{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T06:07:11Z","timestamp":1766815631781,"version":"3.48.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T00:00:00Z","timestamp":1766793600000},"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":["Netw Model Anal Health Inform Bioinforma"],"DOI":"10.1007\/s13721-025-00692-1","type":"journal-article","created":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T04:16:51Z","timestamp":1766809011000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability analysis of a fractional prey\u2013predator model with Holling type III functional response and disease in both populations"],"prefix":"10.1007","volume":"15","author":[{"given":"Halet","family":"Ismail","sequence":"first","affiliation":[]},{"given":"S.","family":"Hariharan","sequence":"additional","affiliation":[]},{"given":"L.","family":"Shangerganesh","sequence":"additional","affiliation":[]},{"given":"V.","family":"Govindaraj","sequence":"additional","affiliation":[]},{"given":"Ilker","family":"Ozsahin","sequence":"additional","affiliation":[]},{"given":"Dilber Uzun","family":"Ozsahin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5438-5407","authenticated-orcid":false,"given":"Hijaz","family":"Ahmad","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,12,27]]},"reference":[{"key":"692_CR1","first-page":"21","volume":"11","author":"FB Adda","year":"1997","unstructured":"Adda FB (1997) Geometric interpretation of the fractional derivative. J Fract Calc Appl Anal 11:21\u201352","journal-title":"J Fract Calc Appl Anal"},{"issue":"1","key":"692_CR2","doi-asserted-by":"publisher","DOI":"10.1063\/5.0262460","volume":"3302","author":"SN Afiyah","year":"2025","unstructured":"Afiyah SN, Fatmawati W (2025) Dynamical analysis of a Leslie\u2013Gower predator\u2013prey model with Holling type IV functional response incorporating fear and Allee effect. AIP Conf Proc 3302(1):030001","journal-title":"AIP Conf Proc"},{"issue":"4","key":"692_CR3","doi-asserted-by":"publisher","first-page":"1690","DOI":"10.19139\/soic-2310-5070-2341","volume":"13","author":"SN Afiyah","year":"2025","unstructured":"Afiyah SN, Fatmawati A, Windarto A, Abidemi A (2025) Dynamics of a fractional order harvested predator\u2013prey model incorporating fear effect and refuge. Stat Optim Inf Comput 13(4):1690\u20131713","journal-title":"Stat Optim Inf Comput"},{"issue":"1","key":"692_CR4","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1016\/j.jmaa.2006.01.087","volume":"325","author":"E Ahmed","year":"2007","unstructured":"Ahmed E, El-Sayed AMA, El-Saka HAA (2007) Equilibrium points, stability and numerical solutions of fractional-order predator\u2013prey and rabies models. J Math Anal Appl 325(1):542\u2013553","journal-title":"J Math Anal Appl"},{"key":"692_CR5","doi-asserted-by":"publisher","first-page":"342","DOI":"10.1016\/j.apm.2019.11.025","volume":"81","author":"J Alidousti","year":"2020","unstructured":"Alidousti J (2020) Stability and bifurcation analysis for a fractional prey\u2013predator scavenger model. Appl Math Model 81:342\u2013355","journal-title":"Appl Math Model"},{"key":"692_CR6","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.apm.2016.10.054","volume":"43","author":"I Ameen","year":"2017","unstructured":"Ameen I, Novati P (2017) The solution of fractional order epidemic model by implicit Adams methods. Appl Math Model 43:78\u201384","journal-title":"Appl Math Model"},{"issue":"1","key":"692_CR7","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1186\/s13662-018-1535-9","volume":"2018","author":"K Baisad","year":"2018","unstructured":"Baisad K, Moonchai S (2018) Analysis of stability and Hopf bifurcation in a fractional Gauss-type predator\u2013prey model with Allee effect and Holling type-III functional response. Adv Differ Equ 2018(1):82","journal-title":"Adv Differ Equ"},{"key":"692_CR8","first-page":"254","volume":"38","author":"MA Bhat","year":"2018","unstructured":"Bhat MA, Khan A (2018) Multi-switching combination synchronization of different fractional-order non-linear dynamical systems. Int J Model Simul 38:254\u2013261","journal-title":"Int J Model Simul"},{"key":"692_CR9","first-page":"114","volume":"3","author":"MA Biswasa","year":"2016","unstructured":"Biswasa MA, Sk B, Maitib A, Alam S (2016) Large advantage of herd behavior of prey in prey-predator dynamics with disease in predator. Int J Adv Appl Math Mech 3:114\u2013120","journal-title":"Int J Adv Appl Math