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This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number R0 greater than 1, there exists a critical wave speed c* > 0, such that for each c >= c * the system admits a nontrivial TWS and for c < c* there exists no nontrivial TWS for the system. In addition, the boundary asymptotic behaviour of TWS is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Finally, we apply our results to two discrete diffusive epidemic models to verify the existence and nonexistence of TWS.
We analyse a periodically-forced SIR model to investigate the influence of seasonality on the disease dynamics and we show that the condition on the basic reproduction number $mathcal{R}_0<1$ is not enough to guarantee the elimination of the disease.
We consider an epidemic model with direct transmission given by a system of nonlinear partial differential equations and study the existence of traveling wave solutions. When the basic reproductive number of the considered model is less than one, we
In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its corresponding re
In this paper, we consider two types of traveling wave systems of the generalized Kundu-Mukherjee-Naskar equation. Firstly, due to the integrity, we obtain their energy functions. Then, the dynamical system method is applied to study bifurcation beha
This paper is concerned with the globally exponential stability of traveling wave fronts for a class of population dynamics model with quiescent stage and delay. First, we establish the comparison principle of solutions for the population dynamics mo