{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T20:43:59Z","timestamp":1770756239628,"version":"3.50.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T00:00:00Z","timestamp":1767398400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T00:00:00Z","timestamp":1767398400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s12190-025-02727-2","type":"journal-article","created":{"date-parts":[[2026,1,3]],"date-time":"2026-01-03T08:44:10Z","timestamp":1767429850000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantitative assessment of HIV transmission dynamics with spatial diffusion: parameter estimation"],"prefix":"10.1007","volume":"72","author":[{"given":"Yuxin","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinyu","family":"Xia","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengmeng","family":"Bao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anwarud","family":"Din","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,1,3]]},"reference":[{"issue":"3","key":"2727_CR1","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1016\/j.joems.2013.12.001","volume":"22","author":"B. Mahato","year":"2014","unstructured":"Mahato, B., Mishra, B.K., Jayswal, A., Chandra, R.: A mathematical model on acquired immunodeficiency syndrome. J. Egypt. Math. Soc. 22(3), 544\u2013549 (2014). https:\/\/doi.org\/10.1016\/j.joems.2013.12.001","journal-title":"J. Egypt. Math. Soc."},{"issue":"6","key":"2727_CR2","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1080\/09540120020014264","volume":"12","author":"N. Escaffre","year":"2000","unstructured":"Escaffre, N., Morin, M., Bouhnik, A., Fuzibet, J., Gastaut, J., Obadia, Y., Moatti, J.-P.: Injecting drug users\u2019 adherence to HIV antiretroviral treatments: physicians\u2019 beliefs. AIDS Care 12(6), 723\u2013730 (2000). https:\/\/doi.org\/10.1080\/09540120020014264","journal-title":"AIDS Care"},{"issue":"3","key":"2727_CR3","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/s0002-9343(99)00018-2","volume":"106","author":"J.D. Bamberger","year":"1999","unstructured":"Bamberger, J.D., Waldo, C.R., Gerberding, J.L., Katz, M.H.: Postexposure prophylaxis for human immunodeficiency virus (HIV) infection following sexual assault. Amer. J. Med. 106(3), 323\u2013326 (1999). https:\/\/doi.org\/10.1016\/s0002-9343(99)00018-2","journal-title":"Amer. J. Med."},{"issue":"3","key":"2727_CR4","first-page":"183","volume":"13","author":"O.O. Apenteng","year":"2017","unstructured":"Apenteng, O.O., Ismail, N.A.: Modelling the spread of HIV and AIDS epidemic trends in male and female populations. World. J. Model. Simul. 13(3), 183\u2013192 (2017)","journal-title":"World. J. Model. Simul."},{"issue":"3","key":"2727_CR5","doi-asserted-by":"publisher","first-page":"594","DOI":"10.1080\/00207160.2012.726354","volume":"90","author":"F.A. Rihan","year":"2013","unstructured":"Rihan, F.A., Abdel rahman, D.H.: Delay differential model for tumour\u2013immune dynamics with HIV infection of CD4+ T-cells. Int. J. Comput. Math. 90(3), 594\u2013614 (2013). https:\/\/doi.org\/10.1080\/00207160.2012.726354","journal-title":"Int. J. Comput. Math."},{"key":"2727_CR6","first-page":"221","volume-title":"AIP Conference Proceedings","author":"A. Sule","year":"2014","unstructured":"Sule, A., Abdullah, F.A.: Optimal control of HIV\/AIDS dynamic: Education and treatment. In: AIP Conference Proceedings, vol. 1605, pp. 221\u2013226. American Institute of Physics (2014)"},{"issue":"13\u201314","key":"2727_CR7","doi-asserted-by":"publisher","first-page":"6550","DOI":"10.1016\/j.apm.2016.01.054","volume":"40","author":"H.F. 