{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:59:49Z","timestamp":1768741189719,"version":"3.49.0"},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"3","funder":[{"DOI":"10.13039\/501100018818","name":"National Research, Development and Innovation Office","doi-asserted-by":"publisher","award":["BME-NC"],"award-info":[{"award-number":["BME-NC"]}],"id":[{"id":"10.13039\/501100018818","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015498","name":"Ministry for Innovation and Technology","doi-asserted-by":"publisher","award":["SNN125119"],"award-info":[{"award-number":["SNN125119"]}],"id":[{"id":"10.13039\/501100015498","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P1-0292"],"award-info":[{"award-number":["P1-0292"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["N1-0114"],"award-info":[{"award-number":["N1-0114"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["N1-0083"],"award-info":[{"award-number":["N1-0083"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["N1-0064"],"award-info":[{"award-number":["N1-0064"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["J1-8131"],"award-info":[{"award-number":["J1-8131"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this article, a space-dependent epidemic model equipped with a constant latency period is examined.\nWe construct a delay partial integro-differential equation and show that its solution possesses some biologically reasonable features.\nWe propose some numerical schemes and show that, by choosing the time step to be sufficiently small, the schemes preserve the qualitative properties of the original continuous model.\nFinally, some numerical experiments are presented that confirm the aforementioned theoretical results.<\/jats:p>","DOI":"10.1515\/cmam-2021-0208","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T21:36:35Z","timestamp":1653514595000},"page":"713-728","source":"Crossref","is-referenced-by-count":2,"title":["Qualitative Properties of Space-Dependent SIR Models with Constant Delay and Their Numerical Solutions"],"prefix":"10.1515","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7392-7099","authenticated-orcid":false,"given":"B\u00e1lint M.","family":"Tak\u00e1cs","sequence":"first","affiliation":[{"name":"Institute of Mathematics, E\u00f6tv\u00f6s Lor\u00e1nd University ; and Institute of Mathematics , Budapest University of Technology and Economics ; and MTA-ELTE NumNet Research Group, 1111 Budapest , Egry J\u00f3zsef u. 1 , Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4615-7615","authenticated-orcid":false,"given":"Istv\u00e1n","family":"Farag\u00f3","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, E\u00f6tv\u00f6s Lor\u00e1nd University ; and Department of Differential Equations , Budapest University of Technology and Economics; and MTA-ELTE NumNet Research Group, 1111 Budapest , Egry J\u00f3zsef u. 1 , Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2205-4299","authenticated-orcid":false,"given":"R\u00f3bert","family":"Horv\u00e1th","sequence":"additional","affiliation":[{"name":"Department of Analysis , Budapest University of Technology and Economics ; and MTA-ELTE NumNet Research Group, 1111 Budapest , Egry J\u00f3zsef u. 1 , Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6643-1271","authenticated-orcid":false,"given":"Du\u0161an","family":"Repov\u0161","sequence":"additional","affiliation":[{"name":"Faculty of Education , Faculty of Mathematics and Physics at University of Ljubljana ; and Institute of Mathematics, Physics and Mechanics, Jadranska ul. 19, 1000 Ljubljana , Slovenia"}]}],"member":"374","published-online":{"date-parts":[[2022,5,26]]},"reference":[{"key":"2023033112440937381_j_cmam-2021-0208_ref_001","doi-asserted-by":"crossref","unstructured":"A. Alsenafi and A. B. T. Barbaro,\nA convection-diffusion model for gang territoriality,\nPhys. A 510 (2018), 