{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T18:44:36Z","timestamp":1791225876671,"version":"4.1.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T00:00:00Z","timestamp":1729036800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T00:00:00Z","timestamp":1729036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"DOI":"10.1038\/s41598-024-66843-y","type":"journal-article","created":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T05:02:32Z","timestamp":1729054952000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Investigating the impact of stochasticity on HIV infection dynamics in CD4$$^{+}$$ T cells using a reaction-diffusion model"],"prefix":"10.1038","volume":"14","author":[{"given":"Nauman","family":"Ahmed","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad W.","family":"Yasin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Syed Mansoor","family":"Ali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Akg\u00fcl","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ali","family":"Raza","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Rafiq","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shah","family":"Muhammad","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mubasher","family":"Ali","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,10,16]]},"reference":[{"key":"66843_CR1","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/4217548","author":"OM Ogunlaran","year":"2016","unstructured":"Ogunlaran, O. M. & Oukouomi Noutchie, S. C. Mathematical model for an effective management of HIV infection. BioMed Res. Int.https:\/\/doi.org\/10.1155\/2016\/4217548 (2016).","journal-title":"BioMed Res. Int."},{"issue":"Suppl 3","key":"66843_CR2","doi-asserted-by":"publisher","first-page":"iii49","DOI":"10.1136\/sextrans-2012-050844","volume":"89","author":"GR Mumtaz","year":"2013","unstructured":"Mumtaz, G. R. et al. The distribution of new HIV infections by mode of exposure in Morocco. Sex. Transm. Infect. 89(Suppl 3), iii49\u2013iii56 (2013).","journal-title":"Sex. Transm. Infect."},{"issue":"7","key":"66843_CR3","doi-asserted-by":"publisher","DOI":"10.1371\/journal.pmed.1001239","volume":"9","author":"W Delva","year":"2012","unstructured":"Delva, W. et al. HIV treatment as prevention: Principles of good HIV epidemiology modelling for public health decision-making in all modes of prevention and evaluation. PLoS Med. 9(7), e1001239 (2012).","journal-title":"PLoS Med."},{"issue":"suppl 1","key":"66843_CR4","doi-asserted-by":"publisher","first-page":"i19","DOI":"10.1136\/sti.2004.010165","volume":"80","author":"T Brown","year":"2004","unstructured":"Brown, T. & Peerapatanapokin, W. The Asian Epidemic Model: A process model for exploring HIV policy and programme alternatives in Asia. Sex. Transm. Infect. 80(suppl 1), i19\u2013i24 (2004).","journal-title":"Sex. Transm. Infect."},{"issue":"12","key":"66843_CR5","doi-asserted-by":"publisher","first-page":"1805","DOI":"10.1097\/QAD.0000000000000323","volume":"28","author":"S Qian","year":"2014","unstructured":"Qian, S. et al. Diversity of HIV\/AIDS epidemic in China: A result from hierarchical clustering analysis and spatial autocorrelation analysis. Aids 28(12), 1805\u20131813 (2014).","journal-title":"Aids"},{"key":"66843_CR6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2020.109706","volume":"134","author":"Z Iqbal","year":"2020","unstructured":"Iqbal, Z. et al. Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV\/AIDS transmission. Chaos Solitons Fractals 134, 109706 (2020).","journal-title":"Chaos Solitons Fractals"},{"issue":"6","key":"66843_CR7","doi-asserted-by":"publisher","first-page":"305","DOI":"10.1049\/iet-syb.2019.0051","volume":"13","author":"A Raza","year":"2019","unstructured":"Raza, A. et al. Competitive numerical analysis for stochastic HIV\/AIDS epidemic model in a two-sex population. IET Syst. Biol. 13(6), 305\u2013315 (2019).","journal-title":"IET Syst. Biol."},{"issue":"13\u201314","key":"66843_CR8","doi-asserted-by":"publisher","first-page":"6550","DOI":"10.1016\/j.apm.2016.01.054","volume":"40","author":"HF Huo","year":"2016","unstructured":"Huo, H. F., Chen, R. & Wang, X. Y. Modelling and stability of HIV\/AIDS epidemic model with treatment. Appl. Math. Model. 40(13\u201314), 6550\u20136559 (2016).","journal-title":"Appl. Math. Model."},{"issue":"12","key":"66843_CR9","doi-asserted-by":"publisher","first-page":"852","DOI":"10.1038\/nrmicro2911","volume":"10","author":"T Hatziioannou","year":"2012","unstructured":"Hatziioannou, T. & Evans, D. T. Animal models for HIV\/AIDS research. Nat. Rev. Microbiol. 