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 a SEIR model. I’m using the letter E here to denote environmental stage of the pathogen. While this could also be abbreviated to SIER (or maybe SIRE), if you see the terminology SEIR model somewhere, the authors usually refer to a model with the additional exposed stage, not an 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 explicitly specified by the authors such that there is no ambiguity.

What to do

The tasks below are described in a way that assumes that everything is in units of MONTHS (rate parameters, therefore, have units of inverse months). If any quantity is not given in those units, you need to convert it first.

Task 1:

Task 2:

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.