{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,10]],"date-time":"2026-08-10T20:49:46Z","timestamp":1786394986647,"version":"3.56.0"},"reference-count":82,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T00:00:00Z","timestamp":1619913600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Directorate of Research and Community Service. The Directorate General of Strengthening Research and Development, the Ministry of Research, Technology and Higher Education (Brawijaya University), Indonesia, via Doctoral Dissertation Research","award":["No. 037\/ SP2H\/ LT\/ DRPM\/ 2020"],"award-info":[{"award-number":["No. 037\/ SP2H\/ LT\/ DRPM\/ 2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we consider a fractional-order eco-epidemic model based on the Rosenzweig\u2013MacArthur predator\u2013prey model. The model is derived by assuming that the prey may be infected by a disease. In order to take the memory effect into account, we apply two fractional differential operators, namely the Caputo fractional derivative (operator with power-law kernel) and the Atangana\u2013Baleanu fractional derivative in the Caputo (ABC) sense (operator with Mittag\u2013Leffler kernel). We take the same order of the fractional derivative in all equations for both senses to maintain the symmetry aspect. The existence and uniqueness of solutions of both eco-epidemic models (i.e., in the Caputo sense and in ABC sense) are established. Both models have the same equilibrium points, namely the trivial (origin) equilibrium point, the extinction of infected prey and predator point, the infected prey free point, the predator-free point and the co-existence point. For a model in the Caputo sense, we also show the non-negativity and boundedness of solution, perform the local and global stability analysis and establish the conditions for the existence of Hopf bifurcation. It is found that the trivial equilibrium point is a saddle point while other equilibrium points are conditionally asymptotically stable. The numerical simulations show that the solutions of the model in the Caputo sense strongly agree with analytical results. Furthermore, it is indicated numerically that the model in the ABC sense has quite similar dynamics as the model in the Caputo sense. The essential difference between the two models is the convergence rate to reach the stable equilibrium point. When a Hopf bifurcation occurs, the bifurcation points and the diameter of the limit cycles of both models are different. Moreover, we also observe a bistability phenomenon which disappears via Hopf bifurcation.<\/jats:p>","DOI":"10.3390\/sym13050785","type":"journal-article","created":{"date-parts":[[2021,5,2]],"date-time":"2021-05-02T08:05:21Z","timestamp":1619942721000},"page":"785","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Dynamics of an Eco-Epidemic Predator\u2013Prey Model Involving Fractional Derivatives with Power-Law and Mittag\u2013Leffler Kernel"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0118-2745","authenticated-orcid":false,"given":"Hasan S.","family":"Panigoro","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"},{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, State University of Gorontalo, Bone Bolango 96119, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1335-5631","authenticated-orcid":false,"given":"Agus","family":"Suryanto","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7307-1537","authenticated-orcid":false,"given":"Wuryansari Muharini","family":"Kusumawinahyu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4163-8030","authenticated-orcid":false,"given":"Isnani","family":"Darti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang 65145, Indonesia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1038\/116461b0","article-title":"Elements of physical biology","volume":"116","author":"Lotka","year":"1925","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1093\/icesjms\/3.1.3","article-title":"Variations and fluctuations of the number of individuals in animal species living together","volume":"3","author":"Volterra","year":"1928","journal-title":"ICES J. 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