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Computational and Mathematical Methods in Medicine
Volume 2019, Article ID 4849393, 7 pages
https://doi.org/10.1155/2019/4849393
Research Article

Analytical Solutions of a Modified Predator-Prey Model through a New Ecological Interaction

1Department of Mathematics, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia
2Mathematical Science Department, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Correspondence should be addressed to Noufe H. Aljahdaly; as.ude.uak@yladhajlahn

Received 22 May 2019; Revised 20 August 2019; Accepted 17 September 2019; Published 16 October 2019

Academic Editor: Manuel F. G. Penedo

Copyright © 2019 Noufe H. Aljahdaly and Manar A. Alqudah. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The predator-prey model is a common tool that researchers develop continuously to predict the dynamics of the animal population within a certain phenomenon. Due to the sexual interaction of the predator in the mating period, the males and females feed together on one or more preys. This scenario describes the ecological interaction between two predators and one prey. In this study, the nonlinear diffusive predator-prey model is presented where this type of interaction is accounted for. The influence of this interaction on the population of predators and preys is predicted through analytical solutions of the dynamical system. The solutions are obtained by using two reliable and simple methods and are presented in terms of hyperbolic functions. In addition, the biological relevance of the solutions is discussed.