© 2020 Scholars Journal of Physics, Mathematics and Statistics | Published by SAS Publishers, India 192
Scholars Journal of Physics, Mathematics and Statistics
Abbreviated Key Title: Sch J Phys Math Stat
ISSN 2393-8056 (Print) | ISSN 2393-8064 (Online)
Journal homepage: https://saspublishers.com/sjpms/
Improvement and Application of Logistic Growth Model
Lan Xiao
*
, Yanqiu Chen
College of Applied Mathematics, Chengdu University of Information Technology Chengdu, Sichuan 610225, P. R. China
DOI: 10.36347/sjpms.2020.v07i09.002 | Received: 07.09.2020 | Accepted: 15.09.2020 | Published: 19.09.2020
*Corresponding author: Lan Xiao
Abstract Review Article
Logistic growth model, as an important mathematical model to describe population or population changes, is now
widely used in many fields. Researchers found that the problems involved cover many disciplines such as
mathematics, physics, medicine, and biology. Therefore, the Logistic growth model has a strong application
background and practical significance. This paper improves the logistic growth model that introduces harvest items,
and applies the improved model to population forecasting. And with the help of mathematical software and the
principle of least squares method to estimate the parameters of the improved model, the curve fitting comparison
verifies that the improved model can achieve better results.
Keywords: Logistic growth model, Improvement, mathematics, physics, medicine.
Copyright @ 2020: This is an open-access article distributed under the terms of the Creative Commons Attribution license which permits unrestricted
use, distribution, and reproduction in any medium for non-commercial use (NonCommercial, or CC-BY-NC) provided the original author and source
are credited.
INTRODUCTION
Logistic Model Background and Research Status
The Logistic model was proposed by the
Dutch mathematical biologist verhulst [1] in 1838. It is
a commonly used model in biology. It describes a
population growth law. The population initially grows
in an accelerated manner. When a threshold is reached,
the growth rate will decrease, and finally the growth
rate will drop to zero and stop growing. At the same
time, the Logistic growth model is often used to
confirm the interaction (such as complementarity,
competition) between populations. In actual research,
there are continuous and discrete logistic models. In
order to improve the accuracy and practicability of the
Logistic growth model in predicting population
numbers, many scholars have improved the Logistic
growth model based on actual needs and promoted it to
be rewarding The form of the function item.
In the literature [2], Laham et al., improved the
Logistic model and used the model to formulate a fish
capture plan, that is, when fishing can achieve the
maximum profit without affecting the next stage of fish
growth. So the harvest function is introduced, and the
classic Logistic model.
, 0 , 0 , )
) (
1 )( (
) (
C r
C
t x
t rx
dt
t dx
……………………………….…. (1-1)
Amended to
, 0 , 0 , ) ( )
) (
1 )( (
) (
C r t H
C
t x
t rx
dt
t dx
………………………..… (1-2)
Where
) (t x represents the number of the
population at time
t ,
r represents the inherent growth
rate of the population (that is, the birth rate minus the
death rate),
C represents the environmental carrying
capacity, and
) (t H is the harvest function.
In 2016, Alfred [3] studied the capture strategy
of wrasse farming and discussed three types of harvest
growth models: