The Ninth q-bio Summer School - Albuquerque: Viral dynamics

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About the Viral Dynamics focus area

Lead scientific organizer: Ruy Ribeiro

Faculty

• Tanmoy Bhattacharya, Los Alamos National Laboratory & Santa Fe Institute
• Youfang Cao, Los Alamos National Laboratory
• Mario Castro, Comillas Pontifical University, Madrid, Spain
• Rob J. de Boer, Utrecht University, Netherlands
• Alan S. Perelson, Los Alamos National Laboratory
• Ruy M. Ribeiro, Los Alamos National Laboratory

Topics

• Within-host HIV dynamics
• Within-host HCV dynamics
• T cell population dynamics

Projects

Multi-Stage Infections: ODEs vs. Stochastic Models

Multi-stage infections are relatively common interactions between a host and a pathogen in which the infection can be controlled in different stages but, if the pathogen escapes the immune system, it creates a sustained infection loop that amplifies the severity of the disease. In Ref. [1], a deterministic mathematical model was introduced and analyzed rigorously. However, like in traditional infection models, fluctuations in any stage can remove completely the infection. This stochasticity cannot be fully captured by deterministic models. In this project, a stochastic study of the model in Ref. [1] is proposed to highlight the main differences between both kind of mathematical approaches.

[1] Delgado-Eckert, E., & Shapiro, M. (2011). A model of host response to a multi-stage pathogen. Journal of mathematical biology, 63(2), 201-227.

Spatial Model of HCV Infection

HCV replicates in liver cells called hepatocytes. These are arranged almost as a 2D (irregular) grid. The objective is to build a simulation of HCV infection on a (regular) 2D grid. In each cell HCV RNA replicates according to a dynamical process described by an ODE, or even a simple Hill function. Virus is produced from each cell depending of the level of HCV RNA. Free virus may infect uninfected cells with probability p, which depends on the viral load and the number of uninfected cells.

Construct a simulation of this system and investigate how viral load increases at the start of infection. How does the initial slope of VL increase depend on virus export rate and probability of infection.

Reactivation from HIV Latency

In a macaque model of HIV infection, the following observations were made: 1) The viral load is controlled below detection without treatment (likely by the immune responses); 2) When an activation agent is administered the viral load increases in a patter similar to primary infection. The objective is to develop a model based on the standard model of viral dynamics that captures this behavior.

Software

Please install the following software to prepare for scheduled computer labs:

• R
• R Studio
• TinkerCell

Recommended Reading

• Ribeiro RM, et al. (2012) Quantifying the Diversification of Hepatitis C Virus (HCV) during Primary Infection: Estimates of the In Vivo Mutation Rate. PLoS Pathog 8(8): e1002881. doi:10.1371/journal.ppat.1002881

• Graw et al. (2014) Inferring Viral Dynamics in Chronically HCV Infected Patients from the Spatial Distribution of Infected Hepatocytes. PLOS Comp Biol 10(11): e1003934 doi:10.1371/journal.pcbi.1003934

• Perelson AS and Ribeiro RM (2013) Modeling the within-host dynamics of HIV infection. BMC Biology 11: 96 doi:10.1186/1741-7007-11-96

• Delgado-Eckert, E., & Shapiro, M. (2011). A model of host response to a multi-stage pathogen. Journal of mathematical biology, 63(2), 201-227.