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). https:\/\/doi.org\/10.1016\/j.apm.2016.01.054","journal-title":"Appl. Math. Model."},{"issue":"5","key":"2727_CR8","doi-asserted-by":"publisher","first-page":"3690","DOI":"10.1002\/mma.9188","volume":"47","author":"X. Zhao","year":"2024","unstructured":"Zhao, X., Dong, L.: Dynamical behaviors of a stochastic HIV\/AIDS epidemic model with treatment. Math. Meth. Appl. Sci. 47(5), 3690\u20133704 (2024). https:\/\/doi.org\/10.1002\/mma.9188","journal-title":"Math. Meth. Appl. Sci."},{"key":"2727_CR9","doi-asserted-by":"publisher","first-page":"110053","DOI":"10.1016\/j.chaos.2020.110053","volume":"139","author":"H. G\u00fcnerhan","year":"2020","unstructured":"G\u00fcnerhan, H., Dutta, H., Dokuyucu, M.A., Adel, W.: Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators. Chaos, Solitons Fractals 139, 110053 (2020). https:\/\/doi.org\/10.1016\/j.chaos.2020.110053","journal-title":"Chaos, Solitons Fractals"},{"key":"2727_CR10","doi-asserted-by":"crossref","unstructured":"Khan, W.A., Zarin, R., Zeb, A., Khan, Y., Khan, A.: Navigating food allergy dynamics via a novel fractional mathematical model for antacid-induced allergies. J. Math. Tech. Model. 1(1) (2024)","DOI":"10.56868\/jmtm.v1i1.3"},{"issue":"1","key":"2727_CR11","first-page":"11","volume":"1","author":"F.M. Khan","year":"2024","unstructured":"Khan, F.M., Khan, Z.U.: Numerical analysis of fractional order drinking mathematical model. J. Math. Tech. Model 1(1), 11\u201324 (2024)","journal-title":"J. Math. Tech. Model"},{"key":"2727_CR12","doi-asserted-by":"publisher","unstructured":"Wu, P., Fang, C.: Spatiotemporal dynamics of syphilis in Xinjiang via a demographic-geographic data-validated reaction diffusion model. J. Math. Phys. 66(62704) (2025). https:\/\/doi.org\/10.1063\/5.0273893","DOI":"10.1063\/5.0273893"},{"key":"2727_CR13","doi-asserted-by":"publisher","first-page":"109539","DOI":"10.1016\/j.mbs.2025.109539","volume":"389","author":"P. Wu","year":"2025","unstructured":"Wu, P., Chen, T., Ruan, S.: Spatio-temporal modeling and analysis of two HIV strain infections via demographic\u2013geographic data. Math. Biosci. 389, 109539 (2025). https:\/\/doi.org\/10.1016\/j.mbs.2025.109539","journal-title":"Math. Biosci."},{"issue":"11","key":"2727_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/s13360-023-04633-7","volume":"138","author":"Q. Liu","year":"2023","unstructured":"Liu, Q., Din, A., Allali, A.: Analysis of a multiply delayed stochastic ebola model based on probability density function with case study. Eur. Phys. J. Plus 138(11), 1\u201318 (2023). https:\/\/doi.org\/10.1140\/epjp\/s13360-023-04633-7","journal-title":"Eur. Phys. J. Plus"},{"key":"2727_CR15","doi-asserted-by":"publisher","first-page":"121548","DOI":"10.1016\/j.physa.2019.121548","volume":"531","author":"X.B. Zhang","year":"2019","unstructured":"Zhang, X.B., Wang, X.D., Huo, H.F.: Extinction and stationary distribution of a stochastic sirs epidemic model with standard incidence rate and partial immunity. Physica A: Stat. Mech. Appl. 531, 121548 (2019). https:\/\/doi.org\/10.1016\/j.physa.2019.121548","journal-title":"Physica A: Stat. Mech. Appl."},{"key":"2727_CR16","doi-asserted-by":"publisher","first-page":"19270","DOI":"10.3934\/mbe.2023852","volume":"20","author":"H.J. Alsakaji","year":"2023","unstructured":"Alsakaji, H.J., Rihan, F.A., Udhayakumar, K., El Ktaibi, F.: Stochastic tumor-immune interaction model with external treatments and time delays: an optimal control problem. Math. Biosci. Eng. 20, 19270\u201319299 (2023). https:\/\/doi.org\/10.3934\/mbe.2023852","journal-title":"Math. Biosci. Eng."