Mech"},{"key":"692_CR10","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/j.chaos.2018.11.017","volume":"118","author":"Y Chatibi","year":"2019","unstructured":"Chatibi Y, El Kinani EH, Ouhadan A (2019) Variational calculus involving nonlocal fractional derivative with Mittag\u2013Leffler kernel. Chaos, Solitons & Fractals 118:117\u2013121","journal-title":"Chaos, Solitons & Fractals"},{"issue":"1","key":"692_CR11","doi-asserted-by":"publisher","DOI":"10.1142\/S0219887820500103","volume":"17","author":"Y Chatibi","year":"2020","unstructured":"Chatibi Y, El Kinani EH, Ouhadan A (2020) Lie symmetry analysis and conservation laws for the time fractional Black\u2013Scholes equation. Int J Geom Methods Mod Phys 17(1):2050010\u20132050155","journal-title":"Int J Geom Methods Mod Phys"},{"issue":"4","key":"692_CR12","doi-asserted-by":"publisher","first-page":"2868","DOI":"10.1002\/mma.6064","volume":"44","author":"Y Chatibi","year":"2021","unstructured":"Chatibi Y, El Kinani H, Ouhadan A (2021) On the discrete symmetry analysis of some classical and fractional differential equations. Math Methods Appl Sci 44(4):2868\u20132878","journal-title":"Math Methods Appl Sci"},{"issue":"6","key":"692_CR13","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1016\/S0362-546X(98)00126-6","volume":"36","author":"J Chattopadhyay","year":"1999","unstructured":"Chattopadhyay J, Arino O (1999) A predator-prey model with disease in the prey. Nonlinear Anal Theory Methods Appl 36(6):747\u2013766","journal-title":"Nonlinear Anal Theory Methods Appl"},{"issue":"1","key":"692_CR14","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.joems.2013.06.006","volume":"22","author":"HAA El-Saka","year":"2014","unstructured":"El-Saka HAA (2014) The fractional-order SIS epidemic model with variable population size. J Egypt Math Soc 22(1):50\u201354","journal-title":"J Egypt Math Soc"},{"issue":"1","key":"692_CR15","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.joems.2014.02.012","volume":"23","author":"HAA El-Saka","year":"2015","unstructured":"El-Saka HAA (2015) Backward bifurcations in fractional-order vaccination models. J Egypt Math Soc 23(1):49\u201355","journal-title":"J Egypt Math Soc"},{"issue":"2","key":"692_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11071-018-4213-2","volume":"93","author":"Y Fan","year":"2018","unstructured":"Fan Y, Huang X, Wang Z, Li Y (2018) Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function. Nonlinear Dyn 93(2):1\u201317","journal-title":"Nonlinear Dyn"},{"key":"692_CR17","unstructured":"Garrappa R (2023) FLMM2 (https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/47081-flmm2), MATLAB Central File Exchange. Retrieved 16 Mar"},{"issue":"3","key":"692_CR18","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1080\/02286203.2019.1596727","volume":"40","author":"D Guha","year":"2020","unstructured":"Guha D, Roy PK, Banerjee S (2020) Grasshopper optimization algorithm-scaled fractional-order PID controller applied to reduced-order model of load frequency control system. Int J Model Simul 40(3):217\u2013242","journal-title":"Int J Model Simul"},{"issue":"3","key":"692_CR19","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1093\/imammb\/dqn017","volume":"25","author":"YH Hsieh","year":"2008","unstructured":"Hsieh YH, Hsiao CK (2008) Predator\u2013prey model with disease infection in both populations. Math Med Biol 25(3):247\u201366","journal-title":"Math Med Biol"},{"issue":"14","key":"692_CR20","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1049\/iet-cta.2017.0196","volume":"11","author":"X Huang","year":"2017","unstructured":"Huang X, Fan Y, Jia J, Li Y (2017) Quasi-synchronisation of fractional-order memristor-based neural networks with parameter mismatches. IET Control Theory Appl 11(14):2317\u20132327","journal-title":"IET Control Theory Appl"},{"key":"692_CR21","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1016\/j.nonrwa.2015.05.014","volume":"26","author":"J Huo","year":"2015","unstructured":"Huo J, Zhao H, Zhu L (2015) The effect of vaccines on backward bifurcation in a fractional order HIV model. Nonlinear Anal Real World Appl 26:289\u2013305","journal-title":"Nonlinear Anal Real World Appl"},{"issue":"20\u201321","key":"692_CR22","doi-asserted-by":"publisher","first-page":"8946","DOI":"10.1016\/j.apm.2013.04.024","volume":"37","author":"M Javidi","year":"2013","unstructured":"Javidi M, Nyamoradi N (2013) Dynamic analysis of a fractional order prey-predator interaction with harvesting. Appl Math Model 37(20\u201321):8946\u20138956","journal-title":"Appl