scholarly journals Verification of the accuracy of the SIR model in forecasting based on the improved SIR model with a constant ratio of recovery to infection rate by comparing with monitored second wave data

2021 ◽  
Vol 8 (9) ◽  
pp. 211379
Author(s):  
M. Kröger ◽  
R. Schlickeiser
Keyword(s):  
Temporal Evolution ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Sir Model ◽  
Peak Time ◽  
Present Contribution ◽  
Analytic Expressions ◽  
Early Peak ◽  
Moderate Change ◽  
Second Wave

The temporal evolution of second and subsequent waves of epidemics such as Covid-19 is investigated. Analytic expressions for the peak time and asymptotic behaviours, early doubling time, late half decay time, and a half-early peak law, characterizing the dynamical evolution of number of cases and fatalities, are derived, where the pandemic evolution exhibiting multiple waves is described by the semi-time SIR model. The asymmetry of the epidemic wave and its exponential tail are affected by the initial conditions, a feature that has no analogue in the all-time SIR model. Our analysis reveals that the immunity is very strongly increasing in several countries during the second Covid-19 wave. Wave-specific SIR parameters describing infection and recovery rates we find to behave in a similar fashion. Still, an apparently moderate change of their ratio can have significant consequences. As we show, the probability of an additional wave is however low in several countries due to the fraction of immune inhabitants at the end of the second wave, irrespective of the ongoing vaccination efforts. We compare with alternate approaches and data available at the time of submission. Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR model in predicting the evolution of pandemic outbreaks as long as the assumption underlying our analysis, an unchanged situation of the distribution of variants of concern and the fatality fraction, do not change dramatically during a wave. With the rise of the α variant at the time of submission the second wave did not terminate in some countries, giving rise to a superposition of waves that is not treated by the present contribution.

scholarly journals Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate

2021 ◽  
Author(s):  
Martin Kröger ◽  
Reinhard Schlickeiser
Keyword(s):  
Initial Conditions ◽  
Dynamical Evolution ◽  
Sir Model ◽  
Constant Ratio ◽  
Exponential Tails ◽  
Analytic Expressions ◽  
Early Peak ◽  
Moderate Change ◽  
Final Amount ◽  
Epidemic Wave

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.

scholarly journals Epidemics forecast from SIR-modeling, verification and calculated effects of lockdown and lifting of interventions

2020 ◽  
Author(s):  
Reinhard Schlickeiser ◽  
Martin Kroger
Keyword(s):  
Temporal Evolution ◽  
Sir Model ◽  
Human Populations ◽  
Cumulative Number ◽  
Analytical Approximations ◽  
Worldwide Population ◽  
Second Wave ◽  
Arbitrary Time Dependence ◽  
Societal Interest ◽  
Pharmaceutical Interventions

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.

scholarly journals Intervention Fatigue is the Primary Cause of Strong Secondary Waves in the COVID-19 Pandemic

2020 ◽  
Vol 17 (24) ◽  
pp. 9592 ◽  
Author(s):  
Kristoffer Rypdal ◽  
Filippo Maria Bianchi ◽  
Martin Rypdal
Keyword(s):  
Incidence Rate ◽  
Initial Conditions ◽  
Sir Model ◽  
Disease Spread ◽  
Social Response ◽  
Social Responses ◽  
Proposed Model ◽  
Reproduction Numbers ◽  
The Impact ◽  
Second Wave

As of November 2020, the number of COVID-19 cases was increasing rapidly in many countries. In Europe, the virus spread slowed considerably in the late spring due to strict lockdown, but a second wave of the pandemic grew throughout the fall. In this study, we first reconstruct the time evolution of the effective reproduction numbers R(t) for each country by integrating the equations of the classic Susceptible-Infectious-Recovered (SIR) model. We cluster countries based on the estimated R(t) through a suitable time series dissimilarity. The clustering result suggests that simple dynamical mechanisms determine how countries respond to changes in COVID-19 case counts. Inspired by these results, we extend the simple SIR model for disease spread to include a social response to explain the number X(t) of new confirmed daily cases. In particular, we characterize the social response with a first-order model that depends on three parameters ν1,ν2,ν3. The parameter ν1 describes the effect of relaxed intervention when the incidence rate is low; ν2 models the impact of interventions when incidence rate is high; ν3 represents the fatigue, i.e., the weakening of interventions as time passes. The proposed model reproduces typical evolving patterns of COVID-19 epidemic waves observed in many countries. Estimating the parameters ν1,ν2,ν3 and initial conditions, such as R0, for different countries helps to identify important dynamics in their social responses. One conclusion is that the leading cause of the strong second wave in Europe in the fall of 2020 was not the relaxation of interventions during the summer, but rather the failure to enforce interventions in the fall.

