scholarly journals A single-agent extension of the SIR model describes the impact of mobility restrictions on the COVID-19 epidemic

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Matteo Paoluzzi ◽  
Nicoletta Gnan ◽  
Francesca Grassi ◽  
Marco Salvetti ◽  
Nicola Vanacore ◽  
...  
Keyword(s):  
Exponential Growth ◽  
Single Agent ◽  
Sir Model ◽  
Epidemic Spreading ◽  
Peak Reduction ◽  
Slowing Down ◽  
Individual Mobility ◽  
Simple Rules ◽  
The Impact ◽  
Second Wave

AbstractMobility restrictions are successfully used to contain the diffusion of epidemics. In this work we explore their effect on the epidemic growth by investigating an extension of the Susceptible-Infected-Removed (SIR) model in which individual mobility is taken into account. In the model individual agents move on a chessboard with a Lévy walk and, within each square, epidemic spreading follows the standard SIR model. These simple rules allow to reproduce the sub-exponential growth of the epidemic evolution observed during the Covid-19 epidemic waves in several countries and which cannot be captured by the standard SIR model. We show that we can tune the slowing-down of the epidemic spreading by changing the dynamics of the agents from Lévy to Brownian and we investigate how the interplay among different containment strategies mitigate the epidemic spreading. Finally we demonstrate that we can reproduce the epidemic evolution of the first and second COVID-19 waves in Italy using only 3 parameters, i.e , the infection rate, the removing rate, and the mobility in the country. We provide an estimate of the peak reduction due to imposed mobility restrictions, i. e., the so-called flattening the curve effect. Although based on few ingredients, the model captures the kinetic of the epidemic waves, returning mobility values that are consistent with a lock-down intervention during the first wave and milder limitations, associated to a weaker peak reduction, during the second wave.

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 The impact of three progressively introduced interventions on second wave daily COVID-19 case numbers in Melbourne, Australia

2021 ◽  
Author(s):  
Allan James Saul ◽  
Nick Scott ◽  
Tim Spelman ◽  
Brendan S Crabb ◽  
Margaret Hellard
Keyword(s):  
Exponential Growth ◽  
Control Measure ◽  
Exponential Model ◽  
Initial Growth ◽  
Primary Analysis ◽  
Daily Growth ◽  
Day Range ◽  
Primary Model ◽  
The Impact ◽  
Second Wave

Background The city of Melbourne, Australia experienced two waves of the COVID-19 epidemic peaking in March and July 2020. During the second wave, a series of control measure were progressively introduced that initially slowed the growth of the epidemic then resulted in decreasing cases until there was no detectable local transmission. Methods To determine the relative efficacy of the progressively introduced intervention measures, we modelled this second wave as a series of exponential growth and decay curves. We used a linear regression of the log of daily cases vs time, using a four-segment linear spline model corresponding to implementation of the three successive major public health measures. The primary model used all reported cases between 14 June and 15 September then compared the projection of the model with observed cases predict future case trajectory up until the 31 October to assess the use of exponential models in projecting the future course and planning future interventions. The main outcome measures were the exponential daily growth constants, analysis of residuals and estimates of the 95% confidence intervals for the expected case distributions, comparison of predicted daily cases. Results: The exponential growth/decay constants in the primary analysis were: 0.122 (s.e. 0.004), 0.035 (s.e. 0.005), -0.037 (s.e. 0.011 ), and -0.069 (s.e. 0.003) for the initial growth rate, Stage 3, stage 3 + compulsory masks and Stage 4, respectively. Extrapolation of the regression model from the 14 September to the 31 October matched the decline in observed cases over this period. Conclusions: The four-segment exponential model provided an excellent fit of the observed reported case data and predicted the day-to-day range of expected cases. The extrapolated regression accurately predicted the decline leading to epidemic control in Melbourne.

scholarly journals Understanding the Spreading Patterns of COVID-19 in UK and Its Impact on Exit Strategies

2020 ◽  
Author(s):  
Maziar Nekovee
Keyword(s):  
Exponential Growth ◽  
Slow Growth ◽  
Contact Tracing ◽  
Mixing Models ◽  
Epidemic Spreading ◽  
Seir Model ◽  
Infected Population ◽  
Exit Strategies ◽  
Spatial Epidemic ◽  
Second Wave

