Virus and PkPD Model

Overview

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.

Learning Objectives

The Model

Model Overview

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:

Model Diagram

The diagram illustrating this compartmental model is shown in the figure.

Flow diagram for a virus infection model with drug treatment and Pk-Pd.

Flow diagram for a virus infection model with drug treatment and Pk-Pd.

Model Equations

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: \[e = E_{max} \frac{C^k}{C^k+C_{50}}\]

What to do

Task 1:

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.

Task 2:

Task 3:

Task 4:

Task 5:

Task 6:

Task 7:

Task 8:

Further Information

References

Canini, Laetitia, Jessica M Conway, Alan S Perelson, and Fabrice Carrat. 2014. “Impact of Different Oseltamivir Regimens on Treating Influenza a Virus Infection and Resistance Emergence: Insights from a Modelling Study.” PLoS Computational Biology 10 (April): e1003568. https://doi.org/10.1371/journal.pcbi.1003568.
Handel, Andreas, Elisa Margolis, and Bruce R Levin. 2009. “Exploring the Role of the Immune Response in Preventing Antibiotic Resistance.” Journal of Theoretical Biology 256 (February): 655–62. https://doi.org/10.1016/j.jtbi.2008.10.025.
Powers, Kimberly A, Narendra M Dixit, Ruy M Ribeiro, Preeti Golia, Andrew H Talal, and Alan S Perelson. 2003. Modeling viral and drug kinetics: hepatitis C virus treatment with pegylated interferon alfa-2b.” Semin Liver Dis 23 Suppl 1: 13–18. https://doi.org/10.1055/s-2003-41630.
Talal, Andrew H, Ruy M Ribeiro, Kimberly A Powers, Michael Grace, Constance Cullen, Musaddeq Hussain, Marianthi Markatou, and Alan S Perelson. 2006. “Pharmacodynamics of PEG-IFn Alpha Differentiate HIV/HCV Coinfected Sustained Virological Responders from Nonresponders.” Hepatology 43 (5): 943–53.