scholarly journals Network model and analysis of the spread of Covid-19 with social distancing

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Parul Maheshwari ◽  
Réka Albert
Keyword(s):  
Network Model ◽  
Transmission Rate ◽  
Real Data ◽  
Disease Spread ◽  
Prevention Measures ◽  
Social Distancing ◽  
Workplace Interactions ◽  
Human Interactions ◽  
Reproduction Numbers ◽  
Second Wave

AbstractThe first mitigation response to the Covid-19 pandemic was to limit person-to-person interaction as much as possible. This was implemented by the temporary closing of many workplaces and people were required to follow social distancing. Networks are a great way to represent interactions among people and the temporary severing of these interactions. Here, we present a network model of human–human interactions that could be mediators of disease spread. The nodes of this network are individuals and different types of edges denote family cliques, workplace interactions, interactions arising from essential needs, and social interactions. Each individual can be in one of four states: susceptible, infected, immune, and dead. The network and the disease parameters are informed by the existing literature on Covid-19. Using this model, we simulate the spread of an infectious disease in the presence of various mitigation scenarios. For example, lockdown is implemented by deleting edges that denote non-essential interactions. We validate the simulation results with the real data by matching the basic and effective reproduction numbers during different phases of the spread. We also simulate different possibilities of the slow lifting of the lockdown by varying the transmission rate as facilities are slowly opened but people follow prevention measures like wearing masks etc. We make predictions on the probability and intensity of a second wave of infection in each of these scenarios.

scholarly journals Modifying the network-based stochastic SEIR model to account for quarantine: an application to COVID-19

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Chris Groendyke ◽  
Adam Combs
Keyword(s):  
Network Model ◽  
Transmission Rate ◽  
Disease Spread ◽  
Contact Network ◽  
Model Parameters ◽  
Seir Model ◽  
Disease States ◽  
Potential Contact ◽  
The Mean ◽  
Infectious State

Abstract Objectives: Diseases such as SARS-CoV-2 have novel features that require modifications to the standard network-based stochastic SEIR model. In particular, we introduce modifications to this model to account for the potential changes in behavior patterns of individuals upon becoming symptomatic, as well as the tendency of a substantial proportion of those infected to remain asymptomatic. Methods: Using a generic network model where every potential contact exists with the same common probability, we conduct a simulation study in which we vary four key model parameters (transmission rate, probability of remaining asymptomatic, and the mean lengths of time spent in the exposed and infectious disease states) and examine the resulting impacts on various metrics of epidemic severity, including the effective reproduction number. We then consider the effects of a more complex network model. Results: We find that the mean length of time spent in the infectious state and the transmission rate are the most important model parameters, while the mean length of time spent in the exposed state and the probability of remaining asymptomatic are less important. We also find that the network structure has a significant impact on the dynamics of the disease spread. Conclusions: In this article, we present a modification to the network-based stochastic SEIR epidemic model which allows for modifications to the underlying contact network to account for the effects of quarantine. We also discuss the changes needed to the model to incorporate situations where some proportion of the individuals who are infected remain asymptomatic throughout the course of the disease.

scholarly journals COVID-19 Time-varying Reproduction Numbers Worldwide: An Empirical Analysis of Mandatory and Voluntary Social Distancing

2021 ◽  
Author(s):  
Alexander Chudik ◽  
M. Hashem Pesaran ◽  
Alessandro Rebucci
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Economic Incentives ◽  
Moment Condition ◽  
Time Varying ◽  
Linear Interaction ◽  
Susceptible Population ◽  
Social Distancing ◽  
Transmission Rates ◽  
Reproduction Numbers

