DSAIDE - Dynamical Systems Approach to Infectious Disease Epidemiology

A collection of Shiny/R Apps to explore and simulate the population dynamics of infectious diseases.
Written and maintained by Andreas Handel, with contributions from others.

Environmental Transmission - Practice

Overview

This app allows you to explore a model which allows for both direct transmission and transmission through an environmental stage. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Overview

This is a simple SIR model with an additional environmental compartment.

This model has the following compartments:

The processes being modeled are:

Model Implementation

The flow diagram and the set of ordinary differential equations (ODE) which are used to implement this model are as follows:

Flow diagram for the model with environmental transmission.

Flow diagram for the model with environmental transmission.

\[\dot S =b - b_d S I - b_e S E - nS\] \[\dot I = b_d S I + b_e S E - g I -nI\] \[\dot R = g I - nR\] \[\dot E = p I - cE\]

A comment on terminology

Often the letter E is used for the exposed stage, which would then be called an SEIR model. I’m using the letter E here to denote environmental stage of the pathogen. While this could also be abbreviated to SEIR (or maybe SIRE), if you see the terminology SEIR model somewhere, the authors usually refer to a model with the additional exposed stage, not environmental stage. There are no naming rules for either model compartments or parameters, so you will see all kinds of letters used. They should all be clearly specified by the authors such that there is no ambiguity.

What to do

A general note: Some of the tasks below are fairly open ended. You shouldn’t go through the tasks like a check-list. Instead, explore these simulations, play with them, query them. As you do, loop through iterations of formulating your expectations for a specific scenario/task, running the model and observing results, and if results don’t agree with your expectations, figure out why. Essentially, “do science/research”.

Task 1:

Task 2:

Note: The ‘pathogen in the environment’ units are arbitrary here, and parameters are chosen such that everything fits (mostly) into a single plot. To compare with real data, where environmental pathogen load might be very high, you would need to show separate plots, or plot on a log scale.

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Answers

This section does not have the shinytab label and is therefore ignored and not included in the app. One could provide the answers here. Note that if this file is supplied with the package, the answers are in principle available, so most users might not know where/how to look.

Answer 1:

Answer to task 1.

Further Information

References

Codeço, C T. 2001. “Endemic and Epidemic Dynamics of Cholera: The Role of the Aquatic Reservoir.” BMC Infectious Diseases 1: 1.


This package is built and maintained by Andreas Handel, with contributions from others.
All text and figures are licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. Software/Code is licensed under GPL-3.