Mathematical Theory of Structured Population Models and its Applications to Demography and Epidemiology

2018 Fiscal Year Final Research Report

• Project/Area Number: 16K05266
• 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, 大学院数理科学研究科, 教授 (80282531)
• Project Period (FY): 2016-04-01 – 2019-03-31
• Keywords: 構造化個体群 / 基本再生産数 / 感染症数理モデル / 閾値現象

Outline of Final Research Achievements

(1) We formulated sufficient conditions for existence of backward bifurcation in the Kermack and McKendrick reinfection model.(2) For the multistate age-structured SIR epidemic model, we formulated sufficient conditions for the endemic steady state to be globally stable.(3) We formulated the demographic transition as an epidemic model, in which innovative cultural norms that lower the number of births could be transmitted from individuals with low fertility (infecteds or innovators) to traditional individuals with high fertility (susceptibles or conservatives), and considered sufficient conditions for the demographic transition to occur. We have shown that there exists at least one coexistence growth orbit if two trivial exponential growth orbits become bi-unstable.(4) For the age-structured SIS epidemic model with spatial diffusion, we have shown that the disease-free steady state is globally stable if R0<1, while the endemic steady state uniquely exists and globally stable if R0>1.

Free Research Field

数理人口学・数理生物学

Academic Significance and Societal Importance of the Research Achievements

本研究では、とくに再感染現象を含む感染症数理モデルにおける閾値現象と一般化された変動環境における基本再生産数と世代推進作用素の役割の解明等に焦点をあてて，ケルマック・マッケンドリック再感染モデルにおける分岐現象，多状態SIR型年齢構造化モデル，人口転換の感染症モデル，空間拡散のあるSIS年齢構造化モデルなどの閾値現象を検討した．これらは感染という普遍的な非線形力学の基本構造と，それが個体群動態に対して持つ意義を明らかにするという点で基本的な貢献である．感染症の制御は現代社会の基本的課題であり，基本再生産数理論にもとづく感染症数理モデルは効果的な感染制御政策の策定にとって不可欠なツールである．