},{"key":"2727_CR17","doi-asserted-by":"publisher","first-page":"114714","DOI":"10.1016\/j.chaos.2024.114714","volume":"181","author":"A. Din","year":"2024","unstructured":"Din, A.: Bifurcation analysis of a delayed stochastic HBV epidemic model: cell-to-cell transmission. Chaos, Solitons Fractals 181, 114714 (2024). https:\/\/doi.org\/10.1016\/j.chaos.2024.114714","journal-title":"Chaos, Solitons Fractals"},{"issue":"14","key":"2727_CR18","doi-asserted-by":"publisher","first-page":"14983","DOI":"10.1002\/mma.9357","volume":"46","author":"F. Mahroug","year":"2023","unstructured":"Mahroug, F., Bentout, S.: Dynamics of a diffusion dispersal viral epidemic model with age infection in a spatially heterogeneous environment with general nonlinear function. Math. Methods In The Appl. Sci. 46(14), 14983\u201315010 (2023). https:\/\/doi.org\/10.1002\/mma.9357","journal-title":"Math. Methods In The Appl. Sci."},{"issue":"2","key":"2727_CR19","doi-asserted-by":"publisher","first-page":"306","DOI":"10.3934\/publichealth.2020026","volume":"7","author":"S. Bentout","year":"2020","unstructured":"Bentout, S., Chekroun, A., Kuniya, T.: Parameter estimation and prediction for coronavirus disease outbreak 2019 (covid-19) in Algeria. AIMS Public Health 7(2), 306 (2020). https:\/\/doi.org\/10.3934\/publichealth.2020026","journal-title":"Aims Public Health"},{"issue":"2","key":"2727_CR20","doi-asserted-by":"publisher","first-page":"1211","DOI":"10.1016\/j.jmaa.2015.09.066","volume":"434","author":"B. Soufiane","year":"2016","unstructured":"Soufiane, B., Touaoula, T.M.: Global analysis of an infection age model with a class of nonlinear incidence rates. J. Math. Anal. Appl. 434(2), 1211\u20131239 (2016). https:\/\/doi.org\/10.1016\/j.jmaa.2015.09.066","journal-title":"J. Math. Anal. Appl."},{"issue":"1","key":"2727_CR21","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1002\/mma.10327","volume":"48","author":"S. Djilali","year":"2025","unstructured":"Djilali, S., Chen, Y., Bentout, S.: Dynamics of a delayed nonlocal reaction\u2013diffusion heroin epidemic model in a heterogenous environment. Math. Methods In The Appl. Sci. 48(1), 273\u2013307 (2025). https:\/\/doi.org\/10.1002\/mma.10327","journal-title":"Math. Methods In The Appl. Sci."},{"issue":"4","key":"2727_CR22","doi-asserted-by":"publisher","first-page":"2250028","DOI":"10.1142\/s1793962322500283","volume":"13","author":"S. Djilali","year":"2022","unstructured":"Djilali, S., Bentout, S., Kumar, S., Touaoula, T.M.: Approximating the asymptomatic infectious cases of the covid-19 disease in Algeria and India using a mathematical model. Int. J. Modeling, Simul., Sci. Comput. 13(4), 2250028 (2022). https:\/\/doi.org\/10.1142\/s1793962322500283","journal-title":"Int. J. Modeling, Simul., Sci. Comput."},{"key":"2727_CR23","doi-asserted-by":"publisher","first-page":"926","DOI":"10.1016\/j.matcom.2022.07.020","volume":"203","author":"S. Bentout","year":"2023","unstructured":"Bentout, S., Djilali, S.: Asymptotic profiles of a nonlocal dispersal sir epidemic model with treat-age in a heterogeneous environment. Math. Comput. Simul. 203, 926\u2013956 (2023). https:\/\/doi.org\/10.1016\/j.matcom.2022.07.020","journal-title":"Math. Comput. Simul."