scholarly journals Fractional Growth Model Applied to COVID-19 Data

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1915
Author(s):  
Fernando Alcántara-López ◽  
Carlos Fuentes ◽  
Carlos Chávez ◽  
Fernando Brambila-Paz ◽  
Antonio Quevedo
Keyword(s):  
Fractional Derivative ◽  
Growth Model ◽  
Inflection Point ◽  
Growth Models ◽  
Coefficient Of Determination ◽  
Proposed Model ◽  
Inflection Points

Growth models have been widely used to describe behavior in different areas of knowledge; among them the Logistics and Gompertz models, classified as models with a fixed inflection point, have been widely studied and applied. In the present work, a model is proposed that contains these growth models as extreme cases; this model is generalized by including the Caputo-type fractional derivative of order 0<β≤1, resulting in a Fractional Growth Model which could be classified as a growth model with non-fixed inflection point. Moreover, the proposed model is generalized to include multiple sigmoidal behaviors and thereby multiple inflection points. The models developed are applied to describe cumulative confirmed cases of COVID-19 in Mexico, US and Russia, obtaining an excellent adjustment corroborated by a coefficient of determination R2>0.999.

scholarly journals A Size-Perimeter Discrete Growth Model for Percolation Clusters

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Bendegúz Dezső Bak ◽  
Tamás Kalmár-Nagy
Keyword(s):  
Growth Model ◽  
Branching Process ◽  
Growth Models ◽  
Square Lattice ◽  
Cluster Growth ◽  
Invasion Percolation ◽  
Percolation Clusters ◽  
Proposed Model ◽  
Wide Range ◽  
The Mean

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

scholarly journals On the Emergence of Islands in Complex Networks

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
J. Esquivel-Gómez ◽  
R. E. Balderas-Navarro ◽  
P. D. Arjona-Villicaña ◽  
P. Castillo-Castillo ◽  
O. Rico-Trejo ◽  
...  
Keyword(s):  
Complex Networks ◽  
Size Distribution ◽  
Growth Model ◽  
Power Law ◽  
Degree Distribution ◽  
Growth Models ◽  
Island Size ◽  
First Case ◽  
Proposed Model ◽  
Power Law Function

Most growth models for complex networks consider networks comprising a single connected block or island, which contains all the nodes in the network. However, it has been demonstrated that some large complex networks have more than one island, with an island size distribution (Is) obeying a power-law function Is~s-α. This paper introduces a growth model that considers the emergence of islands as the network grows. The proposed model addresses the following two features: (i) the probability that a new island is generated decreases as the network grows and (ii) new islands are created with a constant probability at any stage of the growth. In the first case, the model produces an island size distribution that decays as a power-law Is~s-α with a fixed exponent α=1 and in-degree distribution that decays as a power-law Qi~i-γ with γ=2. When the second case is considered, the model describes island size and in-degree distributions that decay as a power-law with 2<α<∞ and 2<γ<∞, respectively.

Characterization of the Growth of Corrosion Defects on Energy Pipelines Using Bayesian Dynamic Linear Model

2014 ◽  
Author(s):  
S. Zhang ◽  
W. Zhou ◽  
S. Kariyawasam ◽  
M. Al-Amin
Keyword(s):  
Linear Model ◽  
Growth Model ◽  
Growth Models ◽  
Model Parameters ◽  
Dynamic Linear Model ◽  
Average Growth ◽  
Imperfect Data ◽  
Natural Gas Pipeline ◽  
Proposed Model ◽  
Corrosion Defects

This paper describes the use of the second-order polynomial dynamic linear model (DLM) to characterize the growth of the depth of corrosion defects on energy pipelines using imperfect data obtained from multiple high-resolution in-line inspections (ILI). The growth model is formulated by incorporating the general form of the measurement error (including the biases and random scattering error) of the ILI tools as well as the correlations between the random scattering errors of different tools. The temporal variability of the corrosion growth is captured by allowing the average growth rate between two successive inspections to vary with time. The Markov Chain Monte Carlo simulation is employed to carry out the Bayesian updating of the growth model and evaluate the posterior distributions of the model parameters. An example involving real ILI data collected from an in-service natural gas pipeline is employed to illustrate and validate the growth model. The analysis results show that the defect depths predicted by the proposed model agree well with the actual depths and are more accurate than those predicted by the Gamma process-based growth models reported in the literature.

