The mathematics behind disease: mapping the virus inside the body

By Adriana Suarez-Gonzalez

A viral infection is a complex, dynamic process. UBC researcher Daniel Coombs uses theoretical and applied mathematics to understand how viruses, such as HIV, function and spread within one person’s body and across individuals. Rumor has it that he is the only math professor at UBC that owns a microscope.

What are your main areas of research?

I use mathematics to study infection disease dynamics and immune cell function inside a person . By applying mathematical models, I explore how viral infections such as HIV change over time, and how immune cells use signalling networks to detect pathogens. I also collaborate with different research groups working in epidemiology and contribute with the modelling of infectious diseases.

What was your most recent work on within host infection disease dynamics?

When a person is infected with HIV and goes under antiretroviral treatment, their viral level becomes so low that it’s undetectable in routine lab tests. But this doesn’t mean the virus is gone. It remains silent inside cells - called latent cells – that do not express the virus. If treatment is interrupted, latent cells are activated and the virus starts replicating exponentially, reaching high viral levels. We used mathematical models to recreate this process and estimated how long it would take for antiretroviral therapy to kill all infected cells, including latent ones. Or, in other words, how many years of antiretroviral therapy a person would need to be cured. Our models show that it would take at least 25 to 50 years, but also that infection recovery happens in different ways. These results could be used as platforms for future experimental work in clinical trials.

What is a mathematician doing with a microscope?

We’re using microscopy to study how B-cells, a type of highly specialised immune cell, respond to infection. A technique called single particle tracking allows us to label proteins on the surface of the cells and track each cell individually. First, we observe the cells — more specifically the fluorescent receptors on the surface of the cells — in the microscope. Then we use multiple modelling approaches to gain insights on cell mobility when microbial molecules are present. Our findings have elucidated new mechanisms for B-cell receptors signalling, and could be used to develop therapeutic targets for treating certain types of B-cell malignancies or autoimmune diseases.