scholarly journals Time-dependent SI model for epidemiology and applications to Covid-19

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Luis Arturo Urena-Lopez
Keyword(s):  
Continuous Function ◽  
Functional Form ◽  
Transmission Rate ◽  
Real Data ◽  
Logistic Function ◽  
Time Dependent ◽  
Initial Amplitude ◽  
Asymptotic Number ◽  
Si Model ◽  
Free Parameters

A generalisation of the Susceptible-Infectious model is made to include a time-dependent transmission rate, which leads to a close analytical expression in terms of a logistic function. The solution can be applied to any continuous function chosen to describe the evolution of the transmission rate with time. Taking inspiration from real data of the Covid-19, for the case of cumulative confirmed positives and deaths, we propose an exponentially decaying transmission rate with two free parameters, one for its initial amplitude and another one for its decaying rate. The resultant time-dependent SI model, which under extra conditions recovers the standard Gompertz functional form, is then compared with data from selected countries and its parameters fit using Bayesian inference. We make predictions about the asymptotic number of confirmed positives and deaths, and discuss the possible evolution of the disease in each country in terms of our parametrisation of the transmission rate.

scholarly journals Exploring the spread dynamics of COVID-19 in Morocco

2020 ◽  
Author(s):  
Mohamed NAJI
Keyword(s):  
Infection Rate ◽  
Transmission Rate ◽  
Real Data ◽  
Peak Position ◽  
Rate Function ◽  
Time Dependent ◽  
Death Rates ◽  
The Real ◽  
Spread Dynamics

Despite some similarities of the dynamic of COVID−19 spread in Morocco and other countries, the infection, recovery and death rates remain very variable. In this paper, we analyze the spread dynamics of COVID−19 in Morocco within a standard susceptible−exposed−infected−recovered−death (SEIRD) model. We have combined SEIRD model with a time−dependent infection rate function, to fit the real data of i) infection counts and ii) death rates due to COVID−19, for the period between March 2nd and Mai 15th 2020. By fitting the infection rate, SEIRD model placed the infection peak on 04/24/2020 and could reproduce it to a large extent on the expense of recovery and death rates. Fitting the SEIRD model to death rates gives rather satisfactory predictions with a maximum of infections on 04/06/2020. Regardless of the low peak position, the peak position, confirmed cases and transmission rate were well reproduced.

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 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 ESTIMATING EXTERIOR ORIENTATION PARAMETERS OF HYPERSPECTRAL BANDS BASED ON POLYNOMIAL MODELS

2017 ◽  
Vol XLII-3/W3 ◽  
pp. 19-25 ◽  
Author(s):  
A. Berveglieri ◽  
A. M. G. Tommaselli ◽  
E. Honkavaara
Keyword(s):  
Real Data ◽  
Bundle Adjustment ◽  
Time Dependent ◽  
Camera Model ◽  
Exterior Orientation ◽  
Spectral Bands ◽  
Acquisition Mode ◽  
Polynomial Models ◽  
Orientation Parameters ◽  
Sequential Acquisition

Hyperspectral camera operating in sequential acquisition mode produces spectral bands that are not recorded at the same instant, thus having different exterior orientation parameters (EOPs) for each band. The study presents experiments on bundle adjustment with time-dependent polynomial models for band orientation of hyperspectral cubes sequentially collected. The technique was applied to a Rikola camera model. The purpose was to investigate the behaviour of the estimated polynomial parameters and the feasibility of using a minimum of bands to estimate EOPs. Simulated and real data were produced for the analysis of parameters and accuracy in ground points. The tests considered conventional bundle adjustment and the polynomial models. The results showed that both techniques were comparable, indicating that the time-dependent polynomial model can be used to estimate the EOPs of all spectral bands, without requiring a bundle adjustment of each band. The accuracy of the block adjustment was analysed based on the discrepancy obtained from checkpoints. The root mean square error (RMSE) indicated an accuracy of 1 GSD in planimetry and 1.5 GSD in altimetry, when using a minimum of four bands per cube.

scholarly journals Efficient estimation of stereo thresholds: what slope should be assumed for the psychometric function?

