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.
This is a simple SIR model with an additional environmental compartment.
This model has the following compartments:
The processes being modeled are:
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.
\[\dot S =b - b_d S I - b_e S E - nS\] \[\dot I = b_d S I + b_e S E - g I -nI\] \[\dot R = g I - nR\] \[\dot E = p I - cE\]
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.
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.
simulate_environmentaltransmission_ode
. You can call them directly, without going through the shiny app. Use the help()
command for more information on how to use the functions directly. 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.Codeço, C T. 2001. “Endemic and Epidemic Dynamics of Cholera: The Role of the Aquatic Reservoir.” BMC Infectious Diseases 1: 1.