Dual Release Model to Evaluate Dissolution Profiles from Swellable Drug Polyelectrolyte Matrices

2020 ◽  
Vol 17 (6) ◽  
pp. 511-522 ◽  
Author(s):  
Alicia Graciela Cid ◽  
María Verónica Ramírez-Rigo ◽  
María Celeste Palena ◽  
Elio Emilio Gonzo ◽  
Alvaro Federico Jimenez-Kairuz ◽  
...  
Keyword(s):  
Experimental Data ◽  
Drug Release ◽  
Inflection Point ◽  
Release Profile ◽  
Experimental Point ◽  
Extended Model ◽  
Release Process ◽  
Proposed Model ◽  
Dual Release ◽  
Release Model

Background: Mathematical modeling in modified drug release is an important tool that allows predicting the release rate of drugs in their surrounding environment and elucidates the transport mechanisms involved in the process. Objective: The aim of this work was to develop a mathematical model that allows evaluating the release profile of drugs from polymeric carriers in which the swelling phenomenon is present. Methods: Swellable matrices based on ionic complexes of alginic acid or carboxymethylcellulose with ciprofloxacin were prepared and the effect of adding the polymer sodium salt on the swelling process and the drug release was evaluated. Experimental data from the ciprofloxacin release profiles were mathematically adjusted, considering the mechanisms involved in each stage of the release process. Results: A proposed model, named “Dual Release” model, was able to properly fit the experimental data of matrices presenting the swelling phenomenon, characterized by an inflection point in their release profile. This entails applying the extended model of Korsmeyer-Peppas to estimate the percentage of drug released from the first experimental point up to the inflection point and then a model called Lumped until the final time, allowing to adequately represent the complete range of the drug release profile. Different parameters of pharmaceutical relevance were calculated using the proposed model to compare the profiles of the studied matrices. Conclusion: The “Dual Release” model proposed in this article can be used to predict the behavior of complex systems in which different mechanisms are involved in the release process.

scholarly journals Modeling Population Spatial-Temporal Distribution Using Taxis Origin and Destination Data

2021 ◽  
Vol 13 (7) ◽  
pp. 3727
Author(s):  
Fatema Rahimi ◽  
Abolghasem Sadeghi-Niaraki ◽  
Mostafa Ghodousi ◽  
Soo-Mi Choi
Keyword(s):  
Regression Analysis ◽  
Mean Squared Error ◽  
Population Distribution ◽  
Temporal Distribution ◽  
Coefficient Of Determination ◽  
Temporal Modeling ◽  
Location Data ◽  
Time Period ◽  
Proposed Model

During dangerous circumstances, knowledge about population distribution is essential for urban infrastructure architecture, policy-making, and urban planning with the best Spatial-temporal resolution. The spatial-temporal modeling of the population distribution of the case study was investigated in the present study. In this regard, the number of generated trips and absorbed trips using the taxis pick-up and drop-off location data was calculated first, and the census population was then allocated to each neighborhood. Finally, the Spatial-temporal distribution of the population was calculated using the developed model. In order to evaluate the model, a regression analysis between the census population and the predicted population for the time period between 21:00 to 23:00 was used. Based on the calculation of the number of generated and the absorbed trips, it showed a different spatial distribution for different hours in one day. The spatial pattern of the population distribution during the day was different from the population distribution during the night. The coefficient of determination of the regression analysis for the model (R2) was 0.9998, and the mean squared error was 10.78. The regression analysis showed that the model works well for the nighttime population at the neighborhood level, so the proposed model will be suitable for the day time population.

scholarly journals Comparison of growth models to describe growth from birth to 6 years in a Beninese cohort of children with repeated measurements

BMJ Open ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. e035785
Author(s):  
Shukrullah Ahmadi ◽  
Florence Bodeau-Livinec ◽  
Roméo Zoumenou ◽  
André Garcia ◽  
David Courtin ◽  
...  
Keyword(s):  
Growth Model ◽  
Goodness Of Fit ◽  
Growth Models ◽  
Information Criterion ◽  
Height Growth ◽  
Sub Saharan Africa ◽  
Individual Growth ◽  
Secondary Outcome ◽  
Growth Trajectories ◽  
Best Fitting