2019 ◽  
Author(s):  
Ignacio Serrano-Pedraza ◽  
Kathleen Vancleef ◽  
William Herbert ◽  
Nicola Goodship ◽  
Maeve Woodhouse ◽  
...  
Keyword(s):  
Psychometric Function ◽  
Population Distribution ◽  
Real Data ◽  
Logistic Function ◽  
Efficient Estimation ◽  
Threshold Estimate ◽  
Bayesian Procedure ◽  
Detection Thresholds ◽  
Bayesian Procedures ◽  
Wide Range

Bayesian staircases are widely used in psychophysics to estimate detection thresholds. Simulations have revealed the importance of the parameters selected for the assumed subject’s psychometric function in enabling thresholds to be estimated with small bias and high precision. One important parameter is the slope of the psychometric function, or equivalently its spread. This is often held fixed, rather than estimated for individual subjects, because much larger numbers of trials are required to estimate the spread as well as the threshold. However, if this fixed value is wrong, the threshold estimate can be biased. Here we determine the optimal slope to minimize bias and maximize precision when measuring stereoacuity with Bayesian staircases. We performed 2- and 4AFC disparity detection stereo experiments in order to measure the spread of the disparity psychometric function in human observers assuming a Logistic function. We found a wide range, between 0.03 and 3.5 log10 arcsec, with little change with age. We then ran simulations to examine the optimal spread using the real data. From our simulations and for three different experiments, we recommend selecting assumed spread values between the percentiles 60-80% of the population distribution of spreads (these percentiles can be extended to other type of thresholds). For stereo thresholds, we recommend a spread σ=1.7 log10 arcsec for 2AFC (slope 𝛽 = 4.3/log10 arcsec), and σ=1.5 log10 arcsec for 4AFC (𝛽 = 4.9/log10 arcsec). Finally, we compared a Bayesian procedure (ZEST using the optimal σ) with five Bayesian procedures that are versions of ZEST-2D, Psi, and Psi-marginal. In general, our recommended procedure showed the lowest threshold bias and highest precision.

Simulation and prediction of dengue outbreaks based on an SIR model with a time-dependent transmission rate including meteorological data. An example for Colombo and Jakarta

2021 ◽  
pp. 2150073
Author(s):  
Peter Heidrich ◽  
Thomas Götz
Keyword(s):  
Transmission Rate ◽  
Meteorological Data ◽  
Weather Conditions ◽  
Time Dependent ◽  
Data Sets ◽  
Vector Borne Diseases ◽  
Dengue Outbreaks ◽  
Vector Borne ◽  
Text Model ◽  
Periodic Transmission

Vector-borne diseases can usually be examined with a vector–host model like the [Formula: see text] model. This, however, depends on parameters that contain detailed information about the mosquito population that we usually do not know. For this reason, in this article, we reduce the [Formula: see text] model to an [Formula: see text] model with a time-dependent and periodic transmission rate [Formula: see text]. Since the living conditions of the mosquitos depend on the local weather conditions, meteorological data sets flow into the model in order to achieve a more realistic behavior. The developed [Formula: see text] model is adapted to existing data sets of hospitalized dengue cases in Jakarta (Indonesia) and Colombo (Sri Lanka) using numerical optimization based on Pontryagin’s maximum principle. A previous data analysis shows that the results of this parameter fit are within a realistic range and thus allow further investigations. Based on this, various simulations are carried out and the prediction quality of the model is examined.

scholarly journals Modelling the time-dependent transmission rate for porcine circovirus type 2 (PCV2) in pigs using data from serial transmission experiments

2008 ◽  
Vol 6 (30) ◽  
pp. 39-50 ◽  
Author(s):  
M Andraud ◽  
B Grasland ◽  
B Durand ◽  
R Cariolet ◽  
A Jestin ◽  
...  
Keyword(s):  
Transmission Rate ◽  
Transmission Function ◽  
Latency Period ◽  
Porcine Circovirus Type ◽  
Time Dependent ◽  
Porcine Circovirus ◽  
Infectious Period ◽  
Post Inoculation ◽  
Unimodal Function ◽  
Reproduction Ratio

Six successive transmission trials were carried out from 4 to 39 days post inoculation (DPI) to determine the features of the infectious period for PCV2-infected pigs. The infectiousness of inoculated pigs, assessed from the frequency of occurrence of infected pigs in susceptible groups in each contact trial, increased from 4 to 18 DPI (0, 7 and 8 infected pigs at 4, 11 and 18 DPI, respectively) and then decreased slowly until 39 days post infection (4, 2 and 1 pigs infected at 25, 32 and 39 DPI, respectively). The estimated time-dependent infectiousness was fitted to three unimodal function shapes (gamma, Weibull and lognormal) for comparison. The absence of infected pigs at 4 DPI revealed a latency period between 4 and 10 DPI. A sensitivity analysis was performed to test whether the parametric shape of the transmission function influenced the estimations. The estimated time-dependent transmission rate was implemented in a deterministic SEIR model and validated by comparing the model prediction with external data. The lognormal-like function shape evidenced the best quality of fit, leading to a latency period of 8 days, an estimated basic reproduction ratio of 5.9 [1.8,10.1] and a mean disease generation time of 18.4 days [18.2, 18.5].

