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Based on hospital capacities, facts from past experience with the coronavirus disease 2019 (COVID-19) virus and the number of dark infections during the second wave (
Reinhard Schlickeiser; Martin Kröger. Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries. COVID 2021, 1, 130 -136.
AMA StyleReinhard Schlickeiser, Martin Kröger. Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries. COVID. 2021; 1 (1):130-136.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Reasonable Limiting of 7-Day Incidence per Hundred Thousand and Herd Immunization in Germany and Other Countries." COVID 1, no. 1: 130-136.
An analytic evaluation of the peak time of a disease allows for the installment of effective epidemic precautions. Recently, an explicit analytic, approximate expression (MT) for the peak time of the fraction of infected persons during an outbreak within the susceptible–infectious–recovered/removed (SIR) model had been presented and discussed (Turkyilmazoglu, 2021). There are three existing approximate solutions (SK-I, SK-II, and CG) of the semi-time SIR model in its reduced formulation that allow one to come up with different explicit expressions for the peak time of the infected compartment (Schlickeiser and Kröger, 2021; Carvalho and Gonçalves, 2021). Here we compare the four expressions for any choice of SIR model parameters and find that SK-I, SK-II and CG are more accurate than MT as long as the amount of population to which the SIR model is applied exceeds hundred by far (countries, ss, cities). For small populations with less than hundreds of individuals (families, small towns), however, the approximant MT outperforms the other approximants. To be able to compare the various approaches, we clarify the equivalence between the four-parametric dimensional SIR equations and their two-dimensional dimensionless analogue. Using Covid-19 data from various countries and sources we identify the relevant regime within the parameter space of the SIR model.
Martin Kröger; Mustafa Turkyilmazoglu; Reinhard Schlickeiser. Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? Physica D. Nonlinear Phenomena 2021, 425, 132981 .
AMA StyleMartin Kröger, Mustafa Turkyilmazoglu, Reinhard Schlickeiser. Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use? Physica D. Nonlinear Phenomena. 2021; 425 ():132981.
Chicago/Turabian StyleMartin Kröger; Mustafa Turkyilmazoglu; Reinhard Schlickeiser. 2021. "Explicit formulae for the peak time of an epidemic from the SIR model. Which approximant to use?" Physica D. Nonlinear Phenomena 425, no. : 132981.
With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate,
Reinhard Schlickeiser; Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. Physics 2021, 3, 386 -426.
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. Physics. 2021; 3 (2):386-426.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations." Physics 3, no. 2: 386-426.
The properties of the collective subluminal electrostatic fluctuations in isotropic plasmas are investigated using the covariant kinetic theory of linear fluctuations based on the correct momentum–velocity relation. The covariant theory correctly accounts for the differences in subluminal and superluminal fluctuations in contrast to the non-covariant theory. The general formalism developed here is valid in unmagnetized plasmas and in magnetized plasmas for wavevectors of electrostatic waves parallel to the direction of the uniform magnetic field. Of particular interest are potential differences between the covariant and the non-covariant approach and the consequences of these differences in modifying observational predictions. For thermal particle distributions of protons and electrons with nonrelativistic equal temperatures, the covariant and non-covariant theories yield exactly the same dispersion function and relation for weakly damped electrostatic waves. Also, the quasi-equilibrium wavenumber spectrum of collective thermal electrostatic noise agrees in both theories apart from the important wavenumber restriction | k | > k c = ω p , e / c. While the non-covariant analysis also yields eigenmode fluctuations at small wavenumbers with superluminal phase speeds, the correct covariant analysis indicates that subluminal electrostatic fluctuations are only generated at wavenumbers | k | > k c by spontaneous emission of the plasma particles. As a consequence, the nonrelativistic thermal electrostatic noise wavenumber spectrum is limited to the wavenumber range ω p , e ≤ | k | ≤ k max. Within a linear fluctuation theory, superluminal electrostatic noise cannot be generated.