Prior to lockdown the spread of COVID-19 in UK is found to be exponential, with an exponent α=0.207 In case of COVID-19 this spreading patterns is quantitatively better described with mobility-driven SIR-SEIR model [2] rather than the homogenous mixing models Lockdown has dramatically slowed down the spread of COVID-19 in UK, and even more significantly has changed the growth in the total number of infected from exponential to quadratic. This significant change is due a transition from a mobility-driven epidemic spreading to a spatial epidemic which is dominated by slow growth of spatially isolated clusters of infected population. Our results strongly indicated that, to avoid a return to exponential growth of COVID-19 (also known as “second wave”) mobility restrictions should not be prematurely lifted. Instead mobility should be kept restricted while new measures, such as wearing mask and contact tracing, get implemented in order to allow a safe exit from lockdown.

scholarly journals Hasty Reduction of COVID-19 Lockdown Measures Leads to the Second Wave of Infection

2020 ◽  
Author(s):  
Yara Hazem ◽  
Suchitra Natarajan ◽  
Essam R. Berikaa
Keyword(s):  
United States ◽  
United Kingdom ◽  
The United States ◽  
Sir Model ◽  
Global Impact ◽  
The United Kingdom ◽  
The Impact ◽  
Second Wave

AbstractThe outbreak of COVID-19 has an undeniable global impact, both socially and economically. March 11th, 2020, COVID-19 was declared as a pandemic worldwide. Many governments, worldwide, have imposed strict lockdown measures to minimize the spread of COVID-19. However, these measures cannot last forever; therefore, many countries are already considering relaxing the lockdown measures. This study, quantitatively, investigated the impact of this relaxation in the United States, Germany, the United Kingdom, Italy, Spain, and Canada. A modified version of the SIR model is used to model the reduction in lockdown based on the already available data. The results showed an inevitable second wave of COVID-19 infection following loosening the current measures. The study tries to reveal the predicted number of infected cases for different reopening dates. Additionally, the predicted number of infected cases for different reopening dates is reported.

scholarly journals Metamorphosis of COVID-19 Pandemic

2020 ◽  
Author(s):  
Farhan Saif
Keyword(s):  
Real Time ◽  
Growth Model ◽  
Exponential Growth ◽  
Impact Point ◽  
Time Data ◽  
Slowing Down ◽  
Real Time Data ◽  
The Usa ◽  
Mathematical Techniques ◽  
The Impact

We show phase-wise growth of COVID 19 pandemic and explain it by comparing real time data with Discrete Generalized Growth model and Discrete Generalized Richard Model. The comparison of COVID 19 is made for China, Italy, Japan and the USA. The mathematical techniques makes it possible to calculate the rate of exponential growth of active cases, estimates the size of the outbreak, and measures the deviation from the exponential growth indicating slowing down effect. The phase-wise pandemic evolution following the real time data of active cases defines the impact-point when the preventive steps, taken to eradicate the pandemic, becomes effective. The study is important to devise the measures to handle emerging threat of similar COVID-19 outbreaks in other countries, especially in the absence of a medicine.

scholarly journals Socio-economic indicators correlate with daily mobility during the second-wave of the Covid-19 pandemic

2021 ◽  
Author(s):  
Jed Long ◽  
Chang Ren
Keyword(s):  
Positive Association ◽  
Economic Indicators ◽  
Mobility Patterns ◽  
Mobility Data ◽  
Individual Mobility ◽  
Mobility Behaviour ◽  
The Impact ◽  
Second Wave ◽  
Pharmaceutical Interventions ◽  
Over Time

Non-pharmaceutical interventions are being used globally to limit the spread of Covid-19, which are in turn affecting individual mobility patterns. Mobility measures were found to be strongly associated with regional socio-economic indicators during the first wave of the pandemic. Here, we use network mobility data from an ~3.5 million person sample of individuals in Ontario, Canada to study the association between three different individual-mobility measures and four socio-economic indicators throughout the first and second wave of Covid-19 (January to December 2020). We demonstrate that understanding how mobility behaviours have changed in response to Covid-19 varies considerably depending on how mobility is measured. We find a strong positive association between different mobility levels and the economic deprivation index, which demonstrates that inequities in the changes to mobility across economic gradients observed during the initial lockdown have persisted into the later stages of the pandemic. However, the associations between mobility and other socio-economic indicators vary over time. We capture a strong day-of-week pattern of association between socio-economic indicators and mobility levels. Our findings have important implications for understanding if and how mobility data should be used to study the impact of non-pharmaceutical interventions on the socio-economic conditions across geographical space, and over time. Our results support that Covid-19 non-pharmaceutical interventions have resulted in geographically disparate responses to mobility behaviour, and quantifying mobility changes at fine geographical scales is crucial to understanding the impacts of Covid-19 on local populations.

