Research projects include: 
  • Stability and dynamical analysis of nonlinear delay equation (from structured population models)
    • A fundamental equation describing population dynamics is Delay Equation, coupled equations of delay differential equations (DDE) and renewal equations (RE). Renewal equation explicitly writes down the reproduction process of individuals, the central concept in the population dynamics. In other words, it is natural to understand the population dynamics in the framework of an infinite dimensional dynamical system. We analyze dynamical aspects, such as (in)stability, emergence of periodic solutions  and asymptotic behavior of solutions, of fairly general population equations formulated as Delay Equations, with dynamical system theories and functional analysis framework. Elaboration of the analysis allows us to understand the mechanism behind the dynamics and robust biological conclusions are also expected.
  • Application: from mathematical analysis to population biology and epidemiology
    • The findings from the study of mathematical models could be used or give an insight to interpret the nonlinear phenomena observed in population dynamics. With an interdisciplinary spirit, with collaborators Ryosuke Omori (Hokkaido University), Satowa Suzuki (NIID), we use various methods ranging from individual based simulations to analysis of infinite dimensional dynamical systems to derive concrete conclusions.
  • Cochrane collaboration and systematic review