R. Schlickeiser; M. M. Martinović; P. H. Yoon. Subluminal electrostatic noise in isotropic space plasmas. General formulas and nonrelativistic thermal limit. Physics of Plasmas 2021, 28, 052110 .
AMA StyleR. Schlickeiser, M. M. Martinović, P. H. Yoon. Subluminal electrostatic noise in isotropic space plasmas. General formulas and nonrelativistic thermal limit. Physics of Plasmas. 2021; 28 (5):052110.
Chicago/Turabian StyleR. Schlickeiser; M. M. Martinović; P. H. Yoon. 2021. "Subluminal electrostatic noise in isotropic space plasmas. General formulas and nonrelativistic thermal limit." Physics of Plasmas 28, no. 5: 052110.
With the now available vaccination against Covid-19 it is quantitatively explored how vaccination campaigns influence the mathematical modeling of epidemics. The standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to the fourth compartment V of vaccinated persons and the vaccination rate v(t) that regulates the relation between susceptible and vaccinated persons. The vaccination rate v(t) competes with the infection (a(t)) and recovery (\mu(t)) rates in determining the time evolution of epidemics. In order for a pandemic outburst with rising rates of new infections it is required that k+b<1-2\eta, where k=\mu_0/a_0 and b=v_0/a_0 denote the initial ratios of the three rates, respectively, and \eta << 1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV-model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and \eta completely determine the reduced time evolution the SIRV-quantities Q(\tau). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from Israel this can happen in all countries considered.
Reinhard Schlickeiser; Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. 2021, 1 .
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations. . 2021; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations." , no. : 1.
The earlier analytical analysis (part A) of the Susceptible-Infectious-Recovered (SIR) epidemics model for a constant ratio $k$ of infection to recovery rates is extended here to the semi-time case which is particularly appropriate for modeling the temporal evolution of later (than the first) pandemic waves when a greater population fraction from the first wave has been infected. In the semi-time case the SIR model does not describe the quantities in the past; instead they only hold for times later than the initial time $t=0$ of the newly occurring wave. Simple exact and approximative expressions are derived for the final and maximum values of the infected, susceptible and revovered/removed population fractions as well the daily rate and cumulative number of new infections. It is demonstrated that two types of temporal evolution of the daily rate of new infections $j(\tau)$ occur depending on the values of $k$ and the initial value of the infected fraction $I(0)=\eta$: in the decay case for $k\ge 1-2\eta $ the daily rate monotonically decreases at all positive times from its initial maximum value $j(0)=\eta (1-\eta )$. Alternatively, in the peak case for $k<1-2\eta $ the daily rate attains a maximum at a finite positive time. By comparing the approximated analytical solutions for $j(\tau )$ and $J(\tau)$ with the exact ones obtained by numerical integration, it is shown that the analytical approximations are accurate within at most only 2.5 percent. It is found that the initial fraction of infected persons sensitively influences the late time dependence of the epidemics, the maximum daily rate and its peak time. Such dependencies do not exist in the earlier investigated all-time case.
Reinhard Schlickeiser; Martin Kröger. Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case. Journal of Physics A: Mathematical and Theoretical 2021, 54, 175601 .
AMA StyleReinhard Schlickeiser, Martin Kröger. Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case. Journal of Physics A: Mathematical and Theoretical. 2021; 54 (17):175601.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2021. "Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case." Journal of Physics A: Mathematical and Theoretical 54, no. 17: 175601.
In collision-poor space plasmas, protons with an excess of kinetic energy or temperature in the direction perpendicular to the background magnetic field can excite the electromagnetic ion cyclotron (EMIC) instability. This instability is expected to be highly sensitive to suprathermal protons, which enhance the high-energy tails of the observed velocity distributions and are well reproduced by the (bi-)Kappa distribution functions. In this paper, we present the results of a refined quasi-linear approach, able to describe the effects of suprathermal protons on the extended temporal evolution of EMIC instability. It is, thus, shown that suprathermals have a systematic stimulating effect on the EMIC instability, enhancing not only the growth rates and the range of unstable wavenumbers but also the magnetic fluctuating energy density reached at the saturation. In effect, the relaxation of anisotropic temperature also becomes more efficient, i.e., faster in time and closer to isotropy.