},{"issue":"9","key":"2727_CR24","doi-asserted-by":"publisher","first-page":"7219","DOI":"10.1002\/mma.9969","volume":"47","author":"S. Bentout","year":"2024","unstructured":"Bentout, S.: Analysis of global behavior in an age-structured epidemic model with nonlocal dispersal and distributed delay. Math. Methods In The Appl. Sci. 47(9), 7219\u20137242 (2024). https:\/\/doi.org\/10.1002\/mma.9969","journal-title":"Math. Methods In The Appl. Sci."},{"issue":"3","key":"2727_CR25","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1007\/s00033-025-02466-1","volume":"76","author":"A. Nabti","year":"2025","unstructured":"Nabti, A., Djilali, S., Bentout, S.: Stability and spatial profiles of a double age-dependent diffusive viral infection model with spatial heterogeneity. Z. f\u00fcr Angew. Math. und Phys. 76(3), 89 (2025). https:\/\/doi.org\/10.1007\/s00033-025-02466-1","journal-title":"Z. f\u00fcr Angew. Math. und Phys."},{"key":"2727_CR26","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1051\/mmnp\/2025015","volume":"20","author":"S. Bentout","year":"2025","unstructured":"Bentout, S., Djilali, S.: Asymptotic dynamics of sirs epidemic model with dispersal budgets and nonlinear rates about heterogenous environments. Math. Modell. Nat. Phenom. 20, 17 (2025)","journal-title":"Math. Modell. Nat. Phenom."},{"key":"2727_CR27","doi-asserted-by":"publisher","unstructured":"Farhan, M., Waseem, Thaljaoui, A., Rahman, M.U.: Data-driven investigation of an epidemic model under saturated incidence rate using deep neural networks. J. Appl. Math. Comput. 1\u201335 (2025). https:\/\/doi.org\/10.1007\/s12190-025-02639-1","DOI":"10.1007\/s12190-025-02639-1"},{"issue":"6","key":"2727_CR28","doi-asserted-by":"publisher","first-page":"13659","DOI":"10.3934\/math.2024667","volume":"9","author":"M.A. El-Shorbagy","year":"2024","unstructured":"El-Shorbagy, M.A., Rahman, M., Nabwey, H.A., Habib, S.: An artificial neural network analysis of the thermal distribution of a fractional-order radial porous fin influenced by an inclined magnetic field. AIMS Math. 9(6), 13659\u201313688 (2024). https:\/\/doi.org\/10.3934\/math.2024667","journal-title":"Aims Math."},{"issue":"4","key":"2727_CR29","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/s40808-025-02481-1","volume":"11","author":"Z. Faiz","year":"2025","unstructured":"Faiz, Z., Habib, S., Yun, W.: Optimizing plastic waste management and pollution control using a deep neural network-based predictive model. Modeling Earth Syst. Environ. 11(4), 297 (2025). https:\/\/doi.org\/10.1007\/s40808-025-02481-1","journal-title":"Modeling Earth Syst. Environ."},{"key":"2727_CR30","doi-asserted-by":"publisher","unstructured":"Faiz, Z., Habib, S., Innab, N.: Optimizing tomato plant and insect disease control using a fractional model and deep neural networks. Comput. Biol. Chem. 119, 108515 (2025). https:\/\/doi.org\/10.1016\/j.compbiolchem.2025.108515","DOI":"10.1016\/j.compbiolchem.2025.108515"},{"key":"2727_CR31","doi-asserted-by":"crossref","unstructured":"Faiza, Waseem, Habib, S., Boulaaras, S., Ur rahman, M., Ali, S., Alharbi, A.: An intelligent framework for hybrid nanofluid flow between two concentric cylinders based on deep neural networks. Fractals 2540182 (2025)","DOI":"10.1142\/S0218348X25401826"},{"key":"2727_CR32","doi-asserted-by":"publisher","first-page":"108291","DOI":"10.1016\/j.compbiolchem.2024.108291","volume":"115","author":"S. Ali","year":"2025","unstructured":"Ali, S., Ali, A., Thaljaoui, A., Meetei, M.Z.: Dynamics of infectious disease mathematical model through unsupervised stochastic neural network paradigm. Comput. Biol. Chem. 115, 108291 (2025). https:\/\/doi.org\/10.1016\/j.compbiolchem.2024.108291","journal-title":"Comput. Biol. Chem."