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 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 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 Mathematical epidemiologic and simulation modelling of first wave COVID-19 in Malaysia

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Rezal Kamel Ariffin ◽  
Kathiresan Gopal ◽  
Isthrinayagy Krishnarajah ◽  
Iszuanie Syafidza Che Ilias ◽  
Mohd Bakri Adam ◽  
...  
Keyword(s):  
Transmission Rate ◽  
Mainland China ◽  
Movement Control ◽  
Simulation Modelling ◽  
Sir Model ◽  
Control Measures ◽  
Cumulative Number ◽  
Severity Of The Disease ◽  
Control Order ◽  
Second Wave

AbstractSince the first coronavirus disease 2019 (COVID-19) outbreak appeared in Wuhan, mainland China on December 31, 2019, the geographical spread of the epidemic was swift. Malaysia is one of the countries that were hit substantially by the outbreak, particularly in the second wave. This study aims to simulate the infectious trend and trajectory of COVID-19 to understand the severity of the disease and determine the approximate number of days required for the trend to decline. The number of confirmed positive infectious cases [as reported by Ministry of Health, Malaysia (MOH)] were used from January 25, 2020 to March 31, 2020. This study simulated the infectious count for the same duration to assess the predictive capability of the Susceptible-Infectious-Recovered (SIR) model. The same model was used to project the simulation trajectory of confirmed positive infectious cases for 80 days from the beginning of the outbreak and extended the trajectory for another 30 days to obtain an overall picture of the severity of the disease in Malaysia. The transmission rate, β also been utilized to predict the cumulative number of infectious individuals. Using the SIR model, the simulated infectious cases count obtained was not far from the actual count. The simulated trend was able to mimic the actual count and capture the actual spikes approximately. The infectious trajectory simulation for 80 days and the extended trajectory for 110 days depicts that the inclining trend has peaked and ended and will decline towards late April 2020. Furthermore, the predicted cumulative number of infectious individuals tallies with the preparations undertaken by the MOH. The simulation indicates the severity of COVID-19 disease in Malaysia, suggesting a peak of infectiousness in mid-March 2020 and a probable decline in late April 2020. Overall, the study findings indicate that outbreak control measures such as the Movement Control Order (MCO), social distancing and increased hygienic awareness is needed to control the transmission of the outbreak in Malaysia.

Modeling COVID-19 Growing Trends to Reveal the Differences in the Effectiveness of Non-Pharmaceutical Interventions among Countries in the World (Preprint)

2020 ◽  
Author(s):  
You Chen ◽  
Yubo Feng ◽  
Chao Yan ◽  
Xinmeng Zhang ◽  
Cheng Gao
Keyword(s):  
Secondary Analysis ◽  
Reproduction Rate ◽  
Cumulative Number ◽  
Linear Regression Models ◽  
Growth Data ◽  
Dynamic Changes ◽  
The World ◽  
Four Levels ◽  
Almost All ◽  
Pharmaceutical Interventions

BACKGROUND Adopting non-pharmaceutical interventions (NPIs) can affect COVID-19 growing trends, decrease the number of infected cases, and thus reduce mortality and healthcare demand. Almost all countries in the world have adopted non-pharmaceutical interventions (NPIs) to control the spread rate of COVID-19; however, it is unclear what are differences in the effectiveness of NPIs among these countries. OBJECTIVE We hypothesize that COVID-19 case growth data reveals the efficacy of NPIs. In this study, we conduct a secondary analysis of COVID-19 case growth data to compare the differences in the effectiveness of NPIs among 16 representative countries in the world. METHODS This study leverages publicly available data to learn patterns of dynamic changes in the reproduction rate for sixteen countries covering Asia, Europe, North America, South America, Australia, and Africa. Furthermore, we model the relationships between the cumulative number of cases and the dynamic reproduction rate to characterize the effectiveness of the NPIs. We learn four levels of NPIs according to their effects in the control of COVID-19 growth and categorize the 16 countries into the corresponding groups. RESULTS The dynamic changes of the reproduction rate are learned via linear regression models for all of the studied countries, with the average adjusted R-squared at 0.96 and the 95% confidence interval as [0.94 0.98]. China, South Korea, Argentina, and Australia are at the first level of NPIs, which are the most effective. Japan and Egypt are at the second level of NPIs, and Italy, Germany, France, Netherlands, and Spain, are at the third level. The US and UK have the most inefficient NPIs, and they are at the fourth level of NPIs. CONCLUSIONS COVID-19 case growth data provides evidence to demonstrate the effectiveness of the NPIs. Understanding the differences in the efficacy of the NPIs among countries in the world can give guidance for emergent public health events. CLINICALTRIAL NA

