Liu ’12 Presents Mathematical Model – Hobart and William Smith Colleges \
The HWS Update

Liu ’12 Presents Mathematical Model

Mathematics major Yaoxin Liu ’12, recently gave a presentation on campus titled,A Mathematical Model of T Cell Exhaustion Caused by HBV/HDV.”

The talk was the topic of research he conducted with Assistant Professor of Mathematics and Computer Science Jonathan Forde and Yixiao Sha ’12. As part of the Summer Research Program, they looked at the interactions between the Hepatitis Beta (HBV) and Hepatitis Delta (HDV) viruses, and the effects they had on human bodies when one, or both of the viruses was infecting a single host.

Liu, Forde and Sha developed an ordinary differential equation model of the interactions of these two viruses and the immune system to study the effect of a second infection on immune exhaustion.

The three started by studying the four-dimensional model (a system using four mathematical equations), with only HBV infection, and then added the second virus, HDV. They also analyzed various steady states and their stability for both systems. All the stability conditions are found for the four dimensional system with only HBV infection. For the five-dimensional system (a system using five mathematical equations) with HDV, numerical simulations show the existence of positive steady states representing chronic co-infection. The model suggests that co-infection does not reduce the exhaustion level, but increases damage due to general inflammation.

Initially, Liu explained, they observed that the infection with HBV would exhaust the immune system of the host, but infection with HDV on top of HBV would reduce immune system exhaustion. With that in mind, they set out to see if co-infection with the two viruses was indeed better than being infected only by HBV.