scholarly journals The SIR model towards the data

2021 ◽  
Vol 136 (8) ◽  
Author(s):  
Ignazio Lazzizzera
Keyword(s):  
Generation Time ◽  
Reproduction Number ◽  
Removal Rate ◽  
Sir Model ◽  
Infectious Period ◽  
Third Wave ◽  
Real Numbers ◽  
The Third ◽  
Study Case ◽  
Good Agreement

AbstractIn this work, the SIR epidemiological model is reformulated so to highlight the important effective reproduction number, as well as to account for the generation time, the inverse of the incidence rate, and the infectious period (or removal period), the inverse of the removal rate. The aim is to check whether the relationships the model poses among the various observables are actually found in the data. The study case of the second through the third wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initially the model is tested with reference to the curve of swab-confirmed infectious individuals only. It is found to match the data, if the curve of the removed (that is healed or deceased) individuals is assumed underestimated by a factor of about 3 together with other related curves. Contextually, the generation time and the removal period, as well as the effective reproduction number, are obtained fitting the SIR equations to the data; the outcomes prove to be in good agreement with those of other works. Then, using knowledge of the proportion of Covid-19 transmissions likely occurring from individuals who didn’t develop symptoms, thus mainly undetected, an estimate of the real numbers of the epidemic is obtained, looking also in good agreement with results from other, completely different works. The line of this work is new, and the procedures, computationally really inexpensive, can be applied to any other national or regional case besides Italy’s study case here.

scholarly journals The SIR model towards the Data One year of Covid-19 pandemic in Italy case study and plausible "real" numbers.

2021 ◽  
Author(s):  
Ignazio Lazzizzera
Keyword(s):  
Generation Time ◽  
Reproduction Number ◽  
Removal Rate ◽  
Infectious Period ◽  
Third Wave ◽  
Real Numbers ◽  
Study Case ◽  
One Year ◽  
Good Agreement

Abstract In this work, the SIR epidemiological model is reformulated so to highlight the important effective reproduction number, as well as to account for the generation time, the inverse of the incidence rate, and the infectious period (or removal period), the inverse of the removal rate. The aim is to check whether the relationships the model poses among the various observables are actually found in the data. The study case of the second through the third wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initially the model is tested with reference to the curve of swab-confirmed infectious individuals only. It is found to match the data if the curve of the removed (that is healed or deceased) individuals is assumed underestimated by a factor of about 3 together with other related curves. Contextually, the generation time and the removal period, as well as the effective reproduction number, are obtained fitting the SIR equations to the data; the outcomes prove to be in good agreement with those of other works. Then, using knowledge of the proportion of Covid-19 transmissions likely occurring from individuals who didn't develop symptoms, thus mainly undetected, an estimate of the "real numbers'' of the epidemic is obtained, looking also in good agreement with results from other, completely different works. The line of this work is new and the procedures, computationally really inexpensive, can be applied to any other national or regional case besides Italy's study case here.

scholarly journals Omicron Impact in India: An Early Analysis of the Ongoing COVID-19 Third Wave

2022 ◽  
Author(s):  
Rajesh Ranjan
Keyword(s):  
Rapid Growth ◽  
Case Fatality Rate ◽  
Reproduction Number ◽  
Case Fatality ◽  
Sir Model ◽  
Third Wave ◽  
Fatality Rate ◽  
Sequencing Data ◽  
The Third ◽  
Second Wave

India is currently experiencing the third wave of COVID-19, which began on around 28 Dec. 2021. Although genome sequencing data of a sufficiently large sample is not yet available, the rapid growth in the daily number of cases, comparable to South Africa, United Kingdom, suggests that the current wave is primarily driven by the Omicron variant. The logarithmic regression suggests the growth rate of the infections during the early days in this wave is nearly four times than that in the second wave. Another notable difference in this wave is the relatively concurrent arrival of outbreaks in all the states; the effective reproduction number (Rt) although has significant variations among them. The test positivity rate (TPR) also displays a rapid growth in the last 10 days in several states. Preliminary estimates with the SIR model suggest that the peak to occur in late January 2022 with peak caseload exceeding that in the second wave. Although the Omicron trends in several countries suggest a decline in case fatality rate and hospitalizations compared to Delta, a sudden surge in active caseload can temporarily choke the already stressed healthcare India is currently experiencing the third wave of COVID-19, which began on around 28 Dec. 2021. Although genome sequencing data of a sufficiently large sample is not yet available, the rapid growth in the daily number of cases, comparable to South Africa, United Kingdom, suggests that the current wave is primarily driven by the Omicron variant. The logarithmic regression suggests the growth rate of the infections during the early days in this wave is nearly four times than that in the second wave. Another notable difference in this wave is the relatively concurrent arrival of outbreaks in all the states; the effective reproduction number (Rt) although has significant variations among them. The test positivity rate (TPR) also displays a rapid growth in the last 10 days in several states. Preliminary estimates with the SIR model suggest that the peak to occur in late January 2022 with peak caseload exceeding that in the second wave. Although the Omicron trends in several countries suggest a decline in case fatality rate and hospitalizations compared to Delta, a sudden surge in active caseload can temporarily choke the already stressed healthcare infrastructure. Therefore, it is advisable to strictly adhere to COVID-19 appropriate behavior for the next few weeks to mitigate an explosion in the number of infections.

