Analisis dinamik model predator-prey tipe Gause dengan wabah penyakit pada prey

Rusdianto Ibrahim (Department of Mathematics, State University of Gorontalo, Indonesia)
Lailany Yahya (Department of Mathematics, State University of Gorontalo, Indonesia)
Emli Rahmi ([SINTA ID: 6039045] Department of Mathematics, State University of Gorontalo)
Resmawan Resmawan (Department of Mathematics, State University of Gorontalo, Indonesia)

Jambura Journal of Biomathematics (JJBM)
Volume 2, Issue 1: June 2021

This article studies the dynamics of a Gause-type predator-prey model with infectious disease in the prey. The constructed model is a deterministic model which assumes the prey is divided into two compartments i.e. susceptible prey and infected prey, and both of them are hunted by predator bilinearly. It is investigated that there exist five biological equilibrium points such as all population extinction point, infected prey and predator extinction point, infected prey extinction point, predator extinction point, and co-existence point. We find that all population extinction point always unstable while others are conditionally locally asymptotically stable. Numerical simulations, as well as the phase portraits, are given to support the analytical results.