People
Toshikazu Kuniya
| tkuniya(@math.sci.osaka-u.ac.jp) | |
| Research |
Mathematical biology |
| Keywords | Epidemic model, nonlinear analysis, differential equations, dynamical systems |
| URL |
Mathematical biology is a research discipline that studies biological problems by using mathematics. I'm especially interested in mathematical models (differential equations) of infectious disease dynamics. Time evolution of solutions in such models represents the time variation of infected and/or immune populations, and is utilized to prediction and evaluation of disease dynamics. As equilibria of such models, there are two equilibria called the disease-free equilibrium in which no infected individual exists, and the endemic equilibrium in which infected individuals constantly exist. We can discuss the long-term behavior of epidemics by investigating the stability of these equilibria. The basic reproduction number Ro, which implies the expected value of secondary cases produced by an infected individual in a fully non-immune population, is one of the important concepts in this field. Ro represents the intensity of epidemic spreading, and it enables us to intuitively judge that the disease will spread if Ro > 1, and not if Ro < 1. However, such threshold property of Ro is not obvious in realistic and complex models such as models with age-structure and spatial-structure. My main research interests include to formulate and prove the threshold property of Ro in various models, and to apply the mathematical results to epidemiological consideration.