AbstractThis paper estimates time-varying COVID-19 reproduction numbers worldwide solely based on the number of reported infected cases, allowing for under-reporting. Estimation is based on a moment condition that can be derived from an agent-based stochastic network model of COVID-19 transmission. The outcomes in terms of the reproduction number and the trajectory of per-capita cases through the end of 2020 are very diverse. The reproduction number depends on the transmission rate and the proportion of susceptible population, or the herd immunity effect. Changes in the transmission rate depend on changes in the behavior of the virus, re-flecting mutations and vaccinations, and changes in people’s behavior, reflecting voluntary or government mandated isolation. Over our sample period, neither mutation nor vaccination are major factors, so one can attribute variation in the transmission rate to variations in behavior. Evidence based on panel data models explaining transmission rates for nine European countries indicates that the diversity of outcomes resulted from the non-linear interaction of mandatory containment measures, voluntary precautionary isolation, and the economic incentives that gov-ernments provided to support isolation. These effects are precisely estimated and robust to various assumptions. As a result, countries with seemingly different social distancing policies achieved quite similar outcomes in terms of the reproduction number. These results imply that ignoring the voluntary component of social distancing could introduce an upward bias in the estimates of the effects of lock-downs and support policies on the transmission rates.JEL ClassificationD0, F6, C4, I120, E7

scholarly journals Control Strategies for the Third wave of COVID-19 infection in India: A Mathematical Model Incorporating Vaccine Effectiveness

2022 ◽  
Author(s):  
Ashutosh Mahajan ◽  
Namitha Sivadas ◽  
Pooja Panda
Keyword(s):  
Transmission Rate ◽  
Control Strategies ◽  
Control Measures ◽  
Disease Spread ◽  
Effective Control ◽  
Third Wave ◽  
Social Distancing ◽  
Vaccination Rates ◽  
New Variant ◽  
The Future

The waning effectiveness of the COVID-19 vaccines and the emergence of a new variant Omicron has given rise to the possibility of another outbreak of the infection in India. COVID-19 has caused more than 34 million reported cases and 475 thousand deaths in India so far, and it has affected the country at the root level, socially as well as economically. After going through different control measures, mass vaccination has been achieved to a large extent for the highly populous country, and currently under progress. India has already been hit by a massive second wave of infection in April-June, 2021 mainly due to the delta variant, and might see a third wave in the near future that needs to be controlled with effective control strategies. In this paper, we present a compartmental epidemiological model with vaccinations incorporating the dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in the future, and bring out the associated predictions for various vaccination rates and point out optimum control measures. Our results show that for transmission rate 30% higher than the current rate due to emergence of new variant or relaxation of social distancing conditions, daily new cases can peak to 250k in March 2022, taking the second dose effectiveness dropping to 50% in the future. A combination of vaccination and controlled lockdown or social distancing is the key to tackling the current situation and for the coming few months. Our simulation results show that social distancing measures show better control over the disease spread than the higher vaccination rates. <br>

scholarly journals Control Strategies for the Third wave of COVID-19 infection in India: A Mathematical Model Incorporating Vaccine Effectiveness

2021 ◽  
Author(s):  
Namitha A Sivadas ◽  
Ashutosh Mahajan ◽  
Pooja Panda
Keyword(s):  
Transmission Rate ◽  
Control Strategies ◽  
Control Measures ◽  
Disease Spread ◽  
Effective Control ◽  
Third Wave ◽  
Social Distancing ◽  
Vaccination Rates ◽  
New Variant ◽  
The Future

The waning effectiveness of the COVID-19 vaccines and the emergence of a new variant Omicron has given rise to the possibility of another outbreak of the infection in India. COVID-19 has caused more than 34 million reported cases and 475 thousand deaths in India so far, and it has affected the country at the root level, socially as well as economically. After going through different control measures, mass vaccination has been achieved to a large extent for the highly populous country, and currently under progress. India has already been hit by a massive second wave of infection in April-June, 2021 mainly due to the delta variant, and might see a third wave in the near future that needs to be controlled with effective control strategies. In this paper, we present a compartmental epidemiological model with vaccinations incorporating the dose-dependent effectiveness. We study a possible sudden outbreak of SARS-CoV2 variants in the future, and bring out the associated predictions for various vaccination rates and point out optimum control measures. Our results show that for transmission rate 30% higher than the current rate due to emergence of new variant or relaxation of social distancing conditions, daily new cases can peak to 250k in March 2022, taking the second dose effectiveness dropping to 50% in the future. Combination of vaccination and controlled lockdown or social distancing is the key to tackling the current situation and for the coming few months. Our simulation results show that social distancing measures show better control over the disease spread than the higher vaccination rates.

