DMS Applied Mathematics Seminar

Speaker: Yusuke Asai (Hokkaido University, Japan)

Title: Development of hepatitis C virus dynamics model and numerical methods for random ordinary differential equations with time delay

Abstract: Mathematical modeling by differential equations plays an important role to understand natural sciences. In particular, required data are frequently not obtained in biology and medicine and simulation using mathematical models helps us to analyze system behavior under various scenarios.

Deterministic models have been long investigated and applied to natural phenomena; however, some factors might be ignored in model building process or we encounter random effect from environment in practice. To handle such uncertain effect, random ordinary differential equations (RODEs) can be an ideal tool because of its simplicity in model building as well as the regularity of the corresponding noise processes. Recently, several classes of numerical methods for RODEs have been developed and applied to real problems, yet time delay has been ignored in those applications. To capture and understand system behavior more accurately, we need to handle both of randomness and time delay simultaneously.

In this talk, development of hepatitis C virus (HCV) dynamics models is briefly introduced and then numerical methods for RODEs with time delay are systematically constructed. The developed methods are applied to the introduced HCV model with target cells, infected cells and viruses compartments, and eclipse phase, the time elapsed between cell infection and virus production, and their behavior will be investigated.