scholarly journals A data first approach to modelling Covid-19

2020 ◽  
Author(s):  
Jayanti Prasad
Keyword(s):  
Reproduction Number ◽  
Model Fitting ◽  
Time Dependent ◽  
Primary Data ◽  
Contact Rate ◽  
Multiple Sources ◽  
Transmission Coefficients ◽  
Varying Coefficients ◽  
Step Procedure ◽  
Time Varying Coefficients

AbstractThe primary data for Covid-19 pandemic is in the form of time series for the number of confirmed, recovered and dead cases. This data is updated every day and is available for most countries from multiple sources such as [Gar20b, iD20]. In this work we present a two step procedure for model fitting to Covid-19 data. In the first step, time dependent transmission coefficients are constructed directly from the data and, in the second step, measures of those (minimum, maximum, mean, median etc.,) are used to set priors for fitting models to data. We call this approach a “data driven approach” or “data first approach”. This scheme is complementary to Bayesian approach and can be used with or without that for parameter estimation. We use the procedure to fit a set of SIR and SIRD models, with time dependent contact rate, to Covid-19 data for a set of most affected countries. We find that SIR and SIRD models with constant transmission coefficients cannot fit Covid-19 data for most countries (mainly because social distancing, lockdown etc., make those time dependent). We find that any time dependent contact rate decaying with time can help to fit SIR and SIRD models for most of the countries. We also present constraints on transmission coefficients and basic reproduction number , as well as effective reproduction number . The main contributions of our work are as follows. (1) presenting a two step procedure for model fitting to Covid-19 data (2) constraining transmission coefficients as well as and , for a set of countries and (3) releasing a python package PyCov19 [Pra20b] that can used to fit a class of compartmental models, with time varying coefficients, to Covid-19 data.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

scholarly journals Climatic responses to systematic time variations of parameters: a dynamical approach

2018 ◽  
Vol 25 (3) ◽  
pp. 649-658 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalized stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

scholarly journals COVID-19 epidemic scenarios into 2021 based on observed key superdispersion events

2021 ◽  
Author(s):  
Mario Santana-Cibrian ◽  
M. Adrian Acuña-Zegarra ◽  
Carlos E. Rodríguez Hernández-Vela ◽  
Jorge X. Velasco-Hernandez ◽  
Ramsés H. Mena
Keyword(s):  
Time Scale ◽  
Reproduction Number ◽  
Social Activity ◽  
Time Dependent ◽  
Contact Rate ◽  
Main Assumption ◽  
Effective Contact ◽  
Incidence And Mortality ◽  
The Status ◽  
Calendar Dates

Key high transmission dates for the year 2020 are used to create scenarios to model the evolution of the COVID-19 pandemic in several states of Mexico for 2021. These scenarios are obtained through the estimation of a time-dependent contact rate, where the main assumption is that the dynamic of the disease is heavily determined by the mobility and social activity of the population during holidays and other important calendar dates. First, changes in the effective contact rate on predetermined dates of 2020 are estimated. Then, using the instantaneous reproduction number to characterize the status of the epidemic (Rt ≈ 1, Rt > 1 or Rt < 1), this information is used to propose different scenarios for the number of cases and deaths for 2021. The main assumption is that the effective contact rate during 2021 will maintain a similar trend to that observed during 2020 on key calendar dates. All other conditions are assumed to remain constant in the time scale of the projections. The objective is to generate a range of scenarios that could be useful to evaluate the possible evolution of the epidemic and its likely impact on incidence and mortality.

scholarly journals Climatic responses to systematic time variations of parameters: A dynamical approach

2018 ◽  
Author(s):  
Catherine Nicolis
Keyword(s):  
Evolution Equations ◽  
Time Dependent ◽  
Time Varying ◽  
Climatic Response ◽  
Varying Coefficients ◽  
Classical Stability ◽  
Theoretical Predictions ◽  
Time Variations ◽  
Time Varying Coefficients ◽  
Climatic Responses

Abstract. The climatic response to time-dependent parameters is revisited from a nonlinear dynamics perspective. Some general trends are identified, based on a generalised stability criterion extending classical stability analysis to account for the presence of time-varying coefficients in the evolution equations of the system's variables. Theoretical predictions are validated by the results of numerical integration of the evolution equations of prototypical systems of relevance in atmospheric and climatic dynamics.

scholarly journals Estimating Survival Functions after Stcox with Time-varying Coefficients

2016 ◽  
Vol 16 (4) ◽  
pp. 867-879 ◽  
Author(s):  
Constantin Ruhe
Keyword(s):  
Proportional Hazards ◽  
Cox Model ◽  
Survival Function ◽  
Time Dependent ◽  
Time Varying ◽  
Survival Functions ◽  
Nonproportional Hazards ◽  
Varying Coefficients ◽  
Proportional Hazards Assumption ◽  
Time Varying Coefficients

