Virus and Drug Treatment Model

Overview

This app allows exploration of the basic virus infection model in the presence of a drug. The idea is to explore the results for two hypothetical mechanisms of a drug. By comparing the model results with data, one can get hints as to the mechanism by which the drug might act. In this app, no explicit, statistical comparison to data (i.e. fitting to data) is implemented. Instead, you are asked to compare patterns obtained from the model and from real data qualitatively. The influenza drug app addresses a similar question and fits to data.

Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab. Learn more about the model and its origins in the “Further Information” tab.

The Model

Model Overview

This model is a variation of the basic virus model. A detailed description of the model can be found in the corresponding app. The model for this app includes drug treatment and differs from the basic virus model in the following ways:

Note that the drug is not explicitly modeled here, it is not given its own compartment/equation. Instead, we model the drug by its effects on some of the model parameters, and assume that this effect is either absent or present but does not otherwise change with time. The Pharmacokinetics and Pharmacodynamics app provides a model that includes explicit modeling of drug uptake and decay.

Model Diagram

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

Flow diagram for the virus infection and drug treatment model.

Model Equations

Implementing this model as a continuous-time, deterministic model leads to the following set of ordinary differential equations.

\[\dot U = n - d_U U - (1-f)bUV\] \[\dot I = (1-f)bUV - d_I I\] \[\dot V = (1-e)pI - d_V V - (1-f)gbUV\]

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:

For the next few tasks, we consider a chronic viral infection and treatment (e.g. HCV or HIV). The model is assumed to run in units of days.

If you need an introduction or refresher on what the steady state means and how one could compute it, see the “Basic Virus” app.

Task 5:

A model like this has been applied to study the interferon treatment for Hepatitis C Virus (Neumann et al. 1998). (Today’s standard of care for HCV does not involve interferon anymore, but it is still a useful example to consider). One question the investigators wanted to answer is if one of the 2 mechanisms, i.e. reduction of cell infection (parameter f) or reduction of virus production (parameter e) is better at explaining/predicting observed viral kinetics.

Task 6:

Source: Neumann et al 1998 Science.

Task 7:

Task 8:

Further Information

References

Beauchemin, Catherine A A, James J McSharry, George L Drusano, Jack T Nguyen, Gregory T Went, Ruy M Ribeiro, and Alan S Perelson. 2008. “Modeling Amantadine Treatment of Influenza a Virus in Vitro.” Journal of Theoretical Biology 254 (September): 439–51. https://doi.org/10.1016/j.jtbi.2008.05.031.
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.
Dixit, Narendra M, Jennifer E Layden-Almer, Thomas J Layden, and Alan S Perelson. 2004. “Modelling How Ribavirin Improves Interferon Response Rates in Hepatitis c Virus Infection.” Nature 432 (December): 922–24. https://doi.org/10.1038/nature03153.
Handel, Andreas, Ira M Longini Jr, and Rustom Antia. 2007. “Neuraminidase Inhibitor Resistance in Influenza: Assessing the Danger of Its Generation and Spread.” PLoS Comput Biol 3 (12): e240. https://doi.org/10.1371/journal.pcbi.0030240.
Neumann, A U, N P Lam, H Dahari, D R Gretch, T E Wiley, T J Layden, and A S Perelson. 1998. “Hepatitis c Viral Dynamics in Vivo and the Antiviral Efficacy of Interferon-Alpha Therapy.” Science (New York, N.Y.) 282 (October): 103–7.