Abstract
Epidemic models governed by reaction–diffusion equations with cross-diffusion can exhibit diversified pattern formations and can characterize important features of some diseases. Considering that populations are usually organized as networks instead of being continuously distributed in space, it is essential to study reaction–diffusion epidemic model with cross-diffusion on networks. Here we investigate Turing instability induced by cross-diffusion for a network organized SI epidemic model and explore Turing patterns on several different networks. Turing instability condition is obtained via linear analysis method and the condition is applied to study pattern formations for the model in question. With the help of numerical simulations, we investigate the influences of network topology and initial infection distribution on pattern formations and disease spreading from the aspects of arrival time of the first peak and steady density of the infected.
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