| Project/Area Number |
12640105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
INABA Hisashi The University of Tokyo, Graduate School of Mathematical Sciences, Associate Professor, 大学院・数理科学研究科, 助教授 (80282531)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAZAWA Minato Yamaguchi Prefectural University, School of Nursing, Associate Professor, 看護学部, 助教授 (40251227)
KAKEHASHI Masayuki Hiroshima University, Faculty of Medicine,Professor, 医学部, 教授 (80177344)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2000: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | age structure / population / epidemic model / evolution equation / semigroup / threshold condition / 人口モデル / 微分方程式 / シャガス病 / エイズ / 定常解 / 分岐 / 個体群動態モデル / 年齢構造化モデル / 伝染病 / 数理モデル |
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| Research Abstract |
(l) We have developed a two-sex age-structured population model with homogeneous marriage function as an evolution equation system and constructed its semigroup solution. Existence of persistent solution (exponential solution) has been proved for general marriage function.
(2) We have formulated a nonlinear age-structured population model for marine invertebrates with density dependent mortality. We have constructed a positive semigroup solution, and proved the sufficient condition for the stability of the steady state solution. We have also the possibility of unstable steady state solution and oscillatory behavior.
(3) We have formulated an epidemic model for type A influenza that takes into account the evolutionary aspects of virus, and examined it as an evolutionary equation. We have established the threshold condition for disease invasion and existence of endemic steady state. The possibility of unstable endemic steady state has been Oalso shown.
(4) We have constructed a duration-dependent epidemic model for vector transmitted diseases like as Chagas disease, and shown that a backward bifurcation of endemic steady states can occur if there exists a disease-induced death rate.
(5) We have formulated and analyzed an age-duration-structured population model for HIV infection in homogeneous community. We have established the threshold condition for invasion and existence of endemic steady states. It was also shown that a backward bifurcation of endemic steady slates can occur, so multiple endemic steady states are possible.
(6) We have analyzed the behavior of a pair formation model for sexually transmitted diseases with subpopulations divided by sexual activity. And we have constructed an individual-based model to simulate sexually transmitted diseases.
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