0ec5e7e9-0806-4297-b8bc-26cfb064f19820240311063648248wseas:wseasmdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON BIOLOGY AND BIOMEDICINE2224-29021109-951810.37394/23208http://wseas.org/wseas/cms.action?id=40111820241820242110.37394/23208.2024.21https://wseas.com/journals/bab/2024.phpThierry Bi BouaLaguiUFR Mathématiques et Informatique University Université Félix Houphouët-Boigny 22 BP 582 Abidjan 22, COTE D'IVOIREMouhamadouDossoUFR Mathématiques et Informatique University Université Félix Houphouët-Boigny 22 BP 582 Abidjan 22, COTE D'IVOIREGossouhonSitiononUFR Mathématiques et Informatique University Université Félix Houphouët-Boigny 22 BP 582 Abidjan 22, COTE D'IVOIREBiological models of basic prey-predator interaction have been studied. This consisted, at first, in analyzing the basic models of population dynamics such as the Malthus model, the Verhulst model, the Gompertz model and the model with Allee effect ; then, in a second step, to analyze the Lotka-Volterra model and its models improved by taking into account certain important hypotheses such as competition and/or cooperation between species, existence of refuge for prey and migration of species. For each population evolution model presented, a numerical illustration was made for its verification.311202431120249310710https://wseas.com/journals/bab/2024/a205103-1318.pdf10.37394/23208.2024.21.10https://wseas.com/journals/bab/2024/a205103-1318.pdfT.R. Malthus, An Essay on the Principle of Population, vol. 2, 6th edition, (1826). P. F. Verhulst, Notice on the law that a population follows in its growth (Notice sur la loi que la population poursuit dans son accroissement). Corr. Math. Phys., 10(1838) 113-121. 10.1007/bf00276199J. Hofbauer, V. Hutson and W. Jansen, Coexistence for systems governed by difference equations of Lotka-Volterra type, J. Math. Biol. 25 (1987) 553-570. V. Volterra, Lessons on the Mathematical Theory of Struggle for Life (Le¸cons sur la Th´eorie Math´ematique de la Lutte pour la Vie), Gauthier-Villars, Paris, (1931). 10.36260/rbr.v9i11.1119E. Ibarguen-Mondragon, M. Vergel-Ortega, & S. Gomez-Vergel, Malthus Model applied to exponential growth of Covid-19. Rebista Boletin Redipe, 9(11)(2020) 159-164. 10.2991/assehr.k.201017.094M. Rayungsari, A. In’am, and M. Aufin, Genetic Algorithm to Estimate Parameters of Indonesian Population Growth Model, in Proceedings of the International Conference on Community Development (ICCD 2020), vol. 477, no. Iccd. Paris, France: Atlantis Press, 2020. ISBN 978-94-6239-253-3 pp. 426–430. 10.1098/rstl.1825.0026B. Gompertz, On the Nature of the Function Expressive of the Law of Human Mortality, and on a New Mode of Determining the Value of Life Contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115, (1825), pp. 513-583. N. Pavlov, G. Spasov, A. Rahnev and N. Kyurkchiev, A New Class Of Gompertz–Type Software Reliability Models, International Electronic Journal of Pure and Applied Mathematics, Vol. 12 No. 1, (2018) 43-57. A. R. Sheergojria, P. Iqbala, P. Agarwalb and N. Ozdemire, Uncertainty-based Gompertz growth model for tumor population and its numerical analysis, An International Journal of Optimization and Control: Theories & Applications, Vol.12, No.2 (2022) pp.137150. 10.1007/s11587-020-00548-yM. Asadi, A. Di Crescenzo, F. A. Sajadi & S. Spina. A generalized Gompertz growth model with applications and related birth-death processes. Ricerche di Matematica, (2020),1-36. 10.1101/2020.03.11.20034363K. Wu, D. Darcet, Q. Wang and D. Sornette, Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world, (2020). 10.1007/s10144-009-0152-6A. M. Kramer, B. Dennis, A. M. Liebhold and J. Drake. The Evidence for Allee Effects. Population Ecology, 51(3)(2009),341-354. 10.1016/j.chaos.2021.111512M. N. Kuperman, G. Abramson, Allee effect in models of interacting species. Chaos, Solitons Fract. (2021), 153:111512 P.A. Stephene, W.J. Sutherland, Consequence of the Allee effet for behaviour, ecology and conservation, Trends Ecol. Evol., vol. 14(10)(1999) 401-405. J.M. Drake, A.M. Kramer, Allee effects. Nat Educ Knowl, 3(10):2, (2011). 10.1109/jrproc.1962.288235J. Nagumo, S. Arimoto and S. Yoshizawa, Proc. IRE, 50(1962)2061–2070. 10.1073/pnas.6.7.410A. J. Lotka, Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. 6, (1920) 410-415. A. J. Lotka, Elements of Physical Biology. Williams & Wilkins, Baltimore, (1925). 10.1038/118558a0V. Volterra, Fluctuations in the abundance of a species considered mathematically. Nature 118 (1926)558–560. Reprinted in L.A. Real, J.H. Brown (eds.) Foundations of Ecology. University of Chicago Press, (1991) pp. 283–285. 10.32920/ryerson.14657946T. Blaszak, Lotka-Volterra models of Predator-Prey Relationships, https://web.mst.edu/huwen/teaching ˜ Predator Prey Tyler Blaszak.pdf, Missouri University of Science and Technology, (last accessed on 2023-04-25). K. Mahtani, An epidemiological application of the Lotka-Volterra model to predict population dynamics of COVID-19, Parabola. Vol. 59, Issue 1 (2023). 10.1016/0040-5809(73)90014-2F. J. Ayala, M. E. Gilpin And J. G. Ehrenfeld, Competition Between Species: Theoretical Models and Experimental Tests, Theoretical Populatfon Biology 4,(1973) 331-356. P. Waltman, Competition Models in Population Biology, SIAM, PA, (1983). J. Hofbauer, K. Sigmund. Evolutionary Games and Population Dynamics, Cambridge University Press (1998). C. Bergeron, Mathematical vision of the equilibrium of biodiversity (Original : Vision math´ematique sur l’´equilibre de la biodiversit´e). Bulletin AMQ, Vol. LV, No 4, (2015) 59. 10.1098/rspb.1998.0454M. Hernandez. Dynamics of transitions between population interactions : a nonlinear interaction α-function defined. Proceedings Royal Society of London B, 265 (1998)pp. 1433-1440. 10.1016/s0304-3800(03)00069-3Z. Zhang, Mutualism or Cooperation among Competitors promotes Coexistence and competitive Ability, Ecological Modelling, 164 (2003) 271-282. 10.1007/978-1-4757-4978-6A. Okubo and S. A. Levin, Diffusion and Ecological Problems : Modern Perspectives, second Edition, Interdisciplinary Applied Mathematics, vol. 14, Springer, New York, (2001). B. I. Camara, Complexity of prey-predator model dynamics with diffusion and applications (Complexit´e de dynamiques de mod`eles proie-pr´edateur avec diffusion et applications), PHD Thesis, Universit´e du Havre, (2009). https;//theses.hal.science/tel00460361/document.