Influence analysis of information erupted on social networks based on SIR model

2015 ◽  
Vol 26 (02) ◽  
pp. 1550018 ◽  
Author(s):  
Xue Zhou ◽  
Yong Hu ◽  
Yue Wu ◽  
Xi Xiong
Keyword(s):  
Social Networks ◽  
Relaxation Time ◽  
Social Network ◽  
Complex Networks ◽  
Evolution Equations ◽  
Dynamical Evolution ◽  
Sir Model ◽  
Peak Time ◽  
Information Propagation ◽  
Chain Reaction

In this paper, according to the similarity of chain reaction principle and the characteristics of information propagation on social network, we proposed a new word "information bomb". Based on the complex networks and SIR model, dynamical evolution equations were setup. Then methods used to evaluate the four indexes of bomb power were given, including influence breadth, influence strength, peak time and relaxation time. At last, the power of information was ascertained through these indexes. The process of information propagation is simulated to illustrate the spreading characteristics through the results. Then parameters which impact on the power of information bomb are analyzed and some methods which control the propagation of information are given.

scholarly journals Epidemics Forecast From SIR-Modeling, Verification and Calculated Effects of Lockdown and Lifting of Interventions

2021 ◽  
Vol 8 ◽  
Author(s):  
R. Schlickeiser ◽  
M. Kröger
Keyword(s):  
Temporal Evolution ◽  
Sir Model ◽  
Human Populations ◽  
Cumulative Number ◽  
Analytical Approximations ◽  
Worldwide Population ◽  
Second Wave ◽  
Arbitrary Time Dependence ◽  
Societal Interest ◽  
Pharmaceutical Interventions

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.

scholarly journals Mass determination of the 1:3:5 near-resonant planets transiting GJ 9827 (K2-135)

2018 ◽  
Vol 618 ◽  
pp. A116 ◽  
Author(s):  
J. Prieto-Arranz ◽  
E. Palle ◽  
D. Gandolfi ◽  
O. Barragán ◽  
E. W. Guenther ◽  
...  
Keyword(s):  
Planetary System ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Space Mission ◽  
Mass Determination ◽  
Velocity Measurements ◽  
Orbital Periods ◽  
The Masses ◽  
Better Than

Context. Multiplanet systems are excellent laboratories to test planet formation models as all planets are formed under the same initial conditions. In this context, systems transiting bright stars can play a key role, since planetary masses, radii, and bulk densities can be measured. Aims. GJ 9827 (K2-135) has recently been found to host a tightly packed system consisting of three transiting small planets whose orbital periods of 1.2, 3.6, and 6.2 days are near the 1:3:5 ratio. GJ 9827 hosts the nearest planetary system (~30 pc) detected by NASA’s Kepler or K2 space mission. Its brightness (V = 10.35 mag) makes the star an ideal target for detailed studies of the properties of its planets. Methods. Combining the K2 photometry with high-precision radial-velocity measurements gathered with the FIES, HARPS, and HARPS-N spectrographs we revised the system parameters and derive the masses of the three planets. Results. We find that GJ 9827 b has a mass of Mb = 3.69−0.46+0.48 M⊕ and a radius of Rb = 1.58−0.13+0.14 R⊕, yielding a mean density of ρb = 5.11−1.27+1.74 g cm−3. GJ 9827 c has a mass of Mc = 1.45−0.57+0.58 M⊕, radius of Rc = 1.24−0.11+0.11 R⊕, and a mean density of ρc = 4.13−1.77+2.31 g cm−3. For GJ 9827 d, we derive Md = 1.45−0.57+0.58 M⊕, Rd = 1.24−0.11+0.11 R⊕, and ρd = 1.51−0.53+0.71 g cm−3. Conclusions. GJ 9827 is one of the few known transiting planetary systems for which the masses of all planets have been determined with a precision better than 30%. This system is particularly interesting because all three planets are close to the limit between super-Earths and sub-Neptunes. The planetary bulk compositions are compatible with a scenario where all three planets formed with similar core and atmosphere compositions, and we speculate that while GJ 9827 b and GJ 9827 c lost their atmospheric envelopes, GJ 9827 d maintained its primordial atmosphere, owing to the much lower stellarirradiation. This makes GJ 9827 one of the very few systems where the dynamical evolution and the atmosphericescape can be studied in detail for all planets, helping us to understand how compact systems form and evolve.

scholarly journals Impact of COVID-19 Variants on the Second Wave in India and Subsequent Discretion of Possibilities of the Third Wave

2021 ◽  
pp. 115-126
Author(s):  
Sudarshan Ramaswamy ◽  
Meera Dhuria ◽  
Sumedha M. Joshi ◽  
Deepa H Velankar
Keyword(s):  
Herd Immunity ◽  
Sir Model ◽  
The Other ◽  
Third Wave ◽  
Focal Points ◽  
Current Analysis ◽  
The Third ◽  
The Impact ◽  
Second Wave ◽  
Insight Into