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.

The discrete-time Kermack–McKendrick model: A versatile and computationally attractive framework for modeling epidemics

2021 ◽  
Vol 118 (39) ◽  
pp. e2106332118
Author(s):  
Odo Diekmann ◽  
Hans G. Othmer ◽  
Robert Planqué ◽  
Martin C. J. Bootsma
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Generation Time ◽  
Time Distribution ◽  
Reproduction Number ◽  
Compartmental Models ◽  
Infectious Period ◽  
Initial Growth ◽  
Fixed Duration ◽  
Spread Of Infection

The COVID-19 pandemic has led to numerous mathematical models for the spread of infection, the majority of which are large compartmental models that implicitly constrain the generation-time distribution. On the other hand, the continuous-time Kermack–McKendrick epidemic model of 1927 (KM27) allows an arbitrary generation-time distribution, but it suffers from the drawback that its numerical implementation is rather cumbersome. Here, we introduce a discrete-time version of KM27 that is as general and flexible, and yet is very easy to implement computationally. Thus, it promises to become a very powerful tool for exploring control scenarios for specific infectious diseases such as COVID-19. To demonstrate this potential, we investigate numerically how the incidence-peak size depends on model ingredients. We find that, with the same reproduction number and the same initial growth rate, compartmental models systematically predict lower peak sizes than models in which the latent and the infectious period have fixed duration.

scholarly journals Dynamics of an SIR-Based COVID-19 Model With Linear Incidence Rate, Nonlinear Removal Rate, and Public Awareness

2021 ◽  
Vol 9 ◽  
Author(s):  
Abdelhamid Ajbar ◽  
Rubayyi T. Alqahtani ◽  
Mourad Boumaza
Keyword(s):  
Incidence Rate ◽  
Reproduction Number ◽  
Removal Rate ◽  
Public Awareness ◽  
Sir Model ◽  
Hopf Bifurcations ◽  
Nonlinear Phenomena ◽  
Hospital Bed ◽  
Population Ratio ◽  
Effects Of Media

The paper studies the dynamics of the classical susceptible-infectious-removed (SIR) model when applied to the transmission of COVID-19 disease. The model includes the classical linear incidence rate but considers a nonlinear removal rate that depends on the hospital-bed population ratio. The model also includes the effects of media on public awareness. We prove that when the basic reproduction number is less than unity the model can exhibit a number of nonlinear phenomena including saddle-node, backward, and Hopf bifurcations. The model is fitted to COVID-19 data pertinent to Saudi Arabia. Numerical simulations are provided to supplement the theoretical analysis and delineate the effects of hospital-bed population ratio and public awareness on the control of the disease.

scholarly journals Realized generation times: contraction and impact of infectious period, reproduction number and population size

2019 ◽  
Author(s):  
Andrea Torneri ◽  
Amin Azmon ◽  
Christel Faes ◽  
Eben Kenah ◽  
Gianpaolo Scalia Tomba ◽  
...  
Keyword(s):  
Infectious Diseases ◽  
Generation Time ◽  
Time Distribution ◽  
Reproduction Number ◽  
Mean Value ◽  
Infectious Period ◽  
Calendar Time ◽  
Generation Times ◽  
The Mean ◽  
Over Time