},{"issue":"2","key":"2727_CR33","doi-asserted-by":"publisher","first-page":"185","DOI":"10.22436\/jmcs.036.02.04","volume":"36","author":"M.A. El-Shorbagy","year":"2025","unstructured":"El-Shorbagy, M.A., Tabussam, S., Rahman, M.U.: Giardiasis transmission dynamics: insights from fractal-fractional modeling and deep neural networks. J. Math. Comput. Sci. 36(2), 185\u2013206 (2025). https:\/\/doi.org\/10.22436\/jmcs.036.02.04","journal-title":"J. Math. Comput. Sci."},{"issue":"3","key":"2727_CR34","doi-asserted-by":"publisher","first-page":"1480","DOI":"10.1016\/j.apm.2012.04.013","volume":"37","author":"H.F. Huo","year":"2013","unstructured":"Huo, H.F., Feng, L.X.: Global stability for an HIV\/AIDS epidemic model with different latent stages and treatment. Appl. Math. Model. 37(3), 1480\u20131489 (2013). https:\/\/doi.org\/10.1016\/j.apm.2012.04.013","journal-title":"Appl. Math. Model."},{"issue":"12","key":"2727_CR35","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1140\/epjp\/s13360-024-05881-x","volume":"139","author":"K. Guedri","year":"2024","unstructured":"Guedri, K., Zarin, R., Zeb, A., Makhdoum, B.M., Niyazi, H.A., Khan, A.: A numerical study of HIV\/AIDS transmission dynamics and the onset of long-term disability in chronic infection. Eur. Phys. J. Plus 139(12), 1\u201324 (2024). https:\/\/doi.org\/10.1140\/epjp\/s13360-024-05881-x","journal-title":"Eur. Phys. J. Plus"},{"key":"2727_CR36","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1016\/j.enganabound.2022.11.026","volume":"147","author":"R. Zarin","year":"2023","unstructured":"Zarin, R., Haider, N., et al.: Numerical solution of COVID-19 pandemic model via finite difference and meshless techniques. Eng. Anal. Bound. Elem. 147, 76\u201389 (2023). https:\/\/doi.org\/10.1016\/j.enganabound.2022.11.026","journal-title":"Eng. Anal. Bound. Elem."},{"issue":"1","key":"2727_CR37","doi-asserted-by":"publisher","first-page":"1322","DOI":"10.3934\/math.2025061","volume":"10","author":"K. Guedri","year":"2025","unstructured":"Guedri, K., Zarin, R., Khan, A., Khan, A., Makhdoum, B.M., Niyazi, H.A.: Modeling hepatitis B transmission dynamics with spatial diffusion and disability potential in the chronic stage. AIMS Math. 10(1), 1322\u20131349 (2025). https:\/\/doi.org\/10.3934\/math.2025061","journal-title":"Aims Math."},{"key":"2727_CR38","doi-asserted-by":"publisher","DOI":"10.1002\/0470871296","volume-title":"Spatial Ecology via Reaction-Diffusion Equations","author":"R.S. Cantrell","year":"2004","unstructured":"Cantrell, R.S., Cosner, C.: Spatial Ecology via Reaction-Diffusion Equations. John Wiley & Sons, Hoboken (2004)"},{"issue":"1","key":"2727_CR39","doi-asserted-by":"publisher","first-page":"17","DOI":"10.2307\/1939378","volume":"75","author":"E.E. Holmes","year":"1994","unstructured":"Holmes, E.E., Lewis, M.A., Banks, J., Veit, R.: Partial differential equations in ecology: spatial interactions and population dynamics. Ecology 75(1), 17\u201329 (1994). https:\/\/doi.org\/10.2307\/1939378","journal-title":"Ecology"},{"issue":"4","key":"2727_CR40","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1007\/bf00178324","volume":"28","author":"O. Diekmann","year":"1990","unstructured":"Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 28(4), 365\u2013382 (1990). https:\/\/doi.org\/10.1007\/bf00178324","journal-title":"J. Math. Biol."