Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions

References

[1] A. Alsenafi and A. B. T. Barbaro, A convection-diffusion model for gang territoriality, Phys. A 510 (2018), 765–786. 10.1016/j.physa.2018.07.004Search in Google Scholar

[2] M. S. Bartlett, Measles periodicity and community size, J. Roy. Stat. Soc. Ser. A 120 (1957), 48–70. 10.2307/2342553Search in Google Scholar

[3] R. Bellman, On the computational solution of differential-difference equations, J. Math. Anal. Appl. 2 (1961), 108–110. 10.1016/0022-247X(61)90049-XSearch in Google Scholar

[4] L. Bonnasse-Gahot, H. Berestycki, M-A. Depuiset, M. B. Gordon, J.-P. Nadal, S. Roché and N. Rodríguez, Epidemiological modeling of the 2005 French riots: A spreading wave and the role of contagion, Sci. Rep. 8 (2018), Article ID 107. 10.1038/s41598-017-18093-4Search in Google Scholar

[5] J. C. Butcher, Numerical Methods for Ordinary Differential Equations, 3rd ed., John Wiley & Sons, Chichester, 2016. 10.1002/9781119121534Search in Google Scholar

[6] V. Capasso, Mathematical Structures of Epidemic Systems, Lecture Notes in Biomath. 97, Springer, Berlin, 1993. 10.1007/978-3-540-70514-7Search in Google Scholar

[7] K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain J. Math. 9 (1979), no. 1, 31–42. 10.1216/RMJ-1979-9-1-31Search in Google Scholar

[8] P. Csomós and B. Takács, Operator splitting for space-dependent epidemic model, Appl. Numer. Math. 159 (2021), 259–280. 10.1016/j.apnum.2020.09.010Search in Google Scholar

[9] R. L. Dougherty, A. S. Edelman and J. M. Hyman, Nonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation, Math. Comp. 52 (1989), no. 186, 471–494. 10.1090/S0025-5718-1989-0962209-1Search in Google Scholar

[10] R. Ducasse, Qualitative properties of spatial epidemiological models, preprint (2020), https://arxiv.org/abs/2005.06781. Search in Google Scholar

[11] L. E. Élgolts, Qualitative Methods in Mathematical Analysis, American Mathematical Society, Providence, 1964. Search in Google Scholar

[12] I. Faragó and R. Horváth, Qualitative properties of some discrete models of disease propagation, J. Comput. Appl. Math. 340 (2018), 486–500. 10.1016/j.cam.2017.09.024Search in Google Scholar

[13] F. N. Fritsch and R. E. Carlson, Monotone piecewise cubic interpolation, SIAM J. Numer. Anal. 17 (1980), no. 2, 238–246. 10.1137/0717021Search in Google Scholar

[14] S. Gottlieb, D. Ketcheson and C.-W. Shu, Strong Stability Preserving Runge–Kutta and Multistep Time Discretizations, World Scientific, Hackensack, 2011. 10.1142/7498Search in Google Scholar

[15] D. G. Kendall, Mathematical models of the spread of infection, Mathematics and Computer Science in Biology and Medicine, HMSO, London (1965), 213–225. Search in Google Scholar

[16] W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. A Math. Phys. Eng. Sci. 115 (1927), no. 772, 235–240. Search in Google Scholar

[17] J. Ma, V. Rokhlin and S. Wandzura, Generalized Gaussian quadrature rules for systems of arbitrary functions, SIAM J. Numer. Anal. 33 (1996), no. 3, 971–996. 10.21236/ADA273610Search in Google Scholar

[18] W. Ma, M. Song and Y. Takeuchi, Global stability of an SIR epidemic model with time delay, Appl. Math. Lett. 17 (2004), no. 10, 1141–1145. 10.1016/j.aml.2003.11.005Search in Google Scholar

[19] S. Rendine, A. Piazza and L. L. Cavalli-Sforza, Simulation and separation by principal components of multiple demic expansions in Europe, Amer. Natur. 128 (1986), no. 5, 681–706. 10.1086/284597Search in Google Scholar

[20] C.-W. Shu, Total-variation-diminishing time discretizations, SIAM J. Sci. Statist. Comput. 9 (1988), no. 6, 1073–1084. 10.1137/0909073Search in Google Scholar

[21] C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (Cetraro 1997), Lecture Notes in Math. 1697, Springer, Berlin (1998), 325–432. 10.1007/BFb0096355Search in Google Scholar

[22] C.-W. Shu and S. Osher, Efficient implementation of essentially nonoscillatory shock-capturing schemes, J. Comput. Phys. 77 (1988), no. 2, 439–471. 10.1016/0021-9991(88)90177-5Search in Google Scholar

[23] B. Takács and Y. Hadjimichael, High order discretization methods for spatial-dependent epidemic models, Math. Comput. Simulation 198 (2022), 211–236. 10.1016/j.matcom.2022.02.021Search in Google Scholar

[24] B. Takács, R. Horváth and I. Faragó, Space dependent models for studying the spread of some diseases, Comput. Math. Appl. 80 (2020), no. 2, 395–404. 10.1016/j.camwa.2019.07.001Search in Google Scholar

[25] A. Volkening, D. F. Linder, M. A. Porter and G. A. Rempala, Forecasting elections using compartmental models of infection, SIAM Rev. 62 (2020), no. 4, 837–865. 10.1137/19M1306658Search in Google Scholar

[26] S.-L. Wu, C.-H. Hsu and Y. Xiao, Global attractivity, spreading speeds and traveling waves of delayed nonlocal reaction-diffusion systems, J. Differential Equations 258 (2015), no. 4, 1058–1105. 10.1016/j.jde.2014.10.009Search in Google Scholar

[27] R. Xu and Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. Real World Appl. 10 (2009), no. 5, 3175–3189. 10.1016/j.nonrwa.2008.10.013Search in Google Scholar