scholarly journals Understanding the spreading patterns of COVID-19 in UK and its impact on exit strategies

2020 ◽  
Author(s):  
Maziar Nekovee
Keyword(s):  
Health Services ◽  
Exponential Growth ◽  
Slow Growth ◽  
Contact Tracing ◽  
Mixing Models ◽  
Epidemic Spreading ◽  
Seir Model ◽  
Infected Population ◽  
Spatial Epidemic ◽  
Second Wave

Prior to lockdown the spread of COVID-19 in UK is found to be exponential, with an exponent 0.207. In case of COVID-19 this spreading behaviour is quantitatively better described with a mobility-driven SIR-SEIR model [2] rather than the homogenous mixing models. Lockdown has dramatically slowed down the spread of COVID-19 in UK, and even more significantly, has changed the growth in the total number of infected from exponential to quadratic. This significant change is due to a transition from a mobility-driven epidemic spreading to a spatial epidemic which is dominated by slow growth of spatially isolated clusters of infected population. Our results strongly indicate that, to avoid a return to exponential growth of COVID-19 (also known as second wave), mobility restrictions should not be prematurely lifted. Instead mobility should be kept restricted while new measures, such as wearing of masks and contact tracing, get implemented in order to prevent health services becoming overwhelmed due to a resurgence of exponential growth.

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.

scholarly journals Discontinuous epidemic transition due to limited testing

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Davide Scarselli ◽  
Nazmi Burak Budanur ◽  
Marc Timme ◽  
Björn Hof
Keyword(s):  
Exponential Growth ◽  
Growth Period ◽  
High Impact ◽  
Contact Tracing ◽  
Epidemic Dynamics ◽  
Slowing Down ◽  
Containment Measures ◽  
Second Wave ◽  
Limited Testing ◽  
Pharmaceutical Interventions

AbstractHigh impact epidemics constitute one of the largest threats humanity is facing in the 21st century. In the absence of pharmaceutical interventions, physical distancing together with testing, contact tracing and quarantining are crucial in slowing down epidemic dynamics. Yet, here we show that if testing capacities are limited, containment may fail dramatically because such combined countermeasures drastically change the rules of the epidemic transition: Instead of continuous, the response to countermeasures becomes discontinuous. Rather than following the conventional exponential growth, the outbreak that is initially strongly suppressed eventually accelerates and scales faster than exponential during an explosive growth period. As a consequence, containment measures either suffice to stop the outbreak at low total case numbers or fail catastrophically if marginally too weak, thus implying large uncertainties in reliably estimating overall epidemic dynamics, both during initial phases and during second wave scenarios.

scholarly journals How Many Can You Infect? Simple (and Naive) Methods of Estimating the Reproduction Number

2020 ◽  
Vol 3 (1) ◽  
pp. 28-36
Author(s):  
H. Susanto ◽  
V.R. Tjahjono ◽  
A. Hasan ◽  
M.F. Kasim ◽  
N. Nuraini ◽  
...  
Keyword(s):  
Basic Reproduction Number ◽  
Exponential Growth ◽  
Reproduction Number ◽  
Sir Model ◽  
Epidemic Outbreak ◽  
Numerical Approximations ◽  
Expected Number ◽  
Slowing Down ◽  
Policy Responses ◽  
Current State

This is a pedagogical paper on estimating the number of people that can be infected by one infectious person during an epidemic outbreak, known as the reproduction number. Knowing the number is crucial for developing policy responses. There are generally two types of such a number, i.e., basic and effective (or instantaneous). While basic reproduction number is the average expected number of cases directly generated by one case in a population where all individuals are susceptible, effective reproduction number is the number of cases generated in the current state of a population. In this paper, we exploit the deterministic susceptibleinfected-removed (SIR) model to estimate them through three different numerical approximations. We apply the methods to the pandemic COVID-19 in Italy to provide insights into the spread of the disease in the country. We see that the effect of the national lockdown in slowing down the disease exponential growth appearedabout two weeks after the implementation date. We also discuss available improvements to the simple (and naive) methods that have been made by researchers in the field. Authors of this paper are members of the SimcovID (Simulasi dan Pemodelan COVID-19 Indonesia) collaboration.

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