Mathematical theory of structured population dynamics and its applications to epidemic models

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400194
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: The University of Tokyo
• Principal Investigator: INABA Hisashi 東京大学, 数理(科)学研究科(研究院), 教授 (80282531)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 感染症数理モデル / 基本再生産数 / 構造化個体群モデル / 閾値現象 / ウィルスダイナミクス

Outline of Final Research Achievements

We developed methods to calculate the basic reproduction number and the type-reproduction number in time-heterogeneous environments, and examined the endemic threshold phenomena in the age-structured SIS epidemic model. The early Kermack-McKendrick model was extended to take into account individual heterogeneity and its pandemic threshold theorem was proved. Next we formulated the Kermack-McKendrick reinfection model as a structured population model, and examined its mathematical nature and showed conditions under which subcritical endemic steady states exist. By extending the basic model, we have suggested possibilities that asymptomatic infection and subclinical infection would lead subcritical endemic states. In collaboration with experimental biologists, we developed in vivo virus dynamics models to show quantitatively that cell-to-cell infection has a large impact to the basic reproduction number, and that some virus protein (HIV-1Vpu) had an important role in the HIV-1 pandemic.

Free Research Field

数理人口学・数理生物学