부산대학교 도서관

Summary: ``This paper is concerned with nonlocal and local diffusiveSIR epidemic model with free boundaries including convolution, which isnatural extension of reaction diffusion systems with free boundaryproblems and local diffusions. The existence of unique global solutionfor this model is considered. Dichotomy of the spreading and vanishingis established. A spreading barrier line is found to determine whetherthe spreading of disease will fail finally. The spreading of diseasewill fail when it cannot spread across the spreading barrier line$l^*$, while it will be successful when it transcends over this barrierline. The results show that if the basic reproduction number $\Cal R_0<1$, the spreading of disease will fail eventually, and if $\CalR_0>1+\frac{d_2}{\mu_2+\alpha}$, the spreading of disease will getsuccess finally. We also find that the spreading coefficients playimportant role in the spreading achievement. When$1+\frac\beta{\theta\mu_1}<\Cal R_0<1+\frac{d_2}{\mu_2+\alpha}$, thespreading coefficient decides whether the spreading of disease will besuccessful. It is shown that the spreading will be successful when thespreading coefficient is relatively big, while the spreading will failif the spreading coefficient is relatively small.''