Abstract
In this paper, a stochastic diffusive infectious model in the population consisting of the susceptible and the infective is proposed. We consider the proliferation with the strong Allee effect, which means that there exists the optimal population density maximizes the per capita proliferation rate and it becomes negative at the low population density. By numerical simulations, we show that spatio-temporal patterns of the epidemic spreading process become the fractal structure like the Sierpinski gasket in some restricted parameter range and the patterns under the noise are very different from ones in the no noise case in the other restricted parameter range.
