Abstract
Abstract The dynamical behaviors of a new multi-cluster S ( 1 ) S ( 2 ) I R (Susceptible 1 - Susceptible 2 - Infected - Recovery) reaction-diffusion rumor propagation model are investigated in this paper. According to the next generation matrix method, we work out the basic reproduction number. Then applying the theory of upper and lower solutions, we have explored the unique existence and boundedness of the nonnegative solution. By using the Lyapunov-LaSalle principle and the graph-theoretic approach, the global dynamics can be obtained for both the rumor-free equilibrium point and the rumor-prevailing equilibrium point. Finally, several numerical simulations are given to illustrate the theoretical results.
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