ObjectiveTo select a growth model that best describes individual growth trajectories of children and to present some growth characteristics of this population.SettingsParticipants were selected from a prospective cohort conducted in three health centres (Allada, Sekou and Attogon) in a semirural region of Benin, sub-Saharan Africa.ParticipantsChildren aged 0 to 6 years were recruited in a cohort study with at least two valid height and weight measurements included (n=961).Primary and secondary outcome measuresThis study compared the goodness-of-fit of three structural growth models (Jenss-Bayley, Reed and a newly adapted version of the Gompertz growth model) on longitudinal weight and height growth data of boys and girls. The goodness-of-fit of the models was assessed using residual distribution over age and compared with the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The best-fitting model allowed estimating mean weight and height growth trajectories, individual growth and growth velocities. Underweight, stunting and wasting were also estimated at age 6 years.ResultsThe three models were able to fit well both weight and height data. The Jenss-Bayley model presented the best fit for weight and height, both in boys and girls. Mean height growth trajectories were identical in shape and direction for boys and girls while the mean weight growth curve of girls fell slightly below the curve of boys after neonatal life. Finally, 35%, 27.7% and 8% of boys; and 34%, 38.4% and 4% of girls were estimated to be underweight, wasted and stunted at age 6 years, respectively.ConclusionThe growth parameters of the best-fitting Jenss-Bayley model can be used to describe growth trajectories and study their determinants.

scholarly journals Comparative Study of Ground Measured, Satellite-Derived, and Estimated Global Solar Radiation Data in Nigeria

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Boluwaji M. Olomiyesan ◽  
Onyedi D. Oyedum
Keyword(s):  
Solar Radiation ◽  
Comparative Study ◽  
Global Radiation ◽  
Statistical Error ◽  
Global Solar Radiation ◽  
Coefficient Of Determination ◽  
Mean Bias Error ◽  
Percentage Error ◽  
Radiation Data ◽  
Proposed Model

In this study, the performance of three global solar radiation models and the accuracy of global solar radiation data derived from three sources were compared. Twenty-two years (1984–2005) of surface meteorological data consisting of monthly mean daily sunshine duration, minimum and maximum temperatures, and global solar radiation collected from the Nigerian Meteorological (NIMET) Agency, Oshodi, Lagos, and the National Aeronautics Space Agency (NASA) for three locations in North-Western region of Nigeria were used. A new model incorporating Garcia model into Angstrom-Prescott model was proposed for estimating global radiation in Nigeria. The performances of the models used were determined by using mean bias error (MBE), mean percentage error (MPE), root mean square error (RMSE), and coefficient of determination (R2). Based on the statistical error indices, the proposed model was found to have the best accuracy with the least RMSE values (0.376 for Sokoto, 0.463 for Kaduna, and 0.449 for Kano) and highest coefficient of determination, R2 values of 0.922, 0.938, and 0.961 for Sokoto, Kano, and Kaduna, respectively. Also, the comparative study result indicates that the estimated global radiation from the proposed model has a better error range and fits the ground measured data better than the satellite-derived data.

scholarly journals Resistance behaviour of carbon fibre-reinforced polymers subjected to lightning strikes: Experimental investigation and application

2019 ◽  
Vol 28 ◽  
pp. 2633366X1989227 ◽  
Author(s):  
Jian Chen ◽  
Zhengcai Fu ◽  
Yang Zhao
Keyword(s):  
Carbon Fibre ◽  
Surface Resistance ◽  
Inflection Point ◽  
Front Surface ◽  
Resistance Change ◽  
Reinforced Polymers ◽  
Change Rate ◽  
Lightning Strikes ◽  
Inflection Points ◽  
Carbon Fibre Reinforced Polymers