scholarly journals No Place Like Home: Cross-National Data Analysis of the Efficacy of Social Distancing During the COVID-19 Pandemic (Preprint)

2020 ◽  
Author(s):  
Dursun Delen ◽  
Enes Eryarsoy ◽  
Behrooz Davazdahemami
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Disease Spread ◽  
Data Sets ◽  
Mobility Patterns ◽  
Social Distancing ◽  
Mobility Data ◽  
Simulation Based ◽  
Transactional Data ◽  
Cross National

BACKGROUND In the absence of a cure in the time of a pandemic, social distancing measures seem to be the most effective intervention to slow the spread of disease. Various simulation-based studies have been conducted to investigate the effectiveness of these measures. While those studies unanimously confirm the mitigating effect of social distancing on disease spread, the reported effectiveness varies from 10% to more than 90% reduction in the number of infections. This level of uncertainty is mostly due to the complex dynamics of epidemics and their time-variant parameters. However, real transactional data can reduce uncertainty and provide a less noisy picture of the effectiveness of social distancing. OBJECTIVE The aim of this paper was to integrate multiple transactional data sets (GPS mobility data from Google and Apple as well as disease statistics from the European Centre for Disease Prevention and Control) to study the role of social distancing policies in 26 countries and analyze the transmission rate of the coronavirus disease (COVID-19) pandemic over the course of 5 weeks. METHODS Relying on the susceptible-infected-recovered (SIR) model and official COVID-19 reports, we first calculated the weekly transmission rate (<i>β</i>) of COVID-19 in 26 countries for 5 consecutive weeks. Then, we integrated these data with the Google and Apple mobility data sets for the same time frame and used a machine learning approach to investigate the relationship between the mobility factors and <i>β</i> values. RESULTS Gradient boosted trees regression analysis showed that changes in mobility patterns resulting from social distancing policies explain approximately 47% of the variation in the disease transmission rates. CONCLUSIONS Consistent with simulation-based studies, real cross-national transactional data confirms the effectiveness of social distancing interventions in slowing the spread of COVID-19. In addition to providing less noisy and more generalizable support for the idea of social distancing, we provide specific insights for public health policy makers regarding locations that should be given higher priority for enforcing social distancing measures.

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 An SIR-type epidemiological model that integrates social distancing as a dynamic law based on point prevalence and socio-behavioral factors

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Maritza Cabrera ◽  
Fernando Córdova-Lepe ◽  
Juan Pablo Gutiérrez-Jara ◽  
Katia Vogt-Geisse
Keyword(s):  
Social Distance ◽  
Transmission Rate ◽  
Close Contact ◽  
Oscillatory Behavior ◽  
Point Prevalence ◽  
Disease Spread ◽  
Epidemic Outbreak ◽  
Social Distancing ◽  
Small Peak ◽  
Functional Forms

AbstractModeling human behavior within mathematical models of infectious diseases is a key component to understand and control disease spread. We present a mathematical compartmental model of Susceptible–Infectious–Removed to compare the infected curves given by four different functional forms describing the transmission rate. These depend on the distance that individuals keep on average to others in their daily lives. We assume that this distance varies according to the balance between two opposite thrives: the self-protecting reaction of individuals upon the presence of disease to increase social distancing and their necessity to return to a culturally dependent natural social distance that occurs in the absence of disease. We present simulations to compare results for different society types on point prevalence, the peak size of a first epidemic outbreak and the time of occurrence of that peak, for four different transmission rate functional forms and parameters of interest related to distancing behavior, such as: the reaction velocity of a society to change social distance during an epidemic. We observe the vulnerability to disease spread of close contact societies, and also show that certain social distancing behavior may provoke a small peak of a first epidemic outbreak, but at the expense of it occurring early after the epidemic onset, observing differences in this regard between society types. We also discuss the appearance of temporal oscillations of the four different transmission rates, their differences, and how this oscillatory behavior is impacted through social distancing; breaking the unimodality of the actives-curve produced by the classical SIR-model.

scholarly journals No Place Like Home: Cross-National Data Analysis of the Efficacy of Social Distancing During the COVID-19 Pandemic

