69d67fe3-6b3c-45df-a131-0255c10c2d3120241112052906104wseas:wseasmdt@crossref.orgMDT DepositInternational Journal of Applied Mathematics, Computational Science and Systems Engineering2766-982310.37394/232026https://wseas.com/journals/amcse/152024152024610.37394/232026.2024.6https://wseas.com/journals/amcse/2024.phpThierry Bi BouaLaguiLaboratoire de Math´ematiques fondamentales et Applications, ´Ecole Doctorale Sciences, Technologie et Agriculture Durable (ED-STAD), CÔTE D'IVOIRESeydouTraoreLaboratoire des Sciences et Technologies de l’Environnement, UFR de Agroforesterie et Environnement, Universit´e Jean Lorougnon Gu´ed´e, (UJLoG) Daloa, CÔTE D'IVOIREMouhamadouDossoLaboratoire de Math´ematiques fondamentales et Applications, UFR Math´ematiques et Informatique, Universit´e F´elix Houphou¨et-Boigny 22 BP 582 Abidjan 22, CÔTE D'IVOIREIn this paper, we first analyzed several basic population dynamics models interpreting the relationships between three species. These are the May-Leonard model with three competitors, some prey-predator models of three-species and a prey-predator model with a super-predator. Subsequently, in our work, we proposed a new three-species model consisting of a prey, a predator and a superpredator, including some important assumptions such as competition, self-defense and infected prey. We examined the various equilibrium points of proposed model, and determined the conditions for extinction and survival of species in the long term. Finally, we performed numerical illustrations using Maltlab software to corroborate the theoretical results.111220241112202419322317https://wseas.com/journals/amcse/2024/a34amcse-017(2024).pdf10.37394/232026.2024.6.17https://wseas.com/journals/amcse/2024/a34amcse-017(2024).pdf10.1016/j.apm.2020.09.046Deeptajyoti Sen, S. 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