Abstract
Nonlocal infection plays an important role in epidemic spread, which can reflect the real rules of infectious disease. To understand its mechanism on disease transmission, we construct an epidemic model with nonlocal delay and logistic growth. The Turing space for the emergence of stationary pattern is determined by series of inequations by mathematical analysis. Moreover, we use the multi-scale analysis to derive the amplitude equation, and obtain rich pattern structures by controlling the variation of the delay parameter. As the increase of delay parameter, the degree of pattern isolation increase as well as the density of the infected population decrease which prohibits the propagation of the disease in space. The results systematically reveal the impact of nonlocal delay on the spread of infectious diseases and provide some new theoretical supports for controlling the spread of infectious diseases.
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