S. M. Shaaban; M. Lazar; R. Schlickeiser. Electromagnetic ion cyclotron instability stimulated by the suprathermal ions in space plasmas: A quasi-linear approach. Physics of Plasmas 2021, 28, 022103 .
AMA StyleS. M. Shaaban, M. Lazar, R. Schlickeiser. Electromagnetic ion cyclotron instability stimulated by the suprathermal ions in space plasmas: A quasi-linear approach. Physics of Plasmas. 2021; 28 (2):022103.
Chicago/Turabian StyleS. M. Shaaban; M. Lazar; R. Schlickeiser. 2021. "Electromagnetic ion cyclotron instability stimulated by the suprathermal ions in space plasmas: A quasi-linear approach." Physics of Plasmas 28, no. 2: 022103.
We start out by deriving simple analytic expressions for all measurable amounts of cases and fatalities during a pandemic evolution exhibiting multiple waves, described by the semi-time SIR model. The approximant shares all relevant features with the exact solution, including time and position of the peak of daily new infections, as well as the asymptotic behaviors at small and large times. We derive exact analytic expressions for the early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution. We show, in particular, how the asymmetry of the first epidemic wave and its exponential tails are affected by the initial conditions; a feature that has no analogue in the all-time SIR model. We apply the approach to available data from different continents. Our analysis reveals that the immunity is very strongly increasing during the 2nd wave, while it was still at a very moderate level of a few percent in several countries at the end of the first wave. The wave-specific SIR parameters describing the infection and recovery rates we find to behave in a similar fashion, while their ratio k was decreasing only by a about 5% for most countries. Still, an apparently moderate change of k can have significant consequences for the relevant numbers like the final amount of infected or deceased population. As we show, the probability for an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the 2nd wave, irrespective the currently ongoing vaccination efforts. We compare with alternate approaches.
Martin Kröger; Reinhard Schlickeiser. Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate. 2021, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate. . 2021; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2021. "Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate." , no. : 1.
Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast. In particular, it is possible to test lockdown and lifting interventions because the new solutions hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.
Reinhard Schlickeiser; M. Kröger. Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions. Frontiers in Physics 2021, 8, 1 .
AMA StyleReinhard Schlickeiser, M. Kröger. Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions. Frontiers in Physics. 2021; 8 ():1.
Chicago/Turabian StyleReinhard Schlickeiser; M. Kröger. 2021. "Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions." Frontiers in Physics 8, no. : 1.
Based on the hospital capacities, facts from the past experience with the Covid-19 virus and the dark number of infections D=10D_{10} a reasonable limiting value of 170/D_{10} for the monitored 7-day incidence per 100000 persons value (MSDIHT) in Germany is calculated. If the MSDIHT is held below this limiting value the German hospital system can cope with the number of new seriously infected persons without any triage decisions. A significant improvement to an almost complete testing of the population would lead to dramatic reduction of the current dark numer value to D_{10}=0.1 so that ten times higher MSDIHT values of 1700 are acceptable. Such a high limiting value would spare Germany from its currently imposed strict lockdown. The costs for such extensive and complete testing campaigns are highly justified as they are orders of magnitudes below the estimated economical costs of more than 3.6 billion Euros for each lockdown day.
Martin Kröger; Reinhard Schlickeiser. Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany. 2021, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany. . 2021; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2021. "Reasonable Limiting 7-day Incidence per Hundred Thousand Value in Germany." , no. : 1.
M Kröger; R Schlickeiser. Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor. Journal of Physics A: Mathematical and Theoretical 2020, 53, 505601 .
