scholarly journals The risk for a new COVID-19 wave and how it depends on R 0 , the current immunity level and current restrictions

2021 ◽  
Vol 8 (7) ◽  
pp. 210386
Author(s):  
Tom Britton ◽  
Pieter Trapman ◽  
Frank Ball
Keyword(s):  
Preventive Measures ◽  
Social Activity ◽  
Herd Immunity ◽  
Data Fitting ◽  
Time Varying ◽  
Two Factors ◽  
Simplistic Model ◽  
Induced Immunity ◽  
Epidemic Wave ◽  
Future Outbreak

The COVID-19 pandemic has hit different regions differently. The current disease-induced immunity level î in a region approximately equals the cumulative fraction infected, which primarily depends on two factors: (i) the initial potential for COVID-19 in the region ( R 0 ), and (ii) the preventive measures put in place. Using a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time are investigated. Focus lies on quantifying the minimal overall effect of preventive measures p Min needed to prevent a future outbreak. It is shown that î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R 0 and î it is shown that regions with lower R 0 and low î may need higher preventive measures ( p Min ) compared with regions having higher R 0 but also higher î , even when such immunity levels are far from herd immunity. Our results are illustrated on different regions but these comparisons contain lots of uncertainty due to simplistic model assumptions and insufficient data fitting, and should accordingly be interpreted with caution.

scholarly journals The risk for a new COVID-19 wave – and how it depends on R0, the current immunity level and current restrictions

2020 ◽  
Author(s):  
Tom Britton ◽  
Pieter Trapman ◽  
Frank Ball
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Time Varying ◽  
The World ◽  
Two Factors ◽  
Second Wave ◽  
Different Parts ◽  
Future Outbreak

AbstractThe COVID-19 pandemic has hit different parts of the world differently: some regions are still in the rise of the first wave, other regions are now facing a decline after a first wave, and yet other regions have started to see a second wave. The current immunity level î in a region is closely related to the cumulative fraction infected, which primarily depends on two factors: a) the initial potential for COVID-19 in the region (often quantified by the basic reproduction number R0), and b) the timing, amount and effectiveness of preventive measures put in place. By means of a mathematical model including heterogeneities owing to age, social activity and susceptibility, and allowing for time-varying preventive measures, the risk for a new epidemic wave and its doubling time, and how they depend on R0, î and the overall effect of the current preventive measures, are investigated. Focus lies on quantifying the minimal overall effect of preventive measures pMin needed to prevent a future outbreak. The first result shows that the current immunity level î plays a more influential roll than when immunity is obtained from vaccination. Secondly, by comparing regions with different R0 and î it is shown that regions with lower R0 and low î may now need higher preventive measures (pMin) compared with other regions having higher R0 but also higher î, even when such immunity levels are far from herd immunity.

scholarly journals A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2

Science ◽  
2020 ◽  
Vol 369 (6505) ◽  
pp. 846-849 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Mathematical Model ◽  
Severe Acute Respiratory Syndrome ◽  
Preventive Measures ◽  
Social Activity ◽  
Herd Immunity ◽  
Population Heterogeneity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Age Structured ◽  
Induced Immunity

Despite various levels of preventive measures, in 2020, many countries have suffered severely from the coronavirus disease 2019 (COVID-19) pandemic caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus. Using a model, we show that population heterogeneity can affect disease-induced immunity considerably because the proportion of infected individuals in groups with the highest contact rates is greater than that in groups with low contact rates. We estimate that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity, then the disease-induced herd immunity level can be ~43%, which is substantially less than the classical herd immunity level of 60% obtained through homogeneous immunization of the population. Our estimates should be interpreted as an illustration of how population heterogeneity affects herd immunity rather than as an exact value or even a best estimate.

