scholarly journals Logistic growth model and modified versions for the cumulative number of confirmed cases of COVID-19 in Saudi Arabia

2021 ◽  
Keyword(s):  
Saudi Arabia ◽  
Growth Model ◽  
Logistic Growth ◽  
Cumulative Number ◽  
Logistic Growth Model

scholarly journals COVID-19 outbreak in Mauritius: Logistic growth and SEIR modelling with quarantine and an effective reproduction number

2020 ◽  
Author(s):  
Antoine Gehin ◽  
Smita Goorah ◽  
Khemanand Moheeput ◽  
Satish Ramchurn
Keyword(s):  
Public Health ◽  
Growth Model ◽  
Reproduction Number ◽  
Control Measures ◽  
Logistic Growth ◽  
Cumulative Number ◽  
Public Health Response ◽  
The Public ◽  
Logistic Growth Model ◽  
Outbreak Size

SUMMARY Background and Objectives The island of Mauritius experienced a COVID-19 outbreak from mid-March to end April 2020. The first three cases were reported on March 18 (Day 1) and the last locally transmitted case occurred on April 26 (Day 40). An island confinement was imposed on March 20 followed by a sanitary curfew on March 23. Supermarkets were closed as from March 25 (Day 8). There were a total of 332 cases including 10 deaths from Day 1 to Day 41. Control of the outbreak depended heavily on contact tracing, testing, quarantine measures and the adoption of personal protective measures (PPMs) such as social distancing, the wearing of face masks and personal hygiene by Mauritius inhabitants. Our objectives were to model and understand the evolution of the Mauritius outbreak using mathematical analysis, a logistic growth model and an SEIR compartmental model with quarantine and a reverse sigmoid effective reproduction number and to relate the results to the public health control measures in Mauritius. Methods The daily reported cumulative number of cases in Mauritius were retrieved from the Worldometer website at https://www.worldometers.info/coronavirus/country/mauritius/. A susceptible-exposed-infectious-quarantined-removed (SEIQR) model was introduced and analytically integrated under the assumption that the daily incidence of infectious cases evolved as the derivative of the logistic growth function. The cumulative incidence data was fitted using a logistic growth model. The SEIQR model was integrated computationally with an effective reproduction number (R_e) varying in time according to a three-parameter reverse sigmoid model. Results were compared with the retrieved data and the parameters were optimised using the normalised root mean square error (NRMSE) as a comparative statistic. Findings A closed-form analytical solution was obtained for the time-dependence of the cumulative number of cases. For a small final outbreak size, the solution tends to a logistic growth. The cumulative number of cases was well described by the logistic growth model (NRMSE = 0.0276, R^2=0.9945) and by the SEIQR model (NRMSE = 0.0270, R^2=0.9952) with the optimal parameter values. The value of R_e on the day of the reopening of supermarkets (Day 16) was found to be approximately 1.6. Interpretation A mathematical basis has been obtained for using the logistic growth model to describe the time evolution of outbreaks with a small final outbreak size. The evolution of the outbreak in Mauritius was consistent with one modulated by a time-varying effective reproduction number resulting from the epidemic control measures implemented by Mauritius authorities and the PPMs adopted by Mauritius inhabitants. The value of R_e≈1.6 on the reopening of supermarkets on Day 16 was sufficient for the outbreak to grow to large-scale proportions in case the Mauritius population did not comply with the PPMs. However, the number of cases remained contained to a small number which is indicative of a significant contribution of the PPMs in the public health response to the COVID-19 outbreak in Mauritius.

scholarly journals Analysis and Prediction for Confirmed COVID-19 Cases in Czech Republic with Uncertain Logistic Growth Model

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2264
Author(s):  
Chunxiao Ding ◽  
Wenjian Liu
Keyword(s):  
Regression Analysis ◽  
Czech Republic ◽  
Growth Model ◽  
Hypothesis Test ◽  
Logistic Growth ◽  
Cumulative Number ◽  
Uncertain Variables ◽  
Stochastic Regression ◽  
Disturbance Term ◽  
Logistic Growth Model

This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

scholarly journals Using different epidemiological models to modeling the epidemic dynamics in Brazil

2020 ◽  
Author(s):  
Lucas Ravellys Pyrrho de Alcantara ◽  
Lucio Silva ◽  
Anderson Rodrigues de Almeida ◽  
Maira Galdino da Rocha Pitta ◽  
Artur Paiva Coutinho
Keyword(s):  
Growth Model ◽  
Logistic Growth ◽  
Cumulative Number ◽  
Mean Square ◽  
Epidemiological Models ◽  
Epidemic Dynamics ◽  
Absolute Relative Error ◽  
Logistic Growth Model ◽  
Richards Growth Model

In this paper we provide forecasts of the cumulative number of confirmed reported cases in Brazil, specifically in Pernambuco and Ceara, by using the generalized logistic growth model, the Richards growth model and Susceptible, Un-quanrantined infected, Quarantined infected, Confirmed infected (SUQC) phenomenological model. We rely on the Nash-Sutcliffe efficiency (NSE), root-mean-square error (RMSE) and mean absolute relative error (MARE) to quantify the quality of the models fits during the calibrationAll of these analyzes have been valid until the present date, April 14, 2020. The different models provide insights of our scenario predictions.

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
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