Partial Rank Correlation

Biometrika ◽  
1942 ◽  
Vol 32 (3/4) ◽  
pp. 277 ◽  
Author(s):  
M. G. Kendall
Keyword(s):  
Rank Correlation ◽  
Partial Rank Correlation

Note on Use of phi as a Simplified Partial Rank Correlation Coefficient

1966 ◽  
Vol 18 (3) ◽  
pp. 973-974 ◽  
Author(s):  
Richard W. Johnson
Keyword(s):  
Correlation Coefficient ◽  
Rank Correlation ◽  
Partial Rank Correlation

Use of phi as a simplified partial rank correlation coefficient is described and illustrated.

scholarly journals Quantifying the dose-dependent impact of intracellular amyloid beta in a mathematical model of calcium regulation in xenopus oocyte

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0246116
Author(s):  
Joseph Minicucci ◽  
Molly Alfond ◽  
Angelo Demuro ◽  
David Gerberry ◽  
Joe Latulippe
Keyword(s):  
Mathematical Model ◽  
Amyloid Beta ◽  
Rank Correlation ◽  
Correlation Coefficients ◽  
Dependent Manner ◽  
Partial Rank Correlation ◽  
Dose Dependent ◽  
Detrimental Impact ◽  
Oligomeric Forms

Alzheimer’s disease (AD) is a devastating illness affecting over 40 million people worldwide. Intraneuronal rise of amyloid beta in its oligomeric forms (iAβOs), has been linked to the pathogenesis of AD by disrupting cytosolic Ca2+ homeostasis. However, the specific mechanisms of action are still under debate and intense effort is ongoing to improve our understanding of the crucial steps involved in the mechanisms of AβOs toxicity. We report the development of a mathematical model describing a proposed mechanism by which stimulation of Phospholipase C (PLC) by iAβO, triggers production of IP3 with consequent abnormal release of Ca2+ from the endoplasmic reticulum (ER) through activation of IP3 receptor (IP3R) Ca2+ channels. After validating the model using experimental data, we quantify the effects of intracellular rise in iAβOs on model solutions. Our model validates a dose-dependent influence of iAβOs on IP3-mediated Ca2+ signaling. We investigate Ca2+ signaling patterns for small and large iAβOs doses and study the role of various parameters on Ca2+ signals. Uncertainty quantification and partial rank correlation coefficients are used to better understand how the model behaves under various parameter regimes. Our model predicts that iAβO alter IP3R sensitivity to IP3 for large doses. Our analysis also shows that the upstream production of IP3 can influence Aβ-driven solution patterns in a dose-dependent manner. Model results illustrate and confirm the detrimental impact of iAβOs on IP3 signaling.

scholarly journals Stability and global sensitivity analysis of the transmission dynamics of malaria with relapse and ignorant infected humans

2022 ◽  
Author(s):  
Yves Tinda Mangongo ◽  
Joseph-Désiré Kyemba Bukweli ◽  
Justin Dupar Busili Kampempe ◽  
Rostin Matendo Mabela ◽  
Justin Manango Wazute Munganga
Keyword(s):  
Sensitivity Analysis ◽  
Recovery Rate ◽  
Global Sensitivity Analysis ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Transmission Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Global Sensitivity ◽  
Partial Rank Correlation

Abstract In this paper we present a more realistic mathematical model for the transmission dynamics of malaria by extending the classical SEIRS scheme and the model of Hai-Feng Huo and Guang-Ming Qiu [21] by adding the ignorant infected humans compartment. We analyze the global asymptotically stabilities of the model by the use of the basic reproduction number R_0 and we prove that when R_0≦1, the disease-free equilibrium is globally asymptotically stable. That is malaria dies out in the population. When R_0>1, there exists a co-existing unique endemic equilibrium which is globally asymptotically stable. The global sensitivity analysis have been done through the partial rank correlation coefficient using the samples generated by the use of latin hypercube sampling method and shows that the most influence parameters in the spread of malaria are the proportion θ of infectious humans who recover and the recovery rate γ of infectious humans. In order to eradicate malaria, we have to decrease the number of ignorant infected humans by testing peoples and treat them. Numerical simulations show that malaria can be also controlled or eradicated by increasing the recovery rate γ of infectious humans, decreasing the number of ignorant infected humans and decreasing the average number n of mosquito bites.

scholarly journals Mathematical Modeling to Estimate the Reproductive Number and the Outbreak Size of COVID-19: The case of India and the World

2020 ◽  
Author(s):  
Durgesh Nandini Sinha
Keyword(s):  
Mathematical Model ◽  
Reproduction Number ◽  
Model Fitting ◽  
Rank Correlation ◽  
Latin Hypercube Sampling ◽  
Reproductive Number ◽  
Global Pandemic ◽  
The World ◽  
Partial Rank Correlation ◽  
Coefficient Method

Abstract Coronavirus disease (COVID-19) has become a global pandemic with more than 218,000 deaths in 211 different countries around the world. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the virus responsible for this deadliest disease. This paper describes a mathematical model for India, a country with the second highest population in the world with an extremely high population density of about 464 people per km2. This disease has multiphasic actions and reaction mode and our model SEIAQIm is based on six compartmental groups in the form of susceptible, exposed, infectious, asymptomatic, quarantine, and recovered immune factions. Latin Hypercube Sampling Partial Rank Correlation Coefficient method was used for the data analysis and model fitting. According to our model, India would reach its basic reproduction number R0=0.97 on May 14, 2020 with a total number of 73,800 estimated cases. Further, this study also equates the world's situation using the same model system and predicts by May 7, 2020 with a total number of 3,772,000 estimated confirmed cases. Moreover, the current mathematical model highlights the importance of social distancing as an effective method of containing spread of COVID-19.

scholarly journals Modelling the transmission dynamics of COVID-19 in six high burden countries

2020 ◽  
Author(s):  
Azizur Rahman ◽  
Md Abdul Kuddus
Keyword(s):  
Disease Transmission ◽  
Compartmental Model ◽  
Transmission Rate ◽  
Control Strategies ◽  
Rank Correlation ◽  
Decision Makers ◽  
High Burden ◽  
Epidemic Period ◽  
Partial Rank Correlation ◽  
Coefficient Method

AbstractThe new coronavirus disease, officially known as COVID-19, originated in China in 2019 and has since spread around the globe. We presented a modified Susceptible-Latent-Infected-Removed (SLIR) compartmental model of COVID-19 disease transmission with nonlinear incidence during the epidemic period. We provided the model calibration to estimate parameters with day wise corona virus (COVID-19) data i.e. reported cases by worldometer from the period of 15th February to 30th March, 2020 in six high burden countries including Australia, Italy, Spain, USA, UK and Canada. We estimate transmission rates for each countries and found that the highest transmission rate country in Spain, which may be increase the new cases and deaths in Spain than the other countries. Sensitivity analysis was used to identify the most important parameters through the partial rank correlation coefficient method. We found that the transmission rate of COVID-19 had the largest influence on the prevalence. We also provides the prediction of new cases in COVID-19 until May 18, 2020 using the developed model and recommends, control strategies of COVID-19. The information that we generated from this study would be useful to the decision makers of various organizations across the world including the Ministry of Health in Australia, Italy, Spain, USA, UK and Canada to control COVID-19.

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