scholarly journals The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level

2020 ◽  
Author(s):  
Tom Britton ◽  
Frank Ball ◽  
Pieter Trapman
Keyword(s):  
Preventive Measures ◽  
Reproduction Number ◽  
Social Activity ◽  
Herd Immunity ◽  
Contact Rates ◽  
Mixing Rates ◽  
Disease Spreading ◽  
Age Structured ◽  
Induced Immunity ◽  
The Basic Reproduction Number

AbstractMost countries are suffering severely from the ongoing covid-19 pandemic despite various levels of preventive measures. A common question is if and when a country or region will reach herd immunity h. The classical herd immunity level hC is defined as hC = 1−1/R0, where R0 is the basic reproduction number, for covid-19 estimated to lie somewhere in the range 2.2-3.5 depending on country and region. It is shown here that the disease-induced herd immunity level hD, after an outbreak has taken place in a country/region with a set of preventive measures put in place, is actually substantially smaller than hC. As an illustration we show that if R0 = 2.5 in an age-structured community with mixing rates fitted to social activity studies, and also categorizing individuals into three categories: low active, average active and high active, and where preventive measures affect all mixing rates proportionally, then the disease-induced herd immunity level is hD = 43% rather than hC = 1−1/2.5 = 60%. Consequently, a lower fraction infected is required for herd immunity to appear. The underlying reason is that when immunity is induced by disease spreading, the proportion infected in groups with high contact rates is greater than that in groups with low contact rates. Consequently, disease-induced immunity is stronger than when immunity is uniformly distributed in the community as in the classical herd immunity level.

scholarly journals Estimating SARS-CoV-2 infections from deaths, confirmed cases, tests, and random surveys

2021 ◽  
Vol 118 (31) ◽  
pp. e2103272118
Author(s):  
Nicholas J. Irons ◽  
Adrian E. Raftery
Keyword(s):  
Herd Immunity ◽  
The United States ◽  
Sir Model ◽  
Mitigation Strategies ◽  
Time Varying ◽  
Fatality Rate ◽  
Multiple Sources ◽  
Population Prevalence ◽  
Sample Testing ◽  
True Infection

There are multiple sources of data giving information about the number of SARS-CoV-2 infections in the population, but all have major drawbacks, including biases and delayed reporting. For example, the number of confirmed cases largely underestimates the number of infections, and deaths lag infections substantially, while test positivity rates tend to greatly overestimate prevalence. Representative random prevalence surveys, the only putatively unbiased source, are sparse in time and space, and the results can come with big delays. Reliable estimates of population prevalence are necessary for understanding the spread of the virus and the effectiveness of mitigation strategies. We develop a simple Bayesian framework to estimate viral prevalence by combining several of the main available data sources. It is based on a discrete-time Susceptible–Infected–Removed (SIR) model with time-varying reproductive parameter. Our model includes likelihood components that incorporate data on deaths due to the virus, confirmed cases, and the number of tests administered on each day. We anchor our inference with data from random-sample testing surveys in Indiana and Ohio. We use the results from these two states to calibrate the model on positive test counts and proceed to estimate the infection fatality rate and the number of new infections on each day in each state in the United States. We estimate the extent to which reported COVID cases have underestimated true infection counts, which was large, especially in the first months of the pandemic. We explore the implications of our results for progress toward herd immunity.

scholarly journals Effect of Vaccination to COVID-19 Disease Progression and Herd Immunity

2021 ◽  
Vol 9 (1) ◽  
pp. 262-272
Author(s):  
Randy L. Caga-anan ◽  
Michelle N. Raza ◽  
Grace Shelda G. Labrador ◽  
Ephrime B. Metillo ◽  
Pierre del Castillo ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Disease Progression ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
The Philippines ◽  
Model Parameters ◽  
Delay Term ◽  
Induced Immunity ◽  
Determining Factor ◽  
Disease Free

Abstract A mathematical model of COVID-19 with a delay-term for the vaccinated compartment is developed. It has parameters accounting for vaccine-induced immunity delay, vaccine effectiveness, vaccination rate, and vaccine-induced immunity duration. The model parameters before vaccination