Super-critical and critical traveling waves in a two-component lattice dynamical model with discrete delay

Abstract A delayed lattice dynamical system arising in a disease model is proposed to model the transmission of communicable disease. The existence of nontrivial, positive, bounded super-critical and critical traveling waves for this system are established, respectively. Meanwhile, the non-existence of such traveling waves for the system is obtained. Moreover, the effects of diffusive rate of infective individuals and time-delay on critical speed are discussed, accordingly.

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