{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,4]],"date-time":"2023-07-04T14:40:31Z","timestamp":1688481631621},"reference-count":37,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,7,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The stochastic multi-group susceptible\u2013infected\u2013recovered (SIR) epidemic model is nonlinear, and so analytical solutions are generally difficult to obtain. Hence, it is often necessary to find numerical solutions, but most existing numerical methods fail to preserve the nonnegativity or positivity of solutions.\nTherefore, an appropriate numerical method for studying the dynamic behavior of epidemic diseases through SIR models is urgently required.\nIn this paper, based on the Euler\u2013Maruyama scheme and a logarithmic transformation, we propose a novel explicit positivity-preserving numerical scheme for a stochastic multi-group SIR epidemic model whose coefficients violate the global monotonicity condition.\nThis scheme not only results in numerical solutions that preserve the domain of the stochastic multi-group SIR epidemic model, but also achieves the \u201c<jats:inline-formula id=\"j_cmam-2022-0143_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>order<\/m:mi>\n                              <m:mo>-<\/m:mo>\n                              <m:mfrac>\n                                 <m:mn>1<\/m:mn>\n                                 <m:mn>2<\/m:mn>\n                              <\/m:mfrac>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2022-0143_eq_0507.png\" \/>\n                        <jats:tex-math>{\\mathrm{order}-\\frac{1}{2}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>\u201d strong convergence rate.\nTaking a two-group SIR epidemic model as an example,\nsome numerical simulations are performed to illustrate the performance of the proposed scheme.<\/jats:p>","DOI":"10.1515\/cmam-2022-0143","type":"journal-article","created":{"date-parts":[[2022,12,6]],"date-time":"2022-12-06T23:44:36Z","timestamp":1670370276000},"page":"671-694","source":"Crossref","is-referenced-by-count":0,"title":["Positivity-Preserving Numerical Method for a Stochastic Multi-Group SIR Epidemic Model"],"prefix":"10.1515","volume":"23","author":[{"given":"Han","family":"Ma","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics , Ningxia University , Yinchuan , 750021 , P. R. China"}]},{"given":"Qimin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Ningxia University , Yinchuan , 750021 , P. R. China"}]},{"given":"Xinzhong","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics , Ningxia University , Yinchuan , 750021 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2022,12,7]]},"reference":[{"key":"2023070413382818502_j_cmam-2022-0143_ref_001","doi-asserted-by":"crossref","unstructured":"F. T.  Akyildiz and F. S.  Alshammari,\nComplex mathematical SIR model for spreading of COVID-19 virus with Mittag\u2013Leffler kernel,\nAdv. Difference Equ. 2021 (2021), Paper No. 319.","DOI":"10.1186\/s13662-021-03470-1"},{"key":"2023070413382818502_j_cmam-2022-0143_ref_002","doi-asserted-by":"crossref","unstructured":"N.  Al-Salti, F.  Al-Musalhi, I.  Elmojtaba and V.  Gandhi,\nSIR model with time-varying contact rate,\nInt. J. 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A 526 (2019), Paper No. 120975.","DOI":"10.1016\/j.physa.2019.04.211"},{"key":"2023070413382818502_j_cmam-2022-0143_ref_022","doi-asserted-by":"crossref","unstructured":"Y.  Luo, S.  Tang, Z.  Teng and L.  Zhang,\nGlobal dynamics in a reaction-diffusion multi-group SIR epidemic model with nonlinear incidence,\nNonlinear Anal. Real World Appl. 50 (2019), 365\u2013385.","DOI":"10.1016\/j.nonrwa.2019.05.008"},{"key":"2023070413382818502_j_cmam-2022-0143_ref_023","doi-asserted-by":"crossref","unstructured":"Y.  Luo, L.  Zhang, Z.  Teng and T.  Zheng,\nAnalysis of a general multi-group reaction-diffusion epidemic model with nonlinear incidence and temporary acquired immunity,\nMath. Comput. Simulation 182 (2021), 428\u2013455.","DOI":"10.1016\/j.matcom.2020.11.002"},{"key":"2023070413382818502_j_cmam-2022-0143_ref_024","doi-asserted-by":"crossref","unstructured":"P.  Magal, O.  Seydi and G.  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