Math Model"},{"key":"692_CR23","volume-title":"Theory and application of fractional differential equations","author":"AA Kilbas","year":"2006","unstructured":"Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and application of fractional differential equations. Elsevier, New York"},{"issue":"1\u20133","key":"692_CR24","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.cnsns.2014.12.013","volume":"24","author":"CVD Leon","year":"2015","unstructured":"Leon CVD (2015) Volterra-type Lyapunov functions for fractional-order epidemic systems. Commun Nonlinear Sci Numer Simul 24(1\u20133):75\u201385","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"1","key":"692_CR25","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s11071-014-1439-5","volume":"78","author":"X Li","year":"2014","unstructured":"Li X, Wu R (2014) Hopf bifurcation analysis of a new commensurate fractional-order hyperchaotic system. Nonlinear Dyn 78(1):279\u2013288","journal-title":"Nonlinear Dyn"},{"issue":"1\u20132","key":"692_CR26","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1007\/s12190-016-1017-8","volume":"54","author":"HL Li","year":"2017","unstructured":"Li HL, Zhang L, Hu C, Jiang YL, Teng Z (2017) Dynamical analysis of a fractional-order predator\u2013prey model incorporating a prey refuge. J Appl Math Comput 54(1\u20132):435\u2013449","journal-title":"J Appl Math Comput"},{"key":"692_CR27","unstructured":"Matignon D (1996) Stability results for fractional differential equations with applications to control processing. In: Proceedings of CESA\u201996 IMACS multiconference on computational engineering systems and applied sciences, Lille, France, vol 2, pp 963\u2013968"},{"issue":"25","key":"692_CR28","doi-asserted-by":"publisher","first-page":"2166","DOI":"10.1016\/j.physleta.2009.04.032","volume":"373","author":"AE Matouk","year":"2009","unstructured":"Matouk AE (2009) Stability conditions, hyperchaos and control in a novel fractional order hyper-chaotic system. Phys Lett A 373(25):2166\u20132173","journal-title":"Phys Lett A"},{"issue":"2","key":"692_CR29","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1016\/j.cnsns.2010.04.027","volume":"16","author":"AE Matouk","year":"2011","unstructured":"Matouk AE (2011) Chaos, feedback control and synchronization of a fractional-order modified autonomous Vander Pol\u2013Duffing circuit. Commun Nonlinear Sci Numer Simul 16(2):975\u2013986","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"18","key":"692_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/mma.4490","volume":"40","author":"S Mondal","year":"2017","unstructured":"Mondal S, Lahiri A, Bairaigi N (2017) Analysis of fractional order eco-epidemiological model with prey infection and type 2 functional response. Math Methods Appl Sci 40(18):1\u201314","journal-title":"Math Methods Appl Sci"},{"key":"692_CR31","first-page":"286","volume":"186","author":"ZM Odibat","year":"2007","unstructured":"Odibat ZM, Shawagfeh NT (2007) Generalized Taylor\u2019s formula. Appl Math Comput 186:286\u2013293","journal-title":"Appl Math Comput"},{"issue":"9","key":"692_CR32","doi-asserted-by":"publisher","first-page":"797","DOI":"10.1046\/j.1461-0248.2003.00500.x","volume":"6","author":"C Packer","year":"2003","unstructured":"Packer C, Holt RD, Hudson PJ, Lafferty KD, Dobson AP (2003) Keeping the herds healthy and alert: implications of predator control for infectious disease. Ecol Lett 6(9):797\u2013802","journal-title":"Ecol Lett"},{"issue":"4","key":"692_CR33","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1080\/02286203.2019.1611311","volume":"39","author":"P Panja","year":"2019","unstructured":"Panja P (2019) Dynamics of a fractional order predator-prey model with intraguild predation. Int J Model Simul 39(4):256\u2013268","journal-title":"Int J Model Simul"},{"key":"692_CR34","volume-title":"Fractional differential equations","author":"I Podlubny","year":"1999","unstructured":"Podlubny I (1999) Fractional differential equations. Academic Press, London"},{"key":"692_CR35","first-page":"367","volume":"5","author":"I Podlubny","year":"2002","unstructured":"Podlubny I (2002) Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calc Appl Anal 5:367\u2013386","journal-title":"Fract Calc Appl Anal"},{"issue":"4","key":"692_CR36","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11071-018-4507-4","volume":"94","author":"U Saeed","year":"2018","unstructured":"Saeed U, Ali I, Din Q (2018) Neimark\u2013Sacker bifurcation and chaos control in discrete-time predator\u2013prey model with parasites. Nonlinear Dyn 94(4):1\u201310","journal-title":"Nonlinear Dyn"},{"issue":"6","key":"692_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S0218127418500736","volume":"28","author":"S Saha","year":"2018","unstructured":"Saha S, Maiti A, Samanta GP (2018) Menten predator-prey model with strong Allee effect and disease in prey incorporating prey refuge. Int J Bifur Chaos 28(6):1\u201321","journal-title":"Int J Bifur Chaos"},{"issue":"7\u20138","key":"692_CR38","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1515\/ijnsns-2017-0273","volume":"19","author":"M Sambath","year":"2018","unstructured":"Sambath M, Ramesh P, Balachandran K (2018) Asymptotic behavior of the fractional order three species prey\u2013predator model. Int J Nonlinear Sci Numer Simul 19(7\u20138):721\u2013733","journal-title":"Int J Nonlinear Sci Numer Simul"},{"issue":"7","key":"692_CR39","doi-asserted-by":"publisher","first-page":"3592","DOI":"10.22436\/jnsa.010.07.19","volume":"10","author":"Q Song","year":"2017","unstructured":"Song Q, Dong X, Bai Z, Chen B (2017) Existence for fractional Dirichlet boundary value problem under barrier strip conditions. J Nonlinear Sci Appl 10(7):3592\u20133598","journal-title":"J Nonlinear Sci Appl"},{"key":"692_CR40","first-page":"1","volume":"1","author":"N Supajaidee","year":"2017","unstructured":"Supajaidee N, Moonchai S (2017) Stability analysis of a fractional-order two-species facultative mutualism model with harvesting. Adv Differ Equ 1:1\u201313","journal-title":"Adv Differ Equ"},{"key":"692_CR41","doi-asserted-by":"publisher","DOI":"10.3390\/math7111100","volume":"7","author":"A Suryanto","year":"2019","unstructured":"Suryanto A, Darti I, Panigoro HS, Kilicman A (2019) A fractional-order predator\u2013prey model with ratio-dependent functional response and linear harvesting. Mathematics 7:1100","journal-title":"Mathematics"},{"key":"692_CR42","first-page":"1","volume":"1","author":"S Wang","year":"2018","unstructured":"Wang S, Ma Z, Wang W (2018) Dynamical behavior of a generalized eco-epidemiological system with prey refuge. Adv Differ Equ 1:1\u201320","journal-title":"Adv Differ Equ"},{"key":"692_CR43","first-page":"320","volume":"292","author":"Y Xie","year":"2017","unstructured":"Xie Y, Wang L, Deng Q, Wu Z (2017) The dynamics of an impulsive predator-prey model with communicable disease in the prey species only. Appl Math Comput 292:320\u2013335","journal-title":"Appl Math Comput"},{"issue":"9","key":"692_CR44","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1016\/j.matcom.2012.01.004","volume":"82","author":"Y Yan","year":"2012","unstructured":"Yan Y, Kou C (2012) Stability analysis for a fractional differential model of HIV infection of CD4+ T-cells with time delay. Math Comput Simul 82(9):1572\u20131585","journal-title":"Math Comput Simul"},{"key":"692_CR45","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S1793524517501194","volume":"10","author":"W Yang","year":"2017","unstructured":"Yang W (2017) Dynamical behaviors of a diffusive predator-prey model with Beddington\u2013DeAngelis functional response and disease in the prey. Int J Biomath 10:1\u201331","journal-title":"Int J Biomath"}],"container-title":["Network Modeling Analysis in Health Informatics and Bioinformatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13721-025-00692-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13721-025-00692-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13721-025-00692-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,27]],"date-time":"2025-12-27T06:02:14Z","timestamp":1766815334000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13721-025-00692-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,27]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,12]]}},"alternative-id":["692"],"URL":"https:\/\/doi.org\/10.1007\/s13721-025-00692-1","relation":{},"ISSN":["2192-6670"],"issn-type":[{"type":"electronic","value":"2192-6670"}],"subject":[],"published":{"date-parts":[[2025,12,27]]},"assertion":[{"value":"15 March 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 November 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 December 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Author declares no competing of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to participate"}},{"value":"Not Applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to publish"}},{"value":"Not applicable.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}}],"article-number":"20"}}