scholarly journals Fitting the Portuguese population from 1850 to 2010 to a logistic growth model

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Carlos Francisco Barbosa ◽  
Michael Rothwell
Keyword(s):  
Growth Rate ◽  
Growth Model ◽  
Separation Of Variables ◽  
Logistic Growth ◽  
Logistic Curve ◽  
Portuguese Population ◽  
Qualitative And Quantitative ◽  
Logistic Growth Model ◽  
Qualitative And Quantitative Study

This work explores how the Portuguese population fits a logistic growth model. The present study is divided into two main sections. The first one consists on the qualitative and quantitative study of the logistic equation. Qualitatively, I will look at various aspects of the differential equation, such as the equilibria and their stability and possible inflections of solutions. Quantitatively, I will use the separation of variables to find explicit solutions. Given the lack of accuracy in the linear fitting to the proportional growth rate against the population, in second chapter, I attempted a polynomial trendline fitting to the growth rate against the population. This led the focus to creating an adapted form of the logistic curve that fits the Portuguese population from 1850 to 2010. With a certain degree of accuracy, the adapted form of the logistic growth model fits the Portuguese population in the period mentioned.

scholarly journals Reconstructing and Forecasting the COVID-19 Epidemic in the US Using a 5-Parameter Logistic Growth Model

2020 ◽  
Author(s):  
Ding-Geng Chen ◽  
Xinguang Chen ◽  
Jenny Ke Chen
Keyword(s):  
Growth Rate ◽  
Growth Model ◽  
Early Period ◽  
Logistic Growth ◽  
Daily Growth ◽  
First Case ◽  
The Us ◽  
Logistic Growth Model ◽  
Using Data ◽  
Public Policy Decisions

Abstract Background: Many studies have modeled and predicted the epidemic of COVID-19 in the US using data that starts from the first reported cases. However, because of the shortage of test services to detect the infected, this approach is subject to error due to under-detection in the early period of the epidemic. We attempted a new approach to overcome this limitation and to provide data supporting the public policy decisions against the life-threatening COVID-19 epidemic.Methods: Documented data by CDC were used, including daily new and cumulative cases of confirmed COVID-19 in the US from January 22 to April 6, 2020. A 5-parameter logistic growth model was used to reconstruct the epidemic. Instead of all data in the whole study period, we fitted data in a 2-week window from March 21 to April 4 (approximately one incubation period) during which massive testing services were in position. With parameters obtained from the modeling, we reconstructed and predicted the epidemic and evaluated the under-detection.Results: The data fit the model satisfactorily. The estimated daily growth rate was 16.8% (95% CI: 15.95%, 17.76%) overall, with 4 consecutive days having a doubling growth rate. Based on the modeling result, the tipping point for new cases to decline will be on April 7 th , 2020, with 32,860 new cases. By the end of the epidemic, a total of 792,548 (95% CI: 789,162-795,934) will be infected. Based on the model, a total of 12,029 cases were not detected from the first case from January 22 to April 4.Conclusions: Study findings suggest the usage of a 5-parameter logistic growth model with reliable data that comes from a specified window period, where governmental interventions are appropriately implemented. In addition to informing decision-making, this model adds one tool for use to capture the underlying COVID-19 epidemic caused by a novel pathogen.

scholarly journals Penerapan Persamaan Diferensial Verhulst dalam Menentukan Proyeksi Penduduk di Kabupaten Tulungagung

2018 ◽  
Vol 7 (2) ◽  
pp. 87-102
Author(s):  
Dewi Anggreini
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Growth Model ◽  
Carrying Capacity ◽  
Applied Mathematics ◽  
Logistic Growth ◽  
Second Stage ◽  
The Subject ◽  
Logistic Growth Model ◽  
To Come

Penelitian ini bertujuan menentukan proyeksi pertumbuhan penduduk di Kabupaten Tulungagung provinsi Jawa Timur dengan model persamaan diferensial Verhulst berdasarkan laju pertumbuhan dan daya tampung (carrying capacity). Target khusus dari hasil penelitian ini adalah model pertumbuhan logistik bisa digunakan sebagai alat untuk mengetahui proyeksi pertumbuhan penduduk berdasarkan laju pertumbuhan dan daya tampung dibeberapa daerah di Indonesia. Metode riset yang digunakan pada tahap pertama adalah menentukan subjek penelitian dan tahap Kedua adalah (1) mengumpulkan data penelitian (2) analisis data dan terakhir menarik kesimpulan. Data penelitian ini diperoleh dari BPS Kabupaten Tulungagung yaitu jumlah penduduk dari tahun 2010-2016. Hasil Penelitian menunjukkan bahwa: 1) Besarnya nilai carrying capacity yang membatasi penduduk di Kabupaten Tulungagung adalah sebesar 1.089.103,3. 2) Laju pertumbuhan intrinsik penduduk di kabupaten Tulungagung dengan menggunakan Model pertumbuhan logistik adalah sebesar r = 0,07480. 3) Jumlah penduduk di Kabupaten Tulungagung pada tahun 2025 dari hasil estimasi menggunakan model pertumbuhan logistik adalah sebesar 1.055.578 jiwa. 4) Proyeksi jumlah penduduk di Kabupaten Tulungagung  lebih tepat menggunakan model logistik I dengan persamaannya . Penelitian ini diharapkan dapat bermanfaat bagi semua pihak khususnya pada bidang matematika terapan serta metode dalam  menghitung pertumbuhan populasi di suatu daerah pada periode yang akan datang. [This study aims to determine the projected population growth in Tulungagung Regency of East Java province with a model of Verhulst differential equations based on growth rate and carrying capacity. The specific target of this research is logistic growth model can be used as a tool to know the projection of population growth based on growth rate and capacity in some regions in Indonesia. Research methods used in the first stage is to determine the subject of research and the second stage is (1) collect research data (2) data analysis and last draw conclusions. The data of this research is obtained from BPS of Tulungagung Regency that is population from 2010-2016. The results showed that: 1) The amount of carrying capacity that limits the population in Tulungagung Regency is equal 1.089.103,3. 2) The intrinsic growth rate of the population in Tulungagung district using the logistic growth model is r = 0,07480 3) The population in Tulungagung District in 2025 from the estimation using the logistic growth model is 1.055.578 soul, 4) The projection of population in Tulungagung is more appropriate using the logistic model I with the equation .  This study is expected to be useful for all parties, especially in the field of applied mathematics and methods in calculating population growth in an area in the period to come.]

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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