In many applications of the Cox model, the proportional-hazards assumption is implausible. In these cases, the solution to nonproportional hazards usually consists of modeling the effect of the variable of interest and its interaction effect with some function of time. Although Stata provides a command to implement this interaction in stcox, it does not allow the typical visualizations using stcurve if stcox was estimated with the tvc() option. In this article, I provide a short workaround that estimates the survival function after stcox with time-dependent coefficients. I introduce and describe the scurve_tvc command, which automates this procedure and allows users to easily visualize survival functions for models with time-varying effects.

scholarly journals Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

2020 ◽  
Author(s):  
Marek Kochańczyk ◽  
Frederic Grabowski ◽  
Tomasz Lipniacki
Keyword(s):  
Reproduction Number ◽  
Exponential Phase ◽  
Time Dependent ◽  
Therapeutic Interventions ◽  
Contact Rate ◽  
Epidemic Spread ◽  
Early Exponential Phase ◽  
Contact Rates ◽  
Multiplication Coefficient

We constructed a simple Susceptible–Infected–Infectious–Excluded model of the spread of COVID-19. The model is parametrised only by the average incubation period, τ, and two rate parameters: contact rate, rC, and exclusion rate, rE. The rates can be manipulated by non-therapeutic interventions and determine the basic reproduction number, R = rC/rE, and, together with τ, the daily multiplication coefficient at the early exponential phase, β. Initial β determines the reduction of rC required to contain epidemic spread. In the long-term, we consider a scenario based on typical social behaviours, in which rC first decreases in response to a surge of daily new cases, forcing people to self-isolate, and then slowly increases when people gradually accept higher risk. Consequently, initial abrupt epidemic spread is followed by a plateau and slow regression. This scenario, although economically and socially devastating, will grant time to develop, produce, and distribute a vaccine, or at least limit daily cases to a manageable number.

COVID-19: Time-Dependent Effective Reproduction Number and Sub-notification Effect Estimation Modeling (Preprint)

2020 ◽  
Author(s):  
Eduardo Atem De Carvalho ◽  
Rogerio Atem De Carvalho
Keyword(s):  
New York ◽  
Reproduction Number ◽  
Moving Average ◽  
Real Data ◽  
Time Dependent ◽  
Initial Value ◽  
Health Authorities ◽  
Reproduction Numbers ◽  
Effect Estimation ◽  
The Impact

BACKGROUND Since the beginning of the COVID-19 pandemic, researchers and health authorities have sought to identify the different parameters that govern their infection and death cycles, in order to be able to make better decisions. In particular, a series of reproduction number estimation models have been presented, with different practical results. OBJECTIVE This article aims to present an effective and efficient model for estimating the Reproduction Number and to discuss the impacts of sub-notification on these calculations. METHODS The concept of Moving Average Method with Initial value (MAMI) is used, as well as a model for Rt, the Reproduction Number, is derived from experimental data. The models are applied to real data and their performance is presented. RESULTS Analyses on Rt and sub-notification effects for Germany, Italy, Sweden, United Kingdom, South Korea, and the State of New York are presented to show the performance of the methods here introduced. CONCLUSIONS We show that, with relatively simple mathematical tools, it is possible to obtain reliable values for time-dependent, incubation period-independent Reproduction Numbers (Rt). We also demonstrate that the impact of sub-notification is relatively low, after the initial phase of the epidemic cycle has passed.

scholarly journals The Impact of Big Data on Electronic Commerce in Profit Organisations in Saudi Arabia

2019 ◽  
Vol 10 (4) ◽  
pp. 106
Author(s):  
Bader A. Alyoubi
Keyword(s):  
Saudi Arabia ◽  
Big Data ◽  
Inventory Management ◽  
New Technologies ◽  
Predictive Analytics ◽  
Business Environment ◽  
Primary Data ◽  
Research Approach ◽  
Multiple Sources ◽  
The Impact

Big Data is gaining rapid popularity in e-commerce sector across the globe. There is a general consensus among experts that Saudi organisations are late in adopting new technologies. It is generally believed that the lack of research in latest technologies that are specific to Saudi Arabia that is culturally, socially, and economically different from the West, is one of the key factors for the delay in technology adoption in Saudi Arabia. Hence, to fill this gap to a certain extent and create awareness about Big Data technology, the primary goal of this research was to identify the impact of Big Data on e-commerce organisations in Saudi Arabia. Internet has changed the business environment of Saudi Arabia too. E-commerce is set for achieving new heights due to latest technological advancements. A qualitative research approach was used by conducting interviews with highly experienced professional to gather primary data. Using multiple sources of evidence, this research found out that traditional databases are not capable of handling massive data. Big Data is a promising technology that can be adopted by e-commerce companies in Saudi Arabia. Big Data’s predictive analytics will certainly help e-commerce companies to gain better insight of the consumer behaviour and thus offer customised products and services. The key finding of this research is that Big Data has a significant impact in e-commerce organisations in Saudi Arabia on various verticals like customer retention, inventory management, product customisation, and fraud detection.

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