10.2196/19862 ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. e19862 ◽  
Author(s):  
Dursun Delen ◽  
Enes Eryarsoy ◽  
Behrooz Davazdahemami
Keyword(s):  
Disease Transmission ◽  
Transmission Rate ◽  
Disease Spread ◽  
Data Sets ◽  
Mobility Patterns ◽  
Social Distancing ◽  
Mobility Data ◽  
Simulation Based ◽  
Transactional Data ◽  
Cross National

Background In the absence of a cure in the time of a pandemic, social distancing measures seem to be the most effective intervention to slow the spread of disease. Various simulation-based studies have been conducted to investigate the effectiveness of these measures. While those studies unanimously confirm the mitigating effect of social distancing on disease spread, the reported effectiveness varies from 10% to more than 90% reduction in the number of infections. This level of uncertainty is mostly due to the complex dynamics of epidemics and their time-variant parameters. However, real transactional data can reduce uncertainty and provide a less noisy picture of the effectiveness of social distancing. Objective The aim of this paper was to integrate multiple transactional data sets (GPS mobility data from Google and Apple as well as disease statistics from the European Centre for Disease Prevention and Control) to study the role of social distancing policies in 26 countries and analyze the transmission rate of the coronavirus disease (COVID-19) pandemic over the course of 5 weeks. Methods Relying on the susceptible-infected-recovered (SIR) model and official COVID-19 reports, we first calculated the weekly transmission rate (β) of COVID-19 in 26 countries for 5 consecutive weeks. Then, we integrated these data with the Google and Apple mobility data sets for the same time frame and used a machine learning approach to investigate the relationship between the mobility factors and β values. Results Gradient boosted trees regression analysis showed that changes in mobility patterns resulting from social distancing policies explain approximately 47% of the variation in the disease transmission rates. Conclusions Consistent with simulation-based studies, real cross-national transactional data confirms the effectiveness of social distancing interventions in slowing the spread of COVID-19. In addition to providing less noisy and more generalizable support for the idea of social distancing, we provide specific insights for public health policy makers regarding locations that should be given higher priority for enforcing social distancing measures.

scholarly journals Modelling the initial epidemic trends of COVID-19 in Italy, Spain, Germany, and France

PLoS ONE ◽  
2020 ◽  
Vol 15 (11) ◽  
pp. e0241743
Author(s):  
Kai Wang ◽  
Lin Ding ◽  
Yu Yan ◽  
Chengguqiu Dai ◽  
Minghan Qu ◽  
...  
Keyword(s):  
Transmission Rate ◽  
Credible Interval ◽  
Seir Model ◽  
Social Distancing ◽  
Initial Stage ◽  
Reproduction Numbers

The Coronavirus Disease 2019 (COVID-19) has fast spread to over 200 countries and regions worldwide since its outbreak, while in March, Europe became the emerging epicentre. In this study, we aimed to model the epidemic trends and estimate the essential epidemic features of COVID-19 in Italy, Spain, Germany, and France at the initial stage. The numbers of daily confirmed cases and total confirmed cases were extracted from the Coronavirus disease (COVID-19) situation reports of WHO. We applied an extended Susceptible-Exposed-Infectious-Removed (SEIR) model to fit the epidemic trend and estimated corresponding epidemic features. The transmission rate estimates were 1.67 (95% credible interval (CrI), 1.64–1.71), 2.83 (2.72–2.85), 1.91 (1.84–1.98), and 1.89 (1.82–1.96) for Italy, Spain, Germany, and France, corresponding to the basic reproduction numbers (R0) 3.44 (3.35–3.54), 6.25 (5.97–6.55), 4.03 (3.84–4.23), and 4.00 (3.82–4.19), respectively. We found Spain had the lowest ascertainment rate of 0.22 (0.19–0.25), followed by France, Germany, and Italy of 0.45 (0.40–0.50), 0.46 (0.40–0.52), and 0.59 (0.55–0.64). The peaks of daily new confirmed cases would reach on April 16, April 5, April 21, and April 19 for Italy, Spain, Germany, and France if no action was taken by the authorities. Given the high transmissibility and high covertness of COVID-19, strict countermeasures, such as national lockdown and social distancing, were essential to be implemented to reduce the spread of the disease.