10(12), 852\u2013867 (2012).","journal-title":"Nat. Rev. Microbiol."},{"key":"66843_CR10","doi-asserted-by":"publisher","first-page":"180","DOI":"10.1016\/j.matcom.2019.03.016","volume":"164","author":"CJ Silva","year":"2019","unstructured":"Silva, C. J. & Torres, D. F. Stability of a fractional HIV\/AIDS model. Math. Comput. Simul. 164, 180\u2013190 (2019).","journal-title":"Math. Comput. Simul."},{"key":"66843_CR11","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.chaos.2019.03.022","volume":"122","author":"A Khan","year":"2019","unstructured":"Khan, A., G\u00f3mez-Aguilar, J. F., Khan, T. S. & Khan, H. Stability analysis and numerical solutions of fractional order HIV\/AIDS model. Chaos Solitons Fractals 122, 119\u2013128 (2019).","journal-title":"Chaos Solitons Fractals"},{"issue":"1","key":"66843_CR12","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1016\/j.cam.2008.10.067","volume":"229","author":"L Cai","year":"2009","unstructured":"Cai, L., Li, X., Ghosh, M. & Guo, B. Stability analysis of an HIV\/AIDS epidemic model with treatment. J. Comput. Appl. Math. 229(1), 313\u2013323 (2009).","journal-title":"J. Comput. Appl. Math."},{"issue":"10","key":"66843_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/s13360-020-00856-0","volume":"135","author":"H El-Metwally","year":"2020","unstructured":"El-Metwally, H., Sohaly, M. A. & Elbaz, I. M. Stochastic global exponential stability of disease-free equilibrium of HIV\/AIDS model. Eur. Phys. J. Plus 135(10), 1\u201314 (2020).","journal-title":"Eur. Phys. J. Plus"},{"issue":"11\u201312","key":"66843_CR14","first-page":"821","volume":"82","author":"C Roth","year":"2002","unstructured":"Roth, C. Difference methods for stochastic partial differential equations. ZAMM J. Appl. Math. Mech.\/Z. Angew. Math. Mech. Appl. Math. Mech. 82(11\u201312), 821\u2013830 (2002).","journal-title":"ZAMM J. Appl. Math. Mech.\/Z. Angew. Math. Mech. Appl. Math. Mech."},{"issue":"1","key":"66843_CR15","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1080\/07362990500397764","volume":"24","author":"C Roth","year":"2006","unstructured":"Roth, C. A combination of finite difference and Wong\u2013Zakai methods for hyperbolic stochastic partial differential equations. Stoch. Anal. Appl. 24(1), 221\u2013240 (2006).","journal-title":"Stoch. Anal. Appl."},{"issue":"5","key":"66843_CR16","doi-asserted-by":"publisher","first-page":"1426","DOI":"10.1016\/j.cam.2010.02.018","volume":"234","author":"M Kamrani","year":"2010","unstructured":"Kamrani, M. & Hosseini, S. M. The role of coefficients of a general SPDE on the stability and convergence of a finite difference method. J. Comput. Appl. Math. 234(5), 1426\u20131434 (2010).","journal-title":"J. Comput. Appl. Math."},{"key":"66843_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2021.105023","volume":"32","author":"MW Yasin","year":"2022","unstructured":"Yasin, M. W. et al. Numerical scheme and stability analysis of stochastic Fitzhugh\u2013Nagumo model. Results Phys. 32, 105023 (2022).","journal-title":"Results Phys."},{"issue":"1","key":"66843_CR18","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/aca847","volume":"98","author":"MW Yasin","year":"2022","unstructured":"Yasin, M. W. et al. Reliable numerical analysis for stochastic reaction-diffusion system. Phys. Scr. 98(1), 015209 (2022).","journal-title":"Phys. Scr."},{"issue":"1","key":"66843_CR19","doi-asserted-by":"publisher","first-page":"1990","DOI":"10.1038\/s41598-023-28324-6","volume":"13","author":"MW Yasin","year":"2023","unstructured":"Yasin, M. W. et al. Spatio-temporal numerical modeling of stochastic predator\u2013prey model. Sci. Rep. 13(1), 1990 (2023).","journal-title":"Sci. Rep."},{"issue":"230","key":"66843_CR20","doi-asserted-by":"publisher","first-page":"653","DOI":"10.1090\/S0025-5718-99-01150-3","volume":"69","author":"H Yoo","year":"2000","unstructured":"Yoo, H. Semi-discretization of stochastic partial differential equations on $$R^1$$ by a finite-difference method. Math. Comput. 69(230), 653\u2013666 (2000).","journal-title":"Math. Comput."