# The Sixth q-bio Summer School: Viral Dynamics

### From Q-bio

This series of lectures focus on viral and immune systems dynamics at the cellular population level, that is the modeling of interactions of immune cells and viruses within an individual. There will be a basic introduction to the biology of these systems, followed by lectures on modeling specific issues/processes/immune systems. We will cover both modeling of the healthy immune system, and viral infections such as human immunodeficiency (HIV), hepatitis (B and C), and influenza. Particular attention will be given to the evolutionary processes shaping these viruses in vivo, including the topic of phylogenetics. The approach to all these subjects will include discussions of the mathematical framework, the types of available data and how to link models and data to generate new hypotheses, estimate parameters and gain the most biological insight from restricted datasets. Group projects will include journal club presentations, small simulations projects, and there will be scope for research-type projects if enough student interest is manifested.

This section of the summer school is organized by Ruy Ribeiro. Please address all questions about this section of the summer school to its organizer.

# Topics

**Introduction to viruses and the immune system**(What is a virus? Viral lifecycles. Viral spread. A simple primer to immunity. Virus and the immune system: a predator-prey system.)

**How to model a viral infection within the host**(Data and model generation, Models for drug treatment, Model interpretation)

**Modeling the immune response**(Chronic infection and immune control, Separation of time scales, Competitive exclusion)

**Spatial models of the immune response**(Agent based model of single cell activation, Understanding empirical data using models)

**Viral evolution**(Introduction to phylogenetics, Tracing HIV evolution, Visualization of sequence diversity and evolution, HIV vaccines)

# Lectures / Tutorials

## Introduction to viruses and immune system modeling – Ruy Ribeiro (LANL)

This series of lectures focus on viral and immune systems dynamics at the cellular population level, that is the modeling of interactions of immune cells and viruses within an individual. The first lecture will be an introduction to the series and a basic introduction to the biology of viruses and their interaction with the immune system.

## How to model a viral infection – Alan S. Perelson (LANL Senior Fellow)

I will show how one goes from empirical data to generating and testing a model of viral infection within a single individual. To showcase the methods I will use two examples, HIV and hepatitis C virus infection. Both viral infections are major health problems in the world today and I will show how modeling has influenced the way people think about the events going on in infected individuals and how modeling has influenced how people are treated for these infections.

## Modeling the immune response – Rob de Boer (Utrecht University, The Netherlands)

In the past few decades the scientific knowledge about the immune system has grown explosively, but this has mainly revealed qualitative information. To properly understand a system as complicated as the immune system, we also need to have a more quantitative understanding. Quantitative interpretation of experimental data typically requires mathematical modeling, and in almost all cases these models are formulated in terms of differential equations. In a tutorial session participants will be introduced to this modeling approach, and learn how to read the equations, understand their basic properties (like steady states), and learn about fitting such models to experimental data. We will close by discussing other modeling approaches, like agent based models.

## Spatial models of the immune response – Frederik Graw (LANL)

The importance of considering spatial aspects when using mathematical models to analyze experimental data on viral infections within a host has become more and more evident. Experimental techniques, such as two-photon microscopy, which allows us to observe immune processes in vivo on a single cell level, have evoked a number of modeling frameworks to study different aspects of viral and immune dynamics. I will present some of these approaches and how the methods have been used. I will show how this kind of modeling has advanced our knowledge about immune processes in general, and how it has helped, and will help, us to identify new possible targets against different diseases, such as HIV infection.

## Introduction to phylogenetics – Tanmoy Bhattacharya (LANL and Santa Fe Institute)

**Nothing in biology makes sense except in the light of evolution**, this is turning out to be ever truer every day. A solid understanding of what methodologically separates the biological and other sciences that are strongly affected by historical contingencies from the physical sciences discovering universal natural laws, is an important component in the training of quantitative biologists. This lecture will cover the basics of why, what, and how of phylogenetics to get students to understand this important fact.

## Applying phylogenetics to understanding virus epidemics – Thomas Leitner (LANL)

In this lecture I will introduce the use of phylogenetics to track infectious diseases, known as molecular epidemiology or phylodynamics. The main examples will come from the worldwide HIV epidemic. I will show how phylogenetics have been used 1) to systematically classify the virus (including recombination), 2) to find and time it's origin in African primates, 3) to trace its pandemic spread, 4) how to infer the actual human spread rate from virus genetics, and 5) how it can be used to trace individual transmissions. The students will see how recombinant virus cannot be accurately placed in a phylogenetic tree and how they may be detected. The students will be introduced to the concept of the molecular clock, how it can be estimated and used to track epidemics. I will try to make this an interactive session, and depending on time, we may touch upon the use of genetics to trace geographical origins, ie phylogeography.

## Visualization of sequence diversity and evolution – William Fischer (LANL)

In recent years, new DNA sequencing technologies have led to a vast increase in the number of sequenced genomes. We use these technologies to study the evolution of viral populations of HIV within individual patients, following the development of immune escape through acute and later stages of infection. Large datasets enable unprecedented sensitivity for detecting early mutations and calculating viral dynamics, but require substantial investments in software (error processing) and visualization. I will discuss the application of deep sequencing techniques to the evolution of immune escape and drug resistance, as well as possible implications for vaccines.

## HIV vaccines – Bette Korber (LANL Fellow)

To be announced.

## Stochastic modelling in viral and immunological systems - Mario Castro (Comillas Pontifical University, Spain)

Modelling population dynamics has been one of the most effective ways to quantitatively approach prediction in biological systems (specially in virus dynamics). In particular, ordinary differential equations have been widely studied to accommodate to different biological setups. However, there are some scenarios where such modelling approach cannot capture the main ingredients of the system. Specifically, when the populations are small or in the proximity of a bifurcation point (for instance close to the epidemic threshold or close to extintion) the fluctuations are large and specific stochastic modelling is required. In this tutorial session participants will be introduced to basic concepts in stochastic methods, both analytical and numerical, and focus on two case studies in which this sort of modelling approach provides different answers than ordinary differential equations.

# Break-out sessions

- Journal clubs
- Project development
- Students' presentations

# Projects

See Projects QB4 for more information.