Evolution of Seasonal Influenza Virus in A Strain Space: Hybrid Dynamical System Approach

     The seasonal human influenza A virus interacts with human immune responses and undergoes year-to-year rapid evolution. Recent studies reveal that host cross-immunity is an important factor to describe actual antigen and genetic evolution of influenza virus. However, because of the large number of strains and the complex structure of cross-immunity, many previous analyses essentially had to rely on individual based simulations or high-dimensional mathematical models. Unfortunately, some of their formulas are not mathematically correct to describe the dynamics of influenza transmission, especially for an accumulation of host cross-immunity. Here we introduced an idea of hybrid dynamical system, which combine continuous and discrete dynamical system, and modeled the year-to-year evolution of influenza virus in human population. Under the condition that the cross-immunity lasts for long time and only one strain becomes dominant within a year, the hybrid dynamical system is reduced to very simple operations. Furthermore, for example, in a 2D strain space, we found that the year-to-year rapid viral evolution behaves like “self-avoiding random walks”. We would like to present our novel approach and to discuss a possibility that the viral evolution in strain space could be formulated by a (diffusion) model. This is a joint work with Dr. Yuya Tachiki in Hokkaido University.