},{"issue":"1\u20132","key":"66843_CR21","first-page":"117","volume":"64","author":"EJ Allen","year":"1998","unstructured":"Allen, E. J., Novosel, S. J. & Zhang, Z. Finite element and difference approximation of some linear stochastic partial differential equations. Stochastics 64(1\u20132), 117\u2013142 (1998).","journal-title":"Stochastics"},{"key":"66843_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2021.103289","volume":"60","author":"P Wu","year":"2021","unstructured":"Wu, P. & Zhao, H. Mathematical analysis of an age-structured HIV\/AIDS epidemic model with HAART and spatial diffusion. Nonlinear Anal. Real World Appl. 60, 103289 (2021).","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"66843_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2022.114309","volume":"412","author":"P Wu","year":"2022","unstructured":"Wu, P., Feng, Z. & Zhang, X. Global dynamics of an age-space structured HIV\/AIDS model with viral load-dependent infection and conversion rates. J. Comput. Appl. Math. 412, 114309 (2022).","journal-title":"J. Comput. Appl. Math."},{"key":"66843_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.matcom.2023.06.018","volume":"214","author":"P Wu","year":"2023","unstructured":"Wu, P., Zhang, R. & Din, A. Mathematical analysis of an age-since infection and diffusion HIV\/AIDS model with treatment adherence and Dirichlet boundary condition. Math. Comput. Simul. 214, 1\u201327 (2023).","journal-title":"Math. Comput. Simul."},{"issue":"5","key":"66843_CR25","doi-asserted-by":"publisher","first-page":"1680","DOI":"10.1137\/22M1485814","volume":"82","author":"H Wang","year":"2022","unstructured":"Wang, H., Wang, K. & Kim, Y. J. Spatial segregation in reaction-diffusion epidemic models. SIAM J. Appl. Math. 82(5), 1680\u20131709 (2022).","journal-title":"SIAM J. Appl. Math."},{"issue":"03","key":"66843_CR26","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1142\/S0218339020500126","volume":"28","author":"WE Fitzgibbon","year":"2020","unstructured":"Fitzgibbon, W. E., Morgan, J. J., Webb, G. F. & Wu, Y. Analysis of a reaction-diffusion epidemic model with asymptomatic transmission. J. Biol. Syst. 28(03), 561\u2013587 (2020).","journal-title":"J. Biol. Syst."},{"key":"66843_CR27","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s11071-021-06998-9","volume":"109","author":"Y Li","year":"2022","unstructured":"Li, Y. & Wei, Z. Dynamics and optimal control of a stochastic coronavirus (COVID-19) epidemic model with diffusion. Nonlinear Dyn. 109, 91\u2013120 (2022).","journal-title":"Nonlinear Dyn."},{"issue":"8","key":"66843_CR28","doi-asserted-by":"publisher","DOI":"10.1063\/5.0010541","volume":"30","author":"N Ahmed","year":"2020","unstructured":"Ahmed, N., Elsonbaty, A., Adel, W., Baleanu, D. & Rafiq, M. Stability analysis and numerical simulations of spatiotemporal HIV CD4+ T cell model with drug therapy. Chaos 30(8), 083122 (2020).","journal-title":"Chaos"},{"issue":"4","key":"66843_CR29","doi-asserted-by":"publisher","first-page":"2189","DOI":"10.1016\/j.apm.2012.05.002","volume":"37","author":"AAM Arafa","year":"2013","unstructured":"Arafa, A. A. M., Rida, S. Z. & Khalil, M. The effect of anti-viral drug treatment of human immunodeficiency virus type 1 (HIV-1) described by a fractional order model. Appl. Math. Model. 37(4), 2189\u20132196 (2013).","journal-title":"Appl. Math. Model."},{"issue":"3","key":"66843_CR30","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.biosystems.2003.11.004","volume":"73","author":"HC Tuckwell","year":"2004","unstructured":"Tuckwell, H. C. & Wan, F. Y. On the behavior of solutions in viral dynamical models. BioSystems 73(3), 157\u2013161 (2004).","journal-title":"BioSystems"},{"key":"66843_CR31","unstructured":"Roth, C. Approximations of solutions of a first order stochastic partial differential equation. Report, Institut Optimierung und Stochastik, Universit\u00e4t Halle-Wittenberg Halle (1989)."},{"key":"66843_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2022.106175","volume":"44","author":"MZ Baber","year":"2023","unstructured":"Baber, M. Z. et al. Comparative analysis of numerical with optical soliton solutions of stochastic Gross\u2013Pitaevskii equation in dispersive media. Results Phys. 44, 106175 (2023).","journal-title":"Results Phys."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66843-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66843-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66843-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,16]],"date-time":"2024-10-16T05:04:54Z","timestamp":1729055094000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-024-66843-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,16]]},"references-count":32,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["66843"],"URL":"https:\/\/doi.org\/10.1038\/s41598-024-66843-y","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,16]]},"assertion":[{"value":"2 February 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 October 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"24222"}}