Spherically Symmetric Vibration of an Elastic Spherical Shell Subject to a Radial and Time-Dependent Body-Force Field

1971 ◽  
Vol 38 (3) ◽  
pp. 702-705 ◽  
Author(s):  
J. M. McKinney
Keyword(s):  
Continuous Function ◽  
Spherical Shell ◽  
Force Field ◽  
Body Force ◽  
Time Dependent ◽  
Symmetric Body ◽  
Spherically Symmetric ◽  
Symmetric Vibration ◽  
Elastic Spherical Shell

A solution, exact within the framework of linear elastokinetics, is obtained for a vibrating, elastic, arbitrarily thick spherical shell subject only to a spherically symmetric body force field of the form FR(r, τ) = Fr(r)Ft(τ). Fr(r) is taken in the form of a polynomial whereas Ft(τ) is restricted only to being a sectionally continuous function of time.

scholarly journals Membrane Currents in Mammalian Ventricular Heart Muscle Fibers Using a Voltage-Clamp Technique

1971 ◽  
Vol 57 (3) ◽  
pp. 290-296 ◽  
Author(s):  
Gerhard Giebisch ◽  
Silvio Weidmann
Keyword(s):  
Action Potential ◽  
Outward Current ◽  
Time Dependent ◽  
Resting Potential ◽  
Equilibrium Potential ◽  
Initial Amplitude ◽  
Inward Current ◽  
Gap Technique ◽  
Sucrose Gap

Bundles of sheep ventricular fibers were voltage-clamped utilizing a modified sucrose gap technique and intracellular voltage control. An action potential was fired off in the usual way, and the clamp circuit was switched on at preselected times during activity. Clamping the membrane back to its resting potential during the early part of an action potential resulted in a surge of inward current. The initial amplitude of this current surge decreased as the clamp was switched on progressively later during the action potential. Inward current decreasing as a function of time was also recorded if the membrane potential was clamped beyond the presumed K equilibrium potential (to -130 mv). Clamping the membrane to the inside positive range (+40 mv to +60 mv) at different times of an action potential resulted in a step of outward current which was not time-dependent. The results suggest that normal repolarization of sheep ventricle depends on a time-dependent decrease of inward current (Na, Ca) rather than on a time-dependent increase of outward current (K).

scholarly journals Nonlinear Combinational Dynamic Transmission Rate Model and Its Application in Global COVID-19 Epidemic Prediction and Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2307
Author(s):  
Xiaojin Xie ◽  
Kangyang Luo ◽  
Zhixiang Yin ◽  
Guoqiang Wang
Keyword(s):  
Social Order ◽  
Transmission Rate ◽  
Real Data ◽  
The United States ◽  
Average Error ◽  
Support Vector ◽  
Rate Model ◽  
Effective Measure ◽  
Out Of Sample ◽  
Discrete Values

The outbreak of coronavirus disease 2019 (COVID-19) has caused a global disaster, seriously endangering human health and the stability of social order. The purpose of this study is to construct a nonlinear combinational dynamic transmission rate model with automatic selection based on forecasting effective measure (FEM) and support vector regression (SVR) to overcome the shortcomings of the difficulty in accurately estimating the basic infection number R0 and the low accuracy of single model predictions. We apply the model to analyze and predict the COVID-19 outbreak in different countries. First, the discrete values of the dynamic transmission rate are calculated. Second, the prediction abilities of all single models are comprehensively considered, and the best sliding window period is derived. Then, based on FEM, the optimal sub-model is selected, and the prediction results are nonlinearly combined. Finally, a nonlinear combinational dynamic transmission rate model is developed to analyze and predict the COVID-19 epidemic in the United States, Canada, Germany, Italy, France, Spain, South Korea, and Iran in the global pandemic. The experimental results show an the out-of-sample forecasting average error rate lower than 10.07% was achieved by our model, the prediction of COVID-19 epidemic inflection points in most countries shows good agreement with the real data. In addition, our model has good anti-noise ability and stability when dealing with data fluctuations.

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