The analysis of mathematical models describing dynamics of infection

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540135
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Okayama University
• Principal Investigator: SASAKI Toru 岡山大学, 環境生命科学研究科, 准教授 (20260664)
• Co-Investigator(Renkei-kenkyūsha): KAJIWARA Tsuyoshi 岡山大学, 大学院環境生命科学研究科 (50169447)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 応用数学 / 関数方程式 / 感染症 / 疫学

Outline of Final Research Achievements

We investigated the behaviour of solutions of mathematical models describing the reproduction of pathogen in vivo and describing the spread of infectious disease. Our main results concern construction of Lyapunov functions. Once a Lyapunov function is obtained, we can know the behaviour of the solution since the solution moves to the direction in which the value of the function decreases. Unfortunately, general methods of constructing a Lyapunov function are unknown, and applications of Lyapunov functions are restricted to some models. In our studies, we used a method to construct a Lyapunov function by using a known Lyapunov function for another model.

Free Research Field

応用解析学，生物数学