AMA StyleM Kröger, R Schlickeiser. Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor. Journal of Physics A: Mathematical and Theoretical. 2020; 53 (50):505601.
Chicago/Turabian StyleM Kröger; R Schlickeiser. 2020. "Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor." Journal of Physics A: Mathematical and Theoretical 53, no. 50: 505601.
Due to the current COVID-19 epidemic plague hitting the worldwide population it is of utmost medical, economical and societal interest to gain reliable predictions on the temporal evolution of the spreading of the infectious diseases in human populations. Of particular interest are the daily rates and cumulative number of new infections, as they are monitored in infected societies, and the influence of non-pharmaceutical interventions due to different lockdown measures as well as their subsequent lifting on these infections. Estimating quantitatively the influence of a later lifting of the interventions on the resulting increase in the case numbers is important to discriminate this increase from the onset of a second wave. The recently discovered new analytical solutions of Susceptible-Infectious-Recovered (SIR) model allow for such forecast and the testing of lockdown and lifting interventions as they hold for arbitrary time dependence of the infection rate. Here we present simple analytical approximations for the rate and cumulative number of new infections.
Reinhard Schlickeiser; Martin Kroger. Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions. 2020, 1 .
AMA StyleReinhard Schlickeiser, Martin Kroger. Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions. . 2020; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kroger. 2020. "Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions." , no. : 1.
We revisit the Susceptible-Infectious-Recovered/Removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic solution to the SIR model is known in parametric form for the case of a time-independent infection rate, we derive an analytic solution for the more general case of a time-dependent infection rate, that is not limited to a certain range of parameter values. Our approach allows us to derive several exact analytic results characterizing all quantities, and moreover explicit, non-parametric, and accurate analytic approximants for the solution of the SIR model for time-independent infection rates. We relate all parameters of the SIR model to a measurable, usually reported quantity, namely the cumulated number of infected population and its first and second derivatives at an initial time t=0, where data is assumed to be available. We address the question on how well the differential rate of infections is captured by the Gauss model (GM). To this end we calculate the peak height, width, and position of the bell-shaped rate analytically. We find that the SIR is captured by the GM within a range of times, which we discuss in detail. We prove that the SIR model exhibits an asymptotic behavior at large times that is different from the logistic model, while the difference between the two models still decreases with increasing reproduction factor. This part A of our work treats the original SIR model to hold at all times, while this assumption will be released in part B. Releasing this assumption allows to formulate initial conditions incompatible with the original SIR model.
Martin Kröger; Reinhard Schlickeiser. Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor. 2020, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor. . 2020; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2020. "Analytical Solution of the SIR-Model for the Temporal Evolution of Epidemics. Part A: Time-Independent Reproduction Factor." , no. : 1.
We study a Gauss model (GM), a map from time to the bell-shaped Gaussian function to model the deaths per day and country, as a simple, analytically tractable model to make predictions on the coronavirus epidemic. Justified by the sigmoidal nature of a pandemic, i.e., initial exponential spread to eventual saturation, and an agent-based model, we apply the GM to existing data, as of 2 April 2020, from 25 countries during first corona pandemic wave and study the model’s predictions. We find that logarithmic daily fatalities caused by the coronavirus disease 2019 (Covid-19) are well described by a quadratic function in time. By fitting the data to second order polynomials from a statistical χ 2 -fit with 95% confidence, we are able to obtain the characteristic parameters of the GM, i.e., a width, peak height, and time of peak, for each country separately, with which we extrapolate to future times to make predictions. We provide evidence that this supposedly oversimplifying model might still have predictive power and use it to forecast the further course of the fatalities caused by Covid-19 per country, including peak number of deaths per day, date of peak, and duration within most deaths occur. While our main goal is to present the general idea of the simple modeling process using GMs, we also describe possible estimates for the number of required respiratory machines and the duration left until the number of infected will be significantly reduced.