scholarly journals Predicting the cumulative medical load of COVID-19 outbreaks after the peak in daily fatalities

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0247272
Author(s):  
Claudius Gros ◽  
Roser Valenti ◽  
Lukas Schneider ◽  
Benedikt Gutsche ◽  
Dimitrije Marković
Keyword(s):  
Phase Space ◽  
Sir Model ◽  
Reaction Model ◽  
Space Representation ◽  
Cumulative Number ◽  
Short Term ◽  
Before And After ◽  
The Status ◽  
Short And Long Term

The distinct ways the COVID-19 pandemic has been unfolding in different countries and regions suggest that local societal and governmental structures play an important role not only for the baseline infection rate, but also for short and long-term reactions to the outbreak. We propose to investigate the question of how societies as a whole, and governments in particular, modulate the dynamics of a novel epidemic using a generalization of the SIR model, the reactive SIR (short-term and long-term reaction) model. We posit that containment measures are equivalent to a feedback between the status of the outbreak and the reproduction factor. Short-term reaction to an outbreak corresponds in this framework to the reaction of governments and individuals to daily cases and fatalities. The reaction to the cumulative number of cases or deaths, and not to daily numbers, is captured in contrast by long-term reaction. We present the exact phase space solution of the controlled SIR model and use it to quantify containment policies for a large number of countries in terms of short and long-term control parameters. We find increased contributions of long-term control for countries and regions in which the outbreak was suppressed substantially together with a strong correlation between the strength of societal and governmental policies and the time needed to contain COVID-19 outbreaks. Furthermore, for numerous countries and regions we identified a predictive relation between the number of fatalities within a fixed period before and after the peak of daily fatality counts, which allows to gauge the cumulative medical load of COVID-19 outbreaks that should be expected after the peak. These results suggest that the proposed model is applicable not only for understanding the outbreak dynamics, but also for predicting future cases and fatalities once the effectiveness of outbreak suppression policies is established with sufficient certainty. Finally, we provide a web app (https://itp.uni-frankfurt.de/covid-19/) with tools for visualising the phase space representation of real-world COVID-19 data and for exporting the preprocessed data for further analysis.

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 Renormalization Group Approach to Pandemics as a Time-Dependent SIR Model

2021 ◽  
Vol 8 ◽  
Author(s):  
Michele Della Morte ◽  
Francesco Sannino
Keyword(s):  
Renormalization Group ◽  
Time Dependence ◽  
Recovery Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Cumulative Number ◽  
Group Approach ◽  
Renormalization Group Approach

We generalise the epidemic Renormalization Group framework while connecting it to a SIR model with time-dependent coefficients. We then confront the model with COVID-19 in Denmark, Germany, Italy and France and show that the approach works rather well in reproducing the data. We also show that a better understanding of the time dependence of the recovery rate would require extending the model to take into account the number of deaths whenever these are over 15% of the cumulative number of infected cases.

scholarly journals Systematic biases in disease forecasting - the role of behavior change

2018 ◽  
Author(s):  
Ceyhun Eksin ◽  
Keith Paarporn ◽  
Joshua S. Weitz
Keyword(s):  
Behavior Change ◽  
Ground Truth ◽  
Sir Model ◽  
Disease Spread ◽  
Forecast Errors ◽  
Cumulative Number ◽  
Initial Speed ◽  
Sir Epidemic Model ◽  
Final Size ◽  
Forecast Models