AbstractOne of the key characteristics of the transmission dynamics of infectious diseases is the generation time which refers to the time interval between the infection of a secondary case and the infection of its infector. The generation time distribution together with the reproduction number determines the rate at which an infection spreads in a population. When defining the generation time distribution at a calendar time t two definitions are plausible according whether we regard t as the infection time of the infector or the infection time of the infectee. The resulting measurements are respectively called forward generation time and backward generation time. It has been observed that the mean forward generation time contracts around the peak of an epidemic. This contraction effect has previously been attributed to either competition among potential infectors or depletion of susceptibles in the population. The first explanation requires many infectives for contraction to occur whereas the latter explanation suggests that contraction occurs even when there are few infectives. With a simulation study we show that both competition and depletion cause the mean forward generation time to contract. Our results also reveal that the distribution of the infectious period and the reproduction number have a strong effect on the size and timing of the contraction, as well as on the mean value of the generation time in both forward and backward scheme.Author summaryInfectious diseases remain one of the greatest threats to human health and commerce, and the analysis of epidemic data is one of the most important applications of statistics in public health. Thus, having reliable estimates of fundamental infectious diseases parameters is critical for public health decision-makers in order to take appropriate actions for the global prevention and management of outbreaks and other health emergencies. A key example is given by the prediction models of the reproduction numbers: these rely on the generation time distribution that is usually estimated from contact tracing data collected at a precise calendar time. The forward scheme is used in such a prediction model and the knowledge of its evolution over time is crucial to correctly estimate the parameters of interest. It is therefore important to characterize the causes that lead to the contraction of the mean forward generation time during the course of an outbreak.In this paper, we firstly identify the impact of the epidemiological quantities as reproduction number, infectious period and population size on the mean forward and backward generation time. Moreover, we analyze the phenomena of competition among infectives and depletion of susceptible individuals highlighting their effects on the contraction of the mean forward generation time. The upshot of this investigation is that the variance of the infectious period distribution and the reproduction number have a strong impact on the generation times affecting both the mean value and the evolution over time. Furthermore, competition and depletion can both cause contraction even for small values of the reproduction number suggesting that, in epidemic models where the generation time is considered time-inhomogeneous, estimators accounting for both depletion and competing risks are to be preferred in the inference of the generation interval distributions.

scholarly journals A Data Driven Analysis and Forecast of COVID-19 Dynamics during the Third Wave Using SIRD Model in Bangladesh

COVID ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 503-517
Author(s):  
Omar Faruk ◽  
Suman Kar
Keyword(s):  
Numerical Simulations ◽  
Basic Reproduction Number ◽  
Goodness Of Fit ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Dynamics ◽  
Third Wave ◽  
The Third ◽  
The Government ◽  
The Basic Reproduction Number

In this study, we developed a compartmental SIRD model to analyze and forecast the transmission dynamics of the COVID-19 pandemic in Bangladesh during the third wave caused by the Indian delta variant. With the help of the nonlinear system of differential equations, this model can analyze the trends and provide reliable predictions regarding how the epidemic would evolve. The basic reproduction number regarding the pandemic has been determined analytically. The parameters used in this model have been estimated by fitting our model to the reported data for the months of May, June, and July 2021 and the goodness of fit of the parameter’s value has been found by the respective regression coefficients. Further, we conducted a sensitivity analysis of the basic reproduction number and observed that decreasing the transmission rate is the most significant factor in disease prevention. Our proposed model’s appropriateness for the available COVID-19 data in Bangladesh has been demonstrated through numerical simulations. According to the numerical simulation, it is evident that a rise in the transmission rate leads to a significant increase in the infected number of the population. Numerical simulations have also been performed by using our proposed model to forecast the future transmission dynamics for COVID-19 over a longer period of time. Knowledge of these forecasts may help the government in adopting appropriate measures to prepare for unforeseen situations that may arise in Bangladesh as well as to minimize detrimental impacts during the outbreak.

scholarly journals Visible and real dynamics of the COVID-19 pandemic in Ukraine in the spring of 2021

2021 ◽  
Author(s):  
Igor Nesteruk
Keyword(s):  
Real Number ◽  
Sir Model ◽  
Real Numbers ◽  
The Real ◽  
Daily Number ◽  
Optimal Value ◽  
Theoretical Predictions ◽  
Epidemic Wave ◽  
Good Agreement

The visible and real sizes the last COVID-19 epidemic wave in Ukraine, estimated in March 2021 with the use of generalized SIR-model, are compared with number of cases registered in the spring of 2021. We have used the optimal value of the visibility coefficient in order to estimate the real numbers of accumulated cases, real daily numbers of new cases and real number of infectious persons. The results show that the latest prediction for Ukraine is in rather good agreement with observations, but the daily number of new cases decreases more slowly than theoretical predictions. The large real number of infectious people threatens the emergence of new strains of coronavirus and the beginning of new epidemic waves.

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