},{"issue":"3","key":"2727_CR41","doi-asserted-by":"publisher","first-page":"288","DOI":"10.1016\/j.idm.2017.06.002","volume":"2","author":"P. Driessche","year":"2017","unstructured":"Driessche, P.: Reproduction numbers of infectious disease models. Infect. Dis. Model. 2(3), 288\u2013303 (2017). https:\/\/doi.org\/10.1016\/j.idm.2017.06.002","journal-title":"Infect. Dis. Model."},{"issue":"8","key":"2727_CR42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11538-020-00788-x","volume":"82","author":"C. Yang","year":"2020","unstructured":"Yang, C., Wang, J.: Basic reproduction numbers for a Class of reaction-diffusion epidemic models. Bull. Math. Biol. 82(8), 1\u201325 (2020)","journal-title":"Bull. Math. Biol."},{"issue":"8","key":"2727_CR43","doi-asserted-by":"publisher","first-page":"1488","DOI":"10.1016\/j.camwa.2013.08.023","volume":"66","author":"K. Hattaf","year":"2013","unstructured":"Hattaf, K., Yousfi, N.: Global stability for reaction\u2013diffusion equations in biology. Comput. Math. Appl. 66(8), 1488\u20131497 (2013). https:\/\/doi.org\/10.1016\/j.camwa.2013.08.023","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"2727_CR44","doi-asserted-by":"publisher","first-page":"2307207","DOI":"10.55630\/j.biomath.2023.07.207","volume":"12","author":"J.P.C. Santos","year":"2023","unstructured":"Santos, J.P.C., Monteiro, E., Ferreira, J.C., Lemes, N.H.T., Rodrigues, D.S.: Well-posedness and qualitative analysis of a SEIR model with spatial diffusion for COVID-19 spreading. Biomath 12(1), 2307207\u20132307207 (2023). https:\/\/doi.org\/10.55630\/j.biomath.2023.07.207","journal-title":"Biomath"},{"key":"2727_CR45","volume-title":"Abstract Parabolic Evolution Equations and Their Applications","author":"A. Yagi","year":"2009","unstructured":"Yagi, A.: Abstract Parabolic Evolution Equations and Their Applications. Springer, Berlin (2009)"},{"key":"2727_CR46","doi-asserted-by":"publisher","unstructured":"Ahmed, N., Rafiq, M., Rehman, M., Iqbal, M., Ali, M.: Numerical modeling of three dimensional brusselator reaction diffusion system. AIP Adv. 9(1) (2019). https:\/\/doi.org\/10.1063\/1.5070093","DOI":"10.1063\/1.5070093"},{"issue":"3","key":"2727_CR47","first-page":"315","volume":"9","author":"A. Nauman","year":"2018","unstructured":"Nauman, A., Rafiq, M., Rehman, M., Ali, M., Ahmad, M.: Numerical modeling of seir measles dynamics with diffusion. Commun. Math. Appl. 9(3), 315 (2018)","journal-title":"Commun. Math. Appl."},{"key":"2727_CR48","unstructured":"Wikipedia: HIV\/AIDS in India \u2013 annual AIDS deaths chart. Preprint at 2025). https:\/\/en.wikipedia.org\/wiki\/HIV\/AIDS_in_India#\/media\/File:Annual_India_AIDS_deaths.svg Accessed: June 17, 2025."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02727-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-025-02727-2","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-025-02727-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T16:12:57Z","timestamp":1770739977000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-025-02727-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,3]]},"references-count":48,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["2727"],"URL":"https:\/\/doi.org\/10.1007\/s12190-025-02727-2","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,3]]},"assertion":[{"value":"15 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 January 2026","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflicts of interest"}}],"article-number":"74"}}