scholarly journals The Dynamics of a Discrete Fractional-Order Logistic Growth Model with Infectious Disease

2021 ◽  
Vol 3 (1) ◽  
pp. 1
Author(s):  
Hasan S Panigoro ◽  
Emli Rahmi
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Growth Model ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Logistic Growth ◽  
Piecewise Constant ◽  
Logistic Growth Model ◽  
Disease Free ◽  
Origin Point

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.

scholarly journals Global stability of a fractional-order logistic growth model with infectious disease

2020 ◽  
Vol 1 (2) ◽  
pp. 49-56
Author(s):  
Hasan S. Panigoro ◽  
Emli Rahmi
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Growth Model ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Population Extinction ◽  
Logistic Growth Model ◽  
Extinction Point

Infectious disease has an influence on the density of a population. In this paper, a fractional-order logistic growth model with infectious disease is formulated. The population grows logistically and divided into two compartments i.e. susceptible and infected populations. We start by investigating the existence, uniqueness, non-negativity, and boundedness of solutions. Furthermore, we show that the model has three equilibrium points namely the population extinction point, the disease-free point, and the endemic point. The population extinction point is always a saddle point while others are conditionally asymptotically stable. For the non-trivial equilibrium points, we successfully show that the local and global asymptotic stability have the similar properties. Especially, when the endemic point exists, it is always globally asymptotically stable. We also show the existence of forward bifurcation in our model. We portray some numerical simulations consist of the phase portraits, time series, and a bifurcation diagram to validate the analytical findings.

scholarly journals Forecasting the Stability of COVID-19 on Indian Dataset with Prophet Logistic Growth Model 

2020 ◽  
Author(s):  
Nishtha Phutela ◽  
Arushi G Bakshi ◽  
Sunil Gupta ◽  
Goldie Gabrani
Keyword(s):  
Infectious Disease ◽  
Mathematical Models ◽  
Growth Model ◽  
Logistic Growth ◽  
The World ◽  
Logistic Growth Model ◽  
The Stability

Abstract Recently COVID-2019, a highly infectious disease has been declared as Pandemic by WHO, and since then the researchers all over the world are making attempts to predict the likely progression of this pandemic using various mathematical models. In this paper, we are using logistic growth model to find out the stability of this pandemic and Prophet Model to forecast the total number of confirmed cases that would be caused by COVID-19 in India.

scholarly journals Extended logistic growth model for heterogeneous populations

2017 ◽  
Author(s):  
Wang Jin ◽  
Scott W McCue ◽  
Matthew J Simpson
Keyword(s):  
Cell Proliferation ◽  
Growth Model ◽  
Numerical Solutions ◽  
Cellular Level ◽  
Logistic Growth ◽  
Logistic Growth Model ◽  
Living Tissues ◽  
Discrete Mathematical Model ◽  
The Continuum

AbstractCell proliferation is the most important cellular-level mechanism responsible for regulating cell population dynamics in living tissues. Modern experimental procedures show that the proliferation rates of individual cells can vary significantly within the same cell line. However, in the mathematical biology literature, cell proliferation is typically modelled using a classical logistic equation which neglects variations in the proliferation rate. In this work, we consider a discrete mathematical model of cell migration and cell proliferation, modulated by volume exclusion (crowding) effects, with variable rates of proliferation across the total population. We refer to this variability as heterogeneity. Constructing the continuum limit of the discrete model leads to a generalisation of the classical logistic growth model. Comparing numerical solutions of the model to averaged data from discrete simulations shows that the new model captures the key features of the discrete process. Applying the extended logistic model to simulate a proliferation assay using rates from recent experimental literature shows that neglecting the role of heterogeneity can, at times, lead to misleading results.

A Neoclassical Growth Model for Population Dynamics in a Homogeneous Habitat

2001 ◽  
Author(s):  
Peter Vadasz ◽  
Alisa S. Vadasz
Keyword(s):  
Experimental Data ◽  
Growth Model ◽  
Logistic Growth ◽  
Lag Phase ◽  
Growth Stages ◽  
Initial Growth ◽  
Neoclassical Model ◽  
Wide Range ◽  
Logistic Growth Model ◽  
Special Case

Abstract A neoclassical model is proposed for the growth of cell and other populations in a homogeneous habitat. The model extends on the Logistic Growth Model (LGM) in a non-trivial way in order to address the cases where the Logistic Growth Model (LGM) fails short in recovering qualitative as well as quantitative features that appear in experimental data. These features include in some cases overshooting and oscillations, in others the existence of a “Lag Phase” at the initial growth stages, as well as an inflection point in the “In curve” of the population size. The proposed neoclassical model recovers also the Logistic Growth Curve as a special case. Comparisons of the solutions obtained from the proposed neoclassical model with experimental data confirm its quantitative validity, as well as its ability to recover a wide range of qualitative features captured in experiments.

scholarly journals Outbreak analysis with a logistic growth model shows COVID-19 suppression dynamics in China

PLoS ONE ◽  
2020 ◽  
Vol 15 (6) ◽  
pp. e0235247 ◽  
Author(s):  
Yi Zou ◽  
Stephen Pan ◽  
Peng Zhao ◽  
Lei Han ◽  
Xiaoxiang Wang ◽  
...  
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Logistic Growth Model

scholarly journals Extended logistic growth model for heterogeneous populations

2018 ◽  
Vol 445 ◽  
pp. 51-61 ◽  
Author(s):  
Wang Jin ◽  
Scott W. McCue ◽  
Matthew J. Simpson
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Heterogeneous Populations ◽  
Logistic Growth Model
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