Long-time numerical properties analysis of a diffusive SIS epidemic model under a linear external source

References

• L.J.S. Allen, B.M. Bolker, Y. Lou, and A.L. Nevai, Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model, Discrete Contin. Dyn. Syst. 21(1) (2008), pp. 1–20.
   Web of Science ®Google Scholar
• G. Akrivis, M. Crouzeix, and C. Makridakis, Implicit–explicit multistep finite element methods for nonlinear parabolic problems, Math. Comp. 67(222) (1998), pp. 457–477.
   Web of Science ®Google Scholar
• U.M. Ascher, S.J. Ruuth, and B.T.R. Wetton, Implicit-explicit methods for time-dependent partial differential equations, SIAM J. Numer. Anal. 32(3) (1995), pp. 797–823.
   Web of Science ®Google Scholar
• F. Brauer and C.C. Chavez, Mathematical Models in Population Biology and Epidemiology, Springer, New York, 2001.
   Google Scholar
• R. Bürger, E. Gavilán, D. Inzunza, P. Mulet, and L.M. Villada, Implicit-explicit methods for a convection-diffusion-reaction model of the propagation of forest fires, Mathematics 8(6) (2020), pp. 1034.
   Web of Science ®Google Scholar
• Y.L. Cai and W.M. Wang, Dynamics of a parasite-host epidemiological model in spatial heterogeneous environment, Discrete Contin. Dyn. Syst. Ser. B 20(4) (2015), pp. 989–1013.
   Web of Science ®Google Scholar
• W. Chen, Implicit–explicit multistep finite element methods for nonlinear convection–diffusion problems, Numer. Math. Partial Differ. Equ. 17 (2001), pp. 93–104.
   Web of Science ®Google Scholar
• R.H. Cui and Y. Lou, A spatial SIS model in advective heterogeneous environments, J. Differ. Equ.261(6) (2016), pp. 3305–3343.
   Web of Science ®Google Scholar
• K. Deng and Y. Wu, Dynamics of a susceptible-infected-susceptible epidemic reaction-diffusion model, Proc. R. Soc. Edinb. 146(5) (2016), pp. 929–946.
   Google Scholar
• L. Galeone and L. Lopez, Decay to spatially homogeneous states for the numerical solution of reaction-diffusion systems, Calcolo. 19(2) (1982), pp. 193–208.
   Google Scholar
• L. Galeone, The use of positive matrices for the analysis of the large time behavior of the numerical solution of reaction-diffusion systems, Math. Comput. 41(164) (1983), pp. 461–472.
   Web of Science ®Google Scholar
• J. Ge, K.I. Kim, Z.G. Lin, and H.P. Zhu, A SIS reaction-diffusion-advection model in a low-risk and high-risk domain, J. Differ. Equ. 259(10) (2015), pp. 5486–5509.
   Web of Science ®Google Scholar
• D. Hoff, Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations, SIAM J. Numer. Anal. 15(6) (1978), pp. 1161–1177.
   Web of Science ®Google Scholar
• T. Koto, IMEX Runge–Kutta schemes for reaction–diffusion equations, J. Comput. Appl. Math. 215(1) (2008), pp. 182–195.
   Web of Science ®Google Scholar
• H. Li, R. Peng, and F.B. Wang, Varying total population enhances disease persistence: Qualitative analysis on a diffusive SIS epidemic model, J. Differ. Equ. 262(2) (2017), pp. 885–913.
   Web of Science ®Google Scholar
• H. Li, R. Peng, and Z.A. Wang, On a diffusive susceptible-infected-susceptible epidemic model with mass action mechanism and birth-death effect: analysis, simulations, and comparison with other mechanisms, SIAM J. Appl. Math. 78(4) (2018), pp. 2129–2153.
   Web of Science ®Google Scholar
• X. Liu and Z.W. Yang, Numerical analysis of a reaction–diffusion susceptible–infected–susceptible epidemic model, Comput. Appl. Math. 41(8) (2022), pp. 392.
   Google Scholar
• L. Luciano, Stability and asymptotic behaviour for the numerical solution of a reaction-diffusion model for a deterministic diffusive epidemic, IMA J. Numer. Anal. 3(3) (1983), pp. 341–351.
   Web of Science ®Google Scholar
• R. Peng and S. Liu, Global stability of the steady states of an SIS epidemic reaction-diffusion model, Nonlinear Anal. 71(1-2) (2009), pp. 239–247.
   Web of Science ®Google Scholar
• R. Peng and X.Q. Zhao, A reaction-diffusion SIS epidemic model in a time-periodic environment, Nonlinearity 25(5) (2012), pp. 1451–1471.
   Web of Science ®Google Scholar
• N. Tuncer and M. Martcheva, Analytical and numerical approaches to coexistence of strains in a two-strain SIS model with diffusion, J. Biol. Dynam. 6(2) (2012), pp. 406–439.
   PubMed Web of Science ®Google Scholar
• Y.X. Wu and X.F. Zou, Asymptotic profiles of steady states for a diffusive SIS epidemic model with mass action infection mechanism, J. Differ. Equ. 261(8) (2016), pp. 4424–4447.
   Web of Science ®Google Scholar
• J.M. Varah, A lower bound for the smallest singular value of a matrix, Linear Alg. Appl. 11(1) (1975), pp. 3–5.
   Web of Science ®Google Scholar
• C. Yang and J. Wang, Basic reproduction numbers for a class of reaction-diffusion epidemic models, Bull. Math. Biol. 82(8) (2020), pp. 1–25.
   Web of Science ®Google Scholar
• Z. Kai, C.F. Wong, and Z. Ran, Second-order implicit–explicit scheme for the Gray–Scott model, J. Comput. Appl. Math. 213(2) (2008), pp. 559–581.
   Web of Science ®Google Scholar
• C.H. Zhang, G.Z. Chen, Z.W. Fang, X.L. Lin, and H.W. Sun, An unconditionally positivity-preserving implicit-explicit scheme for evolutionary stable distribution model, J. Comput. Appl. Math. 403 (2022), pp. 113883.
   Google Scholar