Introduction: Epidemiological comprehension of the COVID-19 situation in India can be of great help in early prediction of any such indications in other countries and possibilities of the third wave in India as well. It is essential to understand the impact of variant strains in the perspective of the rise in daily cases during the second wave – Whether the rise in cases witnessed is due to the reinfections or the surge is dominated by emergence of mutants/variants and reasons for the same. Overall objective of this study is to predict early epidemiological indicators which can potentially lead to COVID-19 third wave in India. Methodology: We analyzed both the first and second waves of COVID-19 in India and using the data of India’s SARS-CoV-2 genomic sequencing, we segregated the impact of the Older Variant (OV) and the other major variants (VOI / VOC).  Applying Kermack–McKendrick SIR model to the segregated data progression of the epidemic in India was plotted in the form of proportion of people infected. An equation to explain herd immunity thresholds was generated and further analyzed to predict the possibilities of the third wave. Results: Considerable difference in ate of progression of the first and second wave was seen. The study also ascertains that the rate of infection spread is higher in Delta variant and is expected to have a higher threshold (>2 times) for herd immunity as compared to the OV. Conclusion: Likelihood of the occurrence of the third wave seems unlikely based on the current analysis of the situation, however the possibilities cannot be ruled out. Understanding the epidemiological details of the first and second wave helped in understanding the focal points responsible for the surge in cases during the second wave and has given further insight into the future.

scholarly journals Prediction of peak and termination of novel coronavirus COVID-19 epidemic in Iran

2020 ◽  
Vol 31 (11) ◽  
pp. 2050152
Author(s):  
Sepehr Rafieenasab ◽  
Amir-Pouyan Zahiri ◽  
Ehsan Roohi
Keyword(s):  
Statistical Data ◽  
Sir Model ◽  
Model Parameters ◽  
Peak Time ◽  
Infected People ◽  
Epidemic Curve ◽  
Immunization Rates ◽  
Long Time ◽  
Novel Coronavirus ◽  
Official Data

The growth and development of COVID-19 transmission have significantly attracted the attention of many societies, particularly Iran, that have been struggling with this contagious, infectious disease since late February 2020. In this study, the known “Susceptible-Infectious-Recovered (SIR)” and some other mathematical approaches were used to investigate the dynamics of the COVID-19 epidemic to provide a suitable assessment of the COVID-19 virus epidemic in Iran. The epidemic curve and SIR model parameters were obtained with the use of Iran’s official data. The recovered people were considered alongside the official number of confirmed victims as the reliable long-time statistical data. The results offer important predictions of the COVID-19 virus epidemic such as the realistic number of victims, infection rate, peak time and other characteristics. Besides, the effectiveness of infection and immunization rates to the number of infected people and epidemic end time are reported. Finally, different suggestions for decreasing victims are offered.

scholarly journals The Dynamical Evolution of Young Clusters and Associations

1986 ◽  
Vol 7 ◽  
pp. 481-488 ◽  
Author(s):  
Robert D. Mathieu
Keyword(s):  
Star Formation ◽  
Formation Process ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Short Review ◽  
Stellar Systems ◽  
Galactic Field ◽  
Dynamical State ◽  
Orbital Mixing ◽  
Formation Efficiency

A young cluster or association bears the imprint of the conditions at its birth for perhaps ten million years, after which the initial conditions are lost to either dilution in the galactic field or erasure by orbital mixing and stellar encounters. In its youngest years, however, the dynamical state of the system can provide valuable information concerning the structure and energetics of the parent gas, the star-formation efficiency and the star-formation process itself. This short review discusses recent theoretical and observational progress in the study of the very youngest of stellar systems.

scholarly journals Using symbolic computation in the characterization of frictional instabilities involving orthotropic materials

2015 ◽  
Vol 25 (2) ◽  
pp. 259-267 ◽  
Author(s):  
Mohamed A. Agwa ◽  
António Pinto Da Costa
Keyword(s):  
Closed Form ◽  
Half Space ◽  
Initial Conditions ◽  
Orthotropic Materials ◽  
Isotropic Case ◽  
Linear Elastic ◽  
Analytic Expressions ◽  
The Coefficient Of Friction ◽  
Unstable Solutions ◽  
Computer Algebra Software

Abstract The present work addresses the problem of determining under what conditions the impending slip state or the steady sliding of a linear elastic orthotropic layer or half space with respect to a rigid flat obstacle is dynamically unstable. In other words, we search the conditions for the occurrence of smooth exponentially growing dynamic solutions with perturbed initial conditions arbitrarily close to the steady sliding state, taking the system away from the equilibrium state or the steady sliding state. Previously authors have shown that a linear elastic isotropic half space compressed against and sliding with respect to a rigid flat surface may get unstable by flutter when the coefficient of friction μ and Poisson’s ratio ν are sufficiently large. In the isotropic case they have been able to derive closed form analytic expressions for the exponentially growing unstable solutions as well as for the borders of the stability regions in the space of parameters, because in the isotropic case there are only two dimensionless parameters (μ and ν). Already for the simplest version of orthotropy (an orthotropic transversally isotropic material) there are seven governing parameters (μ, five independent material constants and the orientation of the principal directions of orthotropy) and the expressions become very lengthy and literally impossible to manipulate manually. The orthotropic case addressed here is impossible to solve with simple closed form expressions, and therefore the use of computer algebra software is required, the main commands being indicated in the text.

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