On the asymptotic behaviour of traveling wave solution for a discrete diffusive epidemic model
Ran Zhang, Shengqiang Liu
Abstract
A recent paper [Y.-Y. Chen, J.-S. Guo, F. Hamel, Traveling waves for a lattice dynamical system arising in a diffusive endemic model, Nonlinearity, 30 (2017), 2334-2359] presented a discrete diffusive Kermack-McKendrick epidemic model, and the authors proved the existence of traveling wave solutions connecting the disease-free equilibrium to the endemic equilibrium. However, the boundary asymptotic behavior of the traveling waves converge to the endemic equilibrium at $ +\infty $ is still an open problem. In this paper, we investigate the above open problem and completely solve it by constructing suitable Lyapunov functional and employing Lebesgue dominated convergence theorem.
Topics & Concepts
Traveling waveEpidemic modelMathematicsConvergence (economics)Boundary (topology)Mathematical analysisNonlinear systemApplied mathematicsLattice (music)Lyapunov functionChenBoundary value problemMathematical physicsMathematical economicsPhysicsEconomicsGeologyQuantum mechanicsPopulationSociologyDemographyEconomic growthAcousticsPaleontologyMathematical and Theoretical Epidemiology and Ecology ModelsStochastic processes and statistical mechanicsFractional Differential Equations Solutions