Janik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. Physics 2020, 2, 197 -212.
AMA StyleJanik Schüttler, Reinhard Schlickeiser, Frank Schlickeiser, Martin Kröger. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. Physics. 2020; 2 (2):197-212.
Chicago/Turabian StyleJanik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. 2020. "Covid-19 Predictions Using a Gauss Model, Based on Data from April 2." Physics 2, no. 2: 197-212.
For Germany, it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on 11 April 2020
Reinhard Schlickeiser; Frank Schlickeiser. A Gaussian Model for the Time Development of the Sars-Cov-2 Corona Pandemic Disease. Predictions for Germany Made on 30 March 2020. Physics 2020, 2, 164 -170.
AMA StyleReinhard Schlickeiser, Frank Schlickeiser. A Gaussian Model for the Time Development of the Sars-Cov-2 Corona Pandemic Disease. Predictions for Germany Made on 30 March 2020. Physics. 2020; 2 (2):164-170.
Chicago/Turabian StyleReinhard Schlickeiser; Frank Schlickeiser. 2020. "A Gaussian Model for the Time Development of the Sars-Cov-2 Corona Pandemic Disease. Predictions for Germany Made on 30 March 2020." Physics 2, no. 2: 164-170.
The Gauss model for the time evolution of the first corona pandemic wave rendered useful in the estimation of peak times, amount of required equipment, and the forecasting of fade out times. At the same time it is probably the simplest analytically tractable model that allows to quantitatively forecast the time evolution of infections and fatalities during a pandemic wave. In light of the various descriptors such as doubling times and reproduction factors currently in use to judge about lock-downs and other measures that aim to prevent spreading of the virus, we hereby provide both exact, and simple approximate relationships between the two relevant parameters of the Gauss model (peak time and width), and the transient behavior of two versions of doubling times, and three variants of reproduction factors including basic reproduction numbers.
Martin Kröger; Reinhard Schlickeiser. Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease. 2020, 1 .
AMA StyleMartin Kröger, Reinhard Schlickeiser. Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease. . 2020; ():1.
Chicago/Turabian StyleMartin Kröger; Reinhard Schlickeiser. 2020. "Gaussian Doubling Times and Reproduction Factors of the COVID-19 Pandemic Disease." , no. : 1.
The Gauss model for the time evolution of the first corona pandemic wave allows to draw conclusions on the dark number of infections, the amount of heard immunization, the used maximum capacity of breathing apparati and the effectiveness of various non-pharmaceutical interventions in different countries. In Germany, Switzerland and Sweden the dark numbers are 7.4 +/- 6.1, 11.1 +/- 8.5 and 25 +/- 25, respectively. Our method of estimating dark numbers from modeling both, infection and death rates simultaneously spares these countries the laborious, time-consuming and costly medical testing for antibodies of large portions of the population. In Germany the total number of infected persons, including the dark number of infections by the first wave is estimated to be 1.06 +/- 0.60 million, corresponding to 1.28 +/- 0.72 percent of the German population. We work out direct implications from these predictions for managing the 2nd and further corona waves.
Reinhard Schlickeiser; Martin Kröger. Clues from the First Covid-19 Wave and Recommendations for Social Measures in the Future. 2020, 1 .
AMA StyleReinhard Schlickeiser, Martin Kröger. Clues from the First Covid-19 Wave and Recommendations for Social Measures in the Future. . 2020; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Martin Kröger. 2020. "Clues from the First Covid-19 Wave and Recommendations for Social Measures in the Future." , no. : 1.