ABSTRACTIn a simple susceptible-infected-recovered (SIR) model, the initial speed at which infected cases increase is indicative of the long-term trajectory of the outbreak. Yet during real-world outbreaks, individuals may modify their behavior and take preventative steps to reduce infection risk. As a consequence, the relationship between the initial rate of spread and the final case count may become tenuous. Here, we evaluate this hypothesis by comparing the dynamics arising from a simple SIR epidemic model with those from a modified SIR model in which individuals reduce contacts as a function of the current or cumulative number of cases. Dynamics with behavior change exhibit significantly reduced final case counts even though the initial speed of disease spread is nearly identical for both of the models. We show that this difference in final size projections depends critically in the behavior change of individuals. These results also provide a rationale for integrating behavior change into iterative forecast models. Hence, we propose to use a Kalman filter to update models with and without behavior change as part of iterative forecasts. When the ground truth outbreak includes behavior change, sequential predictions using a simple SIR model perform poorly despite repeated observations while predictions using the modified SIR model are able to correct for initial forecast errors. These findings highlight the value of incorporating behavior change into baseline epidemic and dynamic forecast models.

scholarly journals Predicting the impact of asymptomatic transmission, non-pharmaceutical intervention and testing on the spread of COVID19

2020 ◽  
Author(s):  
Ira B. Schwartz ◽  
James Kaufman ◽  
Kun Hu ◽  
Simone Bianco
Keyword(s):  
Predictive Models ◽  
Health Interventions ◽  
Strong Impact ◽  
Public Health Interventions ◽  
Removal Time ◽  
The Impact ◽  
Second Wave ◽  
Pharmaceutical Interventions ◽  
Epidemiological Parameters ◽  
Disease Testing

AbstractWe introduce a novel mathematical model to analyze the effect of removing non-pharmaceutical interventions on the spread of COVID19 as a function of disease testing rate. We find that relaxing interventions has a strong impact on the size of the epidemic peak as a function of intervention removal time. We show that it is essential for predictive models to explicitly capture transmission from asymptomatic carriers and important to obtain precise information on asymptomatic transmission by testing. The asymptomatic reservoir, reported to account for as much as 85% of transmission, will contribute to resurgence of the epidemic if public health interventions are removed too soon. Use of more basic models that fail to capture asymptomatic transmission can result in large errors in predicted clinical caseload or in fitted epidemiological parameters and, therefore, may be unreliable in estimating the risk of a second wave based on the timing of terminated interventions.

scholarly journals Prediction of the propagation of SARS-CoV-2 in Amapá State, Amazon Region, Brazil, by mathematical modeling

2020 ◽  
pp. 73-95
Author(s):  
Neylan Leal Dias ◽  
Edcarlos Vasconcelos da Silva ◽  
Marcelo Amanajas Pires ◽  
Daniel Chaves ◽  
Katsumi Letra Sanada ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Temporal Evolution ◽  
Sir Model ◽  
Amazon Region ◽  
The Other ◽  
Short Term ◽  
Exponential Behavior ◽  
Linear Projection ◽  
The Third ◽  
The One

This article presents an analysis of the spread of SARS-CoV-2 in Amapá using three approaches. In the first, the ICL model for the pandemic applied to Brazil was used to implement a comparative linear projection for the Amapá population. The second approach was developed with the short-term solution of the standard SIR model where it was shown that the typical exponential behavior satisfactorily describes the data for the first weeks of the epidemic, but soon after there are early discrepancies due to a sudden slowdown in the temporal evolution number of cases due to isolation measures. This new regime is appropriately described with the third approach which is based on the vSIR model which is a variant of the SIR model. The results presented enable, on the one hand, a better understanding of the scenarios already faced by the population and on the other hand provide short-term projections that will be constantly updated on the link[11].

Sign in / Sign up

Export Citation Format

Share Document