the package (but possibly a bit more buggy), installation from github using the `devtools`

package is also possible:

```
install.packages('devtools')
library('devtools')
install_github("ahgroup/DSAIDE")
```

Package installation is a one-time process, unless R itself is being upgraded/reinstalled.

Every time a new R/Rstudio session is started, the package needs to be loaded:

`library('DSAIDE')`

followed by starting the main menu for the package:

`dsaidemenu()`

This will bring up a graphical menu from which one can select each app. Each app contains the information needed to understand the underlying model, and has a list of (non exhaustive) suggested tasks to learn about the topic covered by the app. After exploring an app, the user returns to the main menu and eventually exits the main menu and closes the R session. No code needs to be written, the user can fully focus on learning the infectious disease dynamics related concepts and topics that are covered by the different apps.

As stated above, the exploration of the models and infectious disease topics through the graphical interface is the main intended use of the package. However, the package is structured such that it is possible, without too much effort, to interact with the code more directly. This will provide more flexibility but will require writing some code.

To facilitate direct interaction and modification of the underlying simulations, each app is structured in such a way that the underlying model/simulation is a stand-alone function. This simulator function can be called directly, without going through the graphical interface. The ‘Further Information’ tab inside each app provides the name of the corresponding simulator function.

Consider as example the first app, called “ID Dynamics Intro”. The simulator function for this model is called `simulate_introduction.R`

, the user can learn about the inputs and outputs of the function by looking at its documentation

`help('simulate_introduction')`

The help file explains that one can run the simulation by specifying initial number of susceptibles and infected, the duration for which the simulation should be run, and the infection and recovery parameters. Unless explicitly specified, the models do not have inherent time units. Instead, those are set by the user based on choices for parameters. It is important to ensure that all quantities have time units. For this simulation, *tmax*, *g*, and *b* are expressed in the same time units, e.g. days or months (or the inverse of those units for the rate parameters). Each parameter has some default. The user can modify those default settings. For instance one can call the simulator with the following settings, overwriting the defaults:

`result <- simulate_introduction(S0 = 500, I0 = 5, tmax = 100, g = 0.1, b = 1/2500)`

Calling the simulation function execuctes the underlying dynamical model (here a simple 3 compartment ODE model, as described in the “Model” section of the app). The simulation function produces and returns time-series for the dynamics of each of the variables that are tracked. Users can produce their own plots, e.g. plotting susceptible as function of time:

`plot(result[,"time"],result[,"S"],xlab='Time',ylab='Number Susceptible',type='l')`

The ability to call the simulation functions directly instead of going through the graphical interface allows additional exploration of the models. For instance if one wanted to explore the behavior of a model systematically for different values of a given parameter, this would need to be done manually if run through the graphical interface. Calling the function directly allows one to automate this by wrapping the function inside a loop over the parameter of interest, recording some quantity of interest for each run, and report the result at the end. The following is a simple example, showing a loop over different values of the recovery rate and recording the peak of the outbreak each time, with the final result *peak of outbreak as function of recovery time* shown in a plot:

```
gvec = seq(0.01,0.3,by=0.01) #values of recovery rate, g, for which to run the simulation
peak = rep(0,length(gvec)) #this will record the peak values for each g
for (n in 1:length(gvec))
{
#call the simulator function with different values of g each time
result <- simulate_introduction(S0 = 500, I0 = 5, tmax = 200, g = gvec[n], b = 1/2500)
peak[n] <- max(result[,"I"]) #record max number of infected for each value of g
}
#plot final result
plot(gvec,peak,type='p',xlab='Rate of recovery',ylab='Max number of infected')
```

devtools::release() Thus, the user can add their own custom code to the existing simulator functions and with a few lines of extra code analyze and explore many more questions and scenarios than those accessible through the graphical interface. This provides a lot more flexibility, but requires writing some R code to interface with the supplied simulator functions.

As a next step, it is possible to not only interact with the simulation functions, but instead directly access the code and modify the underlying simulator functions. To make this easy, copies of all simulator functions are in a subdirectory called *simulatorfunctions* inside the DSAIDE package folder. Each function in that folder starts with `simulate_`

. To find the location where R installed the package, a search on your computer might be needed.

While the functions in this subfolder are not used to run the code in the DSAIDE package, and one could therefore edit them without breaking the package, it is better to make a copy of the whole folder somewhere else. This way the chance of overwriting any modifications - if for instance the package is being re-installed - are reduced.

All simulator functions are (hopefully) well documented. Some basic to intermediate level of R coding experience is likely required to successfully modify the functions. In addition to modifying the simulator function of interest, some additional code to interact with the modified function (as described in *Level 2*) is likely required.

The following provides a simple example of this process of modifying a simulator function and exploring its results. Assume that we want to modify the simple SIR model encoded in `simulate_introduction.R`

. After finding the file and making a copy (let’s call the modified function `mysimulator.R`

), we can make modifications. Say we want to include waning immunity with recovered returning to the susceptible class at rate *w*.

We will need to modify the following lines of code:

old:

`simulate_introduction <- function(S0 = 1000, I0 = 1, tmax = 300, g = 0.5, b = 1/1000)`

new:

`mysimulator <- function(S0 = 1000, I0 = 1, tmax = 300, g = 0.5, b = 1/1000, w = 0)`

old:

`pars = c(b = b, g = g);`

new:

`pars = c(b = b, g = g, w = w);`

old:

```
dS = - b * S * I; #susceptibles
dI = b * S * I - g * I; #infected/infectious
dR = g * I; #recovered
```

new:

```
dS = - b * S * I + w * R; #susceptibles
dI = b * S * I - g * I; #infected/infectious
dR = g * I - w * R; #recovered
```

We could now for instance explore how different rates of waning immunity impact the maximum peak size over all outbreaks. This requires a slight modification of the code shown above in *Level 2* as follows:

```
source('mysimulator.R') #to initialize the new function - it needs to be in same directory as this code
wvec = seq(0,1,by=0.02) #values of immunity loss rate, w, for which to run the simulation
peak = rep(0,length(wvec)) #this will record the peak values for each g
for (n in 1:length(wvec))
{
result <- mysimulator(S0 = 1000, I0 = 1, tmax = 300, g = 0.5, b = 1/1000, w = wvec[n])
peak[n] <- max(result[,"I"])
}
plot(wvec,peak,type='p',xlab='Rate of waning immunity',ylab='Max number of infected')
```

The package is built in a way that makes it (hopefully) easy for others to contribute new simulations/apps. To that end, the package contains a subfolder called *docsfordevelopers*, which provides information on how the apps are structured and how to add new ones. In brief, each app consists of a simulator function and a shiny app function which calls the simulator function. AN R Markdown file, which is turned into multiple HTML files by a provided script, should include the documentation displayed in each app. Developing a new app consists of writing (at least) 2 R functions (*simulate_NNNNNN.R* and the corresponding *app.R*) and filling the provided RMarkdown template for the documentation, then running a few functions to process everything.

The information in the *docsfordevelopers* folder contains more details and is hopefully complete enough to allow fairly easy development and contribution to the package. If you are interested in contributing further apps, I suggest you get in touch with me, either by email (ahandel@uga.edu) or through the github site for the package (https://github.com/ahgroup/DSAIDE).

The following individuals contributed to this package: Spencer Hall, Brian McKay, John Rossow, Sina Solaimanpour.

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.