## 数理人口学・数理生物学セミナー

### 2014年08月06日(水)

14:50-16:20   数理科学研究科棟(駒場) 128号室
Nicolas Bacaer 氏 (Insitut de Recherche pour le Developpement (IRD))
The stochastic SIS epidemic model in a periodic environment (ENGLISH)
[ 講演概要 ]
In the stochastic SIS epidemic model with a contact rate a,
a recovery rate bT is such that (log T)/N converges to c=b/a-1-log(b/a) as N grows to
infinity. We consider the more realistic case where the contact rate
a(t) is a periodic function whose average is bigger than b. Then (log
T)/N converges to a new limit C, which is linked to a time-periodic
Hamilton-Jacobi equation. When a(t) is a cosine function with small
amplitude or high (resp. low) frequency, approximate formulas for C
can be obtained analytically following the method used in [Assaf et
al. (2008) Population extinction in a time-modulated environment. Phys
Rev E 78, 041123]. These results are illustrated by numerical
simulations.