Spatiotemporal Dynamics in a Diffusive Bacterial and Viral Diseases Propagation Model with Chemotaxis

Abstract

In this article, we study the effect of chemotaxis on the dynamics of a diffusive bacterial and viral diseases propagation model. From three aspects: $$\chi >0$$ , $$\chi =0$$ and $$\chi <0$$ , we investigate the existence of Turing bifurcations and stability of positive equilibrium under Neumann boundary conditions. We find that Turing bifurcations can induced by chemotaxis, which does not occur in the original model. Moreover, for the model with diffusion and chemotaxis, we need explore the new expression of the normal form on Turing bifurcation. By the newly obtained normal form, we can determine the properties of Turing bifurcation. Finally, we perform some numerical simulations to verify the theoretical analysis and obtain stable steady state solutions, spots pattern and spots-strip pattern, which also expand the main results in this article.