It is difficult to monitor lightning damage to carbon fibre-reinforced polymers (CFRPs) online. This work experimentally investigates the changes associated with the electrical resistance of CFRPs subjected to lightning strikes. Two kinds of simulated lightning currents with different amplitudes in the range of 10–80 kA were injected into the CFRP samples. By measuring and comparing the changes in the struck-side (front) surface resistance, the surface resistance of the side opposite to the struck-side (back) and the oblique resistance of each sample before and after the lightning strike, it was observed that inflection points exist in the curve of the resistance change rate. The resistance decreases with increasing peak currents before the inflection point and increases when the peak current goes beyond the inflection point. The change rate of the front surface resistance is more sensitive to the lightning damage than are those of the back surface resistance and the oblique resistance. Different simulated lightning currents have approximately the same action integrals at the inflection points of resistance change rate. The characteristics indicate that resistance change detection could be a possible method for the online monitoring of CFRP lightning damage.

scholarly journals Optimization Method for Forecasting Confirmed Cases of COVID-19 in China

2020 ◽  
Vol 9 (3) ◽  
pp. 674 ◽  
Author(s):  
Mohammed A. A. Al-qaness ◽  
Ahmed A. Ewees ◽  
Hong Fan ◽  
Mohamed Abd El Aziz
Keyword(s):  
Relative Error ◽  
Computing Time ◽  
World Health ◽  
Coefficient Of Determination ◽  
Flower Pollination Algorithm ◽  
Percentage Error ◽  
Anfis Model ◽  
Local Optima ◽  
Inference System ◽  
Proposed Model

In December 2019, a novel coronavirus, called COVID-19, was discovered in Wuhan, China, and has spread to different cities in China as well as to 24 other countries. The number of confirmed cases is increasing daily and reached 34,598 on 8 February 2020. In the current study, we present a new forecasting model to estimate and forecast the number of confirmed cases of COVID-19 in the upcoming ten days based on the previously confirmed cases recorded in China. The proposed model is an improved adaptive neuro-fuzzy inference system (ANFIS) using an enhanced flower pollination algorithm (FPA) by using the salp swarm algorithm (SSA). In general, SSA is employed to improve FPA to avoid its drawbacks (i.e., getting trapped at the local optima). The main idea of the proposed model, called FPASSA-ANFIS, is to improve the performance of ANFIS by determining the parameters of ANFIS using FPASSA. The FPASSA-ANFIS model is evaluated using the World Health Organization (WHO) official data of the outbreak of the COVID-19 to forecast the confirmed cases of the upcoming ten days. More so, the FPASSA-ANFIS model is compared to several existing models, and it showed better performance in terms of Mean Absolute Percentage Error (MAPE), Root Mean Squared Relative Error (RMSRE), Root Mean Squared Relative Error (RMSRE), coefficient of determination ( R 2 ), and computing time. Furthermore, we tested the proposed model using two different datasets of weekly influenza confirmed cases in two countries, namely the USA and China. The outcomes also showed good performances.

Prediction of Design Hourly Volume on Rural Roads

2020 ◽  
pp. 036119812096556
Author(s):  
Miloš Petković ◽  
Vladan Tubić ◽  
Nemanja Stepanović
Keyword(s):  
Coefficient Of Determination ◽  
Rural Roads ◽  
The Road ◽  
Annual Average Daily Traffic ◽  
Proposed Model ◽  
Traffic Volumes ◽  
Implementation Costs ◽  
On The Road ◽  
Predicted Values ◽  
Design Hourly Volume

Design hourly volume (DHV) represents one of the most significant parameters in the procedures of developing and evaluating road designs. DHV values can be accurately and precisely calculated only on the road sections with the implemented automatic traffic counters (ATCs) which constantly monitor the traffic volume. Unfortunately, many road sections do not contain ATCs primarily because of the implementation costs. Consequently, for many years, the DHV values have been defined on the basis of occasional counting and the factors related to traffic flow variability over time. However, it has been determined that this approach has significant limitations and that the predicted values considerably deviate from the actual values. Therefore, the main objective of this paper is to develop a model which will enable DHV prediction on rural roads in cases of insufficient data. The suggested model is based on the correlation between DHVs and the parameters defining the characteristics of traffic flows, that is, the relationship between the traffic volumes on design working days and non-working days, and annual average daily traffic. The results of the conducted research indicate that the application of the proposed model enables the prediction of DHV values with a significant level of data accuracy and reliability. The coefficient of determination (R2) shows that more than 98% of the variance of the calculated DHVs was explained by the observed DHV values, while the mean error ranged from 4.86% to 7.84% depending on the number of hours for which DHV was predicted.

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