We propose a Gauss model (GM), a map from time to the bell-shaped Gauss function to model the deaths per day and country, as a quick and simple model to make predictions on the coronavirus epidemic. Justified by the sigmoidal nature of a pandemic, i.e. initial exponential spread to eventual saturation, we apply the GM to existing data, as of April 2, 2020, from 25 countries during first corona pandemic wave and study the model's predictions. We find that logarithmic daily fatalities caused by Covid-19 are well described by a quadratic function in time. By fitting the data to second order polynomials from a statistical chi2-fit with 95\% confidence, we are able to obtain the characteristic parameters of the GM, i.e. a width, peak height and time of peak, for each country separately, with which we extrapolate to future times to make predictions. We provide evidence that this supposedly oversimplifying model might still have predictive power and use it to forecast the further course of the fatalities caused by Covid-19 per country, including peak number of deaths per day, date of peak, and duration within most deaths occur. While our main goal is to present the general idea of the simple modeling process using GMs, we also describe possible estimates for the number of required respiratory machines and the duration left until the number of infected will be significantly reduced.
Janik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. 2020, 1 .
AMA StyleJanik Schüttler, Reinhard Schlickeiser, Frank Schlickeiser, Martin Kröger. Covid-19 Predictions Using a Gauss Model, Based on Data from April 2. . 2020; ():1.
Chicago/Turabian StyleJanik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. 2020. "Covid-19 Predictions Using a Gauss Model, Based on Data from April 2." , no. : 1.
We propose a Gauss model (GM), a map from time to the bell-shaped Gauss function to model the deaths per day and country, as a quick and simple model to make predictions on the coronavirus epidemic. Justified by the sigmoidal nature of a pandemic, i.e. initial exponential spread to eventual saturation, we apply the GM to existing data, as of April 2, 2020, from 25 countries during first corona pandemic wave and study the model’s predictions. We find that logarithmic daily fatalities caused by Covid-19 are well described by a quadratic function in time. By fitting the data to second order polynomials from a statistical χ 2-fit with 95% confidence, we are able to obtain the characteristic parameters of the GM, i.e. a width, peak height and time of peak, for each country separately, with which we extrapolate to future times to make predictions. We provide evidence that this supposedly oversimplifying model might still have predictive power and use it to forecast the further course of the fatalities caused by Covid-19 per country, including peak number of deaths per day, date of peak, and duration within most deaths occur. While our main goal is to present the general idea of the simple modeling process using GMs, we also describe possible estimates for the number of required respiratory machines and the duration left until the number of infected will be significantly reduced.
Janik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. Covid-19 predictions using a Gauss model, based on data from April 2. 2020, 1 .
AMA StyleJanik Schüttler, Reinhard Schlickeiser, Frank Schlickeiser, Martin Kröger. Covid-19 predictions using a Gauss model, based on data from April 2. . 2020; ():1.
Chicago/Turabian StyleJanik Schüttler; Reinhard Schlickeiser; Frank Schlickeiser; Martin Kröger. 2020. "Covid-19 predictions using a Gauss model, based on data from April 2." , no. : 1.
For Germany it is predicted that the first wave of the corona pandemic disease reaches its maximum of new infections on April 11th, 2020 days with 90 percent confidence. With a delay of about 7 days the maximum demand on breathing machines in hospitals occurs on April 18th, 2020 days. The first pandemic wave ends in Germany end of May 2020. The predictions are based on the assumption of a Gaussian time evolution well justified by the central limit theorem of statistics. The width and the maximum time and thus the duration of this Gaussian distribution are determined from a statistical χ 2-fit to the observed doubling times before March 28, 2020.
Reinhard Schlickeiser; Frank Schlickeiser. A Gaussian model for the time development of the Sars-Cov-2 corona pandemic disease. Predictions for Germany made on March 30, 2020. 2020, 1 .
AMA StyleReinhard Schlickeiser, Frank Schlickeiser. A Gaussian model for the time development of the Sars-Cov-2 corona pandemic disease. Predictions for Germany made on March 30, 2020. . 2020; ():1.
Chicago/Turabian StyleReinhard Schlickeiser; Frank Schlickeiser. 2020. "A Gaussian model for the time development of the Sars-Cov-2 corona pandemic disease. Predictions for Germany made on March 30, 2020." , no. : 1.