scholarly journals Comparative Analysis of COVID-19 Transmission Patterns in Three Chinese Regions vs. South Korea, Italy and Iran

2020 ◽  
Author(s):  
Junyu He ◽  
Guangwei Chen ◽  
Yutong Jiang ◽  
Runjie Jin ◽  
Mingjun He ◽  
...  
Keyword(s):  
Public Health ◽  
Comparative Analysis ◽  
South Korea ◽  
Transmission Rate ◽  
Control Measures ◽  
Disease Spread ◽  
Normal Distribution Function ◽  
General Validity ◽  
Social Distancing ◽  
The Impact

AbstractBackgroundThe outbreak of Coronavirus 2019 (COVID-19) began in January 2020 in the city of Wuhan (Hubei province, China). It took about 2 months for China to get this infectious disease under control in its epicenter at Wuhan. Since February 2020, COVID-19 has been spreading around the world, becoming widespread in a number of countries. The timing and nature of government actions in response to the pandemic has varied from country to country, and their role in affecting the spread of the disease has been debated.MethodThe present study proposed a modified susceptible-exposed-infected-removed model (SEIR) model to perform a comparative analysis of the temporal progress of disease spread in six regions worldwide: three Chinese regions (Zhejiang, Guangdong and Xinjiang) vs. three countries (South Korea, Italy and Iran). For each region we developed detailed timelines of reported infections and outcomes, along with government- implemented measures to enforce social distancing. Simulations of the imposition of strong social distancing measures were used to evaluate the impact that these measures might have had on the duration and severity of COVID-19 outbreaks in the three countries.ResultsThe main results of this study are as follows: (a) an empirical COVID-19 growth law provides an excellent fit to the disease data in all study regions and potentially could be of more general validity; (b) significant differences exist in the spread characteristics of the disease among the three regions of China and between the three regions of China and the three countries; (c) under the control measures implemented in the Chinese regions (including the immediate quarantine of infected patients and their close contacts, and considerable restrictions on social contacts), the transmission rate of COVID-19 followed a modified normal distribution function, and it reached its peak after 1 to 2 days and then was reduced to zero 11, 11 and 18 days after a 1st-Level Response to Major Public Health Emergency was declared in Zhejiang, Guangdong and Xinjiang, respectively; moreover, the epidemic control times in Zhejiang, Guangdong and Xinjiang showed that the epidemic reached an “inflection point” after 9, 12 and 17 days, respectively, after a 1st-Level Response was issued; (d) an empirical COVID-19 law provided an excellent fit to the disease data in the six study regions, and the law can be potentially of more general validity; and (e) the curves of infected cases in South Korea, Italy and Iran would had been significantly flattened and shrunken at a relatively earlier stage of the epidemic if similar preventive measures as in the Chinese regions had been also taken in the above three countries on February 25th, February 25th and March 8th, respectively: the simulated maximum number of infected individuals in South Korea, Italy and Iran would had been 4480 cases (March 9th, 2020), 2335 cases (March 10th) and 6969 cases (March 20th), instead of the actual (reported) numbers of 7212 cases (March 9th), 8514 cases (March 10th, 2020) and 11466 cases (March 20th), respectively; moreover, up to March 29th, the simulated reduction in the accumulated number of infected cases would be 1585 for South Korea, 93490 for Italy and 23213 for Iran, respectively, accounting for 16.41% (South Korea), 95.70% (Italy) and 60.59% (Iran) of the accumulated number of actual reported infected cases.ConclusionsThe implemented measures in China were very effective for controlling the spread of COVID-19. These measures should be taken as early as possible, including the early identification of all infection sources and eliminating transmission pathways. Subsequently, the number of infected cases can be controlled at a low level, and existing medical resources could be sufficient for maintaining higher cure rates and lower mortality rate compared to the current situations in these countries. The proposed model can account for these prevention and control measures by properly adjusting its parameters, it computes the corresponding variations in disease transmission rate during the outbreak period, and it can provide valuable information for public health decision- making purposes.

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