Resistance generation during influenza infection and treatment

Overview

This app allows exploration of a stochastic model that simulates emergence of drug resistance during an acute virus infection (e.g. influenza) in the presence of an antiviral. Read about the model in the “Model” tab. Then do the tasks described in the “What to do” tab.

The Model

Model Description

This model is a modification and extension of the model described in the “Model Stochasticity” app. Here, we track 2 types of virus, wild-type and drug sensitive, and a resistant mutant. We also consider the presence of a drug.

This model consists of 5 compartments:

For this model, we consider the following processes:

  1. Drug-sensitive or drug resistant Virus infects uninfected cells at (the same) rate b.
  2. Drug-sensitive infected cells produce new drug-sensitive virus at rate (1-m)p and occasionally generate a resistant mutant virus at rate mp.
  3. Drug-resistant infected cells produce new drug-resistant virus at rate (1-f)p. The factor f accounts for the cost of fitness generally observed for drug resistant strains.
  4. Sensitive and resistant virus are both removed at rate dV, loss of virus due to infecting new cells is ignored.
  5. A drug reduces production of sensitive virus by a factor e, it does not affect resistant virus.

For simplicity, we ignore the possibility that a cell might be infected by both drug sensitive and infected virus and might produce a mix of them.

Model Diagram

Flow diagram for the drug resistance model.

Model Equations

If we were to implement this model as a continuous-time, deterministic model, it would have the following set of ordinary differential equations.

\[\dot U = - bUV_s - bU V_r\] \[\dot I_s = bUV_s - d_I I_s\] \[\dot I_r = bUV_r - d_I I_r\] \[\dot V_s = (1-e)(1-m)pI_s - d_V V_s\] \[\dot V_r = (1-e)mpI_s + (1-f)pI_r - d_V V_r\]

However we use a stochastic model here. For such a model, the differential equation formulation is not valid. One can write down an equivalent formulation as a stochastic model by specifying every possible process (also called transition/event/reaction) that can occur and their propensities (the propensity multiplied with the time step gives the probability that a given process/event/transition occurs). For our model these are the following:

Event type Transitions Propensity
drug sensitive infection U => U-1, I_s => I_s + 1 bUV_s
drug resistant infection U => U-1, I_r => I_r + 1 bUV_r
death if I_s I_s => I_s - 1 dI*I_s
death if I_r I_r => I_r - 1 dI*I_r
production of V_s V_s => V_s + 1 (1-e)(1-m)p*I_s
removal of V_s V_s => V_s - 1 dV*V_s
production of V_r V_r => V_r + 1 (1-e)mpI_s + (1-f)p*I_r
removal of V_r V_r => V_r - 1 dV*V_r

What to do

Notes:

Task 1

Task 2

Task 3

Task 4

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, 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.