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Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III Firdiansyah, Adin Lazuardy
Jambura Journal of Mathematics Vol 3, No 1: January 2021
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

#### Abstract

In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases.Â  In the end, several numerical solutions are presented to check the analytical results.
Dynamics in two competing predators-one prey system with two types of Holling and fear effect Firdiansyah, Adin Lazuardy; Nurhidayati, Nurhidayati
Jambura Journal of Biomathematics (JJBM) Volume 2, Issue 2: December 2021
Publisher : Department of Mathematics, State University of Gorontalo

#### Abstract

In this article, it is formulated a predator-prey model of two predators consuming a single limited prey resource. On the other hand, two predators have to compete with each other for survival. The predation function for two predators is assumed to be different where one predator uses Holling type I while the other uses Holling type II. It is also assumed that the fear effect is considered in this model as indirect influence evoked by both predators. Non-negativity and boundedness is written to show the biological justification of the model. Here, it is found that the model has five equilibrium points existed under certain condition. We also perform the local stability analysis on the equilibrium points with three equilibrium points are stable under certain conditions and two equilibrium points are unstable. Hopf bifurcation is obtained by choosing the consumption rate of the second predator as the bifurcation parameter. In the last part, several numerical solutions are given to support the analysis results.
Dynamical of Ratio-Dependent Eco-epidemical Model with Prey Refuge Firdiansyah, Adin Lazuardy
CAUCHY Vol 6, No 4 (2021): CAUCHY: Jurnal Matematika Murni dan Aplikasi
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

#### Abstract

This paper discusses the dynamic analysis of three species in the eco-epidemiology model by considering the ratio-dependent function and prey refuge. The prey refuge is applied under the fact that infected prey has protection instincts that allow it to reduce predation risk. Here, we get the boundedness and three equilibrium points where are existence under certain conditions. In the model, three equilibrium points are locally asymptotically stable and one of the equilibrium points is globally asymptotically stable. We find that the system undergoes Hopf bifurcation around the interior equilibrium point by choosing Â as a bifurcation parameter. We also find a condition for uniform persistence. Finally, several simulations of numerical are performed not only to illustrate the analytical results but also to illustrate the effect of the prey refuge.Â Â  Â Â Â Â Â Â Â Â Â Â Â