This app allows exploration of a basic virus infection model in the presence of treatment. Drug pharmacokinetics (Pk) and pharmacodynamics (Pd) is included in the model. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.
This model consists of 4 compartments modeling a the basic dynamics of a viral infection in the presence of a drug. In this model, we track the following entities by assigning each to a compartment:
In addition to specifying the compartments of a model, we need to specify the processes governing the model dynamics. For our system, we specify the following processes/flows:
The diagram illustrating this compartmental model is shown in the figure.
Flow diagram for a virus infection model with drug treatment and Pk-Pd.
Implementing this model as a continuous-time, deterministic model leads to the following set of ordinary differential equations.
\[\dot U = n - d_U U - bUV\] \[\dot I = bUV - d_I I\] \[\dot V = (1-e)pI - d_V V - gb UV\] \[\dot C = - d_C C, \qquad C=C+C_0 \textrm{ at } t = t_{interval} \]
tinterval is the time at which a new drug dose is given. Prior to treatment start, i.e. (t < txstart), there is no drug and C=0. The drug efficacy e is given by its own equation which depends on C as follows: \[e = E_{max} \frac{C^k}{C^k+C_{50}}\]
For the first few tasks, we consider an acute viral infection and treatment (e.g. influenza and neuraminidase inhibitor drugs). The model is assumed to run in units of days.
simulate_pkpdmodel_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('DSAIRM')
into the R console.