765\u2013786.","DOI":"10.1016\/j.physa.2018.07.004"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_002","doi-asserted-by":"crossref","unstructured":"M. S. Bartlett,\nMeasles periodicity and community size,\nJ. Roy. Stat. Soc. Ser. A 120 (1957), 48\u201370.","DOI":"10.2307\/2342553"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_003","doi-asserted-by":"crossref","unstructured":"R. Bellman,\nOn the computational solution of differential-difference equations,\nJ. Math. Anal. Appl. 2 (1961), 108\u2013110.","DOI":"10.1016\/0022-247X(61)90049-X"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_004","doi-asserted-by":"crossref","unstructured":"L. Bonnasse-Gahot, H. Berestycki, M-A. Depuiset, M. B. Gordon, J.-P. Nadal, S. Roch\u00e9 and N. Rodr\u00edguez,\nEpidemiological modeling of the 2005 French riots: A spreading wave and the role of contagion,\nSci. Rep. 8 (2018), Article ID 107.","DOI":"10.1038\/s41598-017-18093-4"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_005","doi-asserted-by":"crossref","unstructured":"J. C. Butcher,\nNumerical Methods for Ordinary Differential Equations, 3rd ed.,\nJohn Wiley & Sons, Chichester, 2016.","DOI":"10.1002\/9781119121534"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_006","doi-asserted-by":"crossref","unstructured":"V. Capasso,\nMathematical Structures of Epidemic Systems,\nLecture Notes in Biomath. 97,\nSpringer, Berlin, 1993.","DOI":"10.1007\/978-3-540-70514-7"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_007","doi-asserted-by":"crossref","unstructured":"K. L. Cooke,\nStability analysis for a vector disease model,\nRocky Mountain J. Math. 9 (1979), no. 1, 31\u201342.","DOI":"10.1216\/RMJ-1979-9-1-31"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_008","doi-asserted-by":"crossref","unstructured":"P. Csom\u00f3s and B. Tak\u00e1cs,\nOperator splitting for space-dependent epidemic model,\nAppl. Numer. Math. 159 (2021), 259\u2013280.","DOI":"10.1016\/j.apnum.2020.09.010"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_009","doi-asserted-by":"crossref","unstructured":"R. L. Dougherty, A. S. Edelman and J. M. Hyman,\nNonnegativity-, monotonicity-, or convexity-preserving cubic and quintic Hermite interpolation,\nMath. Comp. 52 (1989), no. 186, 471\u2013494.","DOI":"10.1090\/S0025-5718-1989-0962209-1"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_010","unstructured":"R. Ducasse,\nQualitative properties of spatial epidemiological models,\npreprint (2020), https:\/\/arxiv.org\/abs\/2005.06781."},{"key":"2023033112440937381_j_cmam-2021-0208_ref_011","unstructured":"L. E. \u00c9lgolts,\nQualitative Methods in Mathematical Analysis,\nAmerican Mathematical Society, Providence, 1964."},{"key":"2023033112440937381_j_cmam-2021-0208_ref_012","doi-asserted-by":"crossref","unstructured":"I. Farag\u00f3 and R. Horv\u00e1th,\nQualitative properties of some discrete models of disease propagation,\nJ. Comput. Appl. Math. 340 (2018), 486\u2013500.","DOI":"10.1016\/j.cam.2017.09.024"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_013","doi-asserted-by":"crossref","unstructured":"F. N. Fritsch and R. E. Carlson,\nMonotone piecewise cubic interpolation,\nSIAM J. Numer. Anal. 17 (1980), no. 2, 238\u2013246.","DOI":"10.1137\/0717021"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_014","doi-asserted-by":"crossref","unstructured":"S. Gottlieb, D. Ketcheson and C.-W. Shu,\nStrong Stability Preserving Runge\u2013Kutta and Multistep Time Discretizations,\nWorld Scientific, Hackensack, 2011.","DOI":"10.1142\/7498"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_015","unstructured":"D. G. Kendall,\nMathematical models of the spread of infection,\nMathematics and Computer Science in Biology and Medicine,\nHMSO, London (1965), 213\u2013225."},{"key":"2023033112440937381_j_cmam-2021-0208_ref_016","unstructured":"W. O. Kermack and A. G. McKendrick,\nA contribution to the mathematical theory of epidemics,\nProc. R. Soc. A Math. Phys. Eng. Sci. 115 (1927), no. 772, 235\u2013240."},{"key":"2023033112440937381_j_cmam-2021-0208_ref_017","doi-asserted-by":"crossref","unstructured":"J. Ma, V. Rokhlin and S. Wandzura,\nGeneralized Gaussian quadrature rules for systems of arbitrary functions,\nSIAM J. Numer. Anal. 33 (1996), no. 3, 971\u2013996.","DOI":"10.1137\/0733048"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_018","doi-asserted-by":"crossref","unstructured":"W. Ma, M. Song and Y. Takeuchi,\nGlobal stability of an SIR epidemic model with time delay,\nAppl. Math. Lett. 17 (2004), no. 10, 1141\u20131145.","DOI":"10.1016\/j.aml.2003.11.005"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_019","doi-asserted-by":"crossref","unstructured":"S. Rendine, A. Piazza and L. L. Cavalli-Sforza,\nSimulation and separation by principal components of multiple demic expansions in Europe,\nAmer. Natur. 128 (1986), no. 5, 681\u2013706.","DOI":"10.1086\/284597"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_020","doi-asserted-by":"crossref","unstructured":"C.-W. Shu,\nTotal-variation-diminishing time discretizations,\nSIAM J. Sci. Statist. Comput. 9 (1988), no. 6, 1073\u20131084.","DOI":"10.1137\/0909073"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_021","doi-asserted-by":"crossref","unstructured":"C.-W. Shu,\nEssentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws,\nAdvanced Numerical Approximation of Nonlinear Hyperbolic Equations (Cetraro 1997),\nLecture Notes in Math. 1697,\nSpringer, Berlin (1998), 325\u2013432.","DOI":"10.1007\/BFb0096355"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_022","doi-asserted-by":"crossref","unstructured":"C.-W. Shu and S. Osher,\nEfficient implementation of essentially nonoscillatory shock-capturing schemes,\nJ. Comput. Phys. 77 (1988), no. 2, 439\u2013471.","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_023","doi-asserted-by":"crossref","unstructured":"B. Tak\u00e1cs and Y. Hadjimichael,\nHigh order discretization methods for spatial-dependent epidemic models,\nMath. Comput. Simulation 198 (2022), 211\u2013236.","DOI":"10.1016\/j.matcom.2022.02.021"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_024","doi-asserted-by":"crossref","unstructured":"B. Tak\u00e1cs, R. Horv\u00e1th and I. Farag\u00f3,\nSpace dependent models for studying the spread of some diseases,\nComput. Math. Appl. 80 (2020), no. 2, 395\u2013404.","DOI":"10.1016\/j.camwa.2019.07.001"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_025","doi-asserted-by":"crossref","unstructured":"A. Volkening, D. F. Linder, M. A. Porter and G. A. Rempala,\nForecasting elections using compartmental models of infection,\nSIAM Rev. 62 (2020), no. 4, 837\u2013865.","DOI":"10.1137\/19M1306658"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_026","doi-asserted-by":"crossref","unstructured":"S.-L. Wu, C.-H. Hsu and Y. Xiao,\nGlobal attractivity, spreading speeds and traveling waves of delayed nonlocal reaction-diffusion systems,\nJ. Differential Equations 258 (2015), no. 4, 1058\u20131105.","DOI":"10.1016\/j.jde.2014.10.009"},{"key":"2023033112440937381_j_cmam-2021-0208_ref_027","doi-asserted-by":"crossref","unstructured":"R. Xu and Z. Ma,\nGlobal stability of a SIR epidemic model with nonlinear incidence rate and time delay,\nNonlinear Anal. Real World Appl. 10 (2009), no. 5, 3175\u20133189.","DOI":"10.1016\/j.nonrwa.2008.10.013"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0208\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0208\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T17:02:01Z","timestamp":1680282121000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0208\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,26]]},"references-count":27,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2022,3,26]]},"published-print":{"date-parts":[[2022,7,1]]}},"alternative-id":["10.1515\/cmam-2021-0208"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2021-0208","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,5,26]]}}}