Open AccessThe Dynamics of a Discrete Fractional-Order Logistic Growth Model with Infectious Disease
Author(s) -
Hasan S. Panigoro,
Emli Rahmi
Publication year - 2021
Publication title -
contemporary mathematics and applications
Language(s) - English
Resource type - Journals
ISSN - 2686-5564
DOI - 10.20473/conmatha.v3i1.26938
Subject(s) - mathematics , bifurcation , logistic function , chaotic , piecewise , discrete time and continuous time , order (exchange) , nonlinear system , statistical physics , mathematical analysis , statistics , computer science , physics , economics , finance , quantum mechanics , artificial intelligence
In this paper, we study the dynamics of a discrete fractional-order logistic growth model with infectious disease. We obtain the discrete model by applying the piecewise constant arguments to the fractional-order model. This model contains three fixed points namely the origin point, the disease-free point, and the endemic point. We confirm that the origin point is always exists and unstable, the disease-free point is always exists and conditionally stable, and the endemic point is conditionally exists and stable. We also investigate the existence of forward, period-doubling, and Neimark-Sacker bifurcation. The numerical simulations are also presented to confirm the analytical results. We also show numerically the existence of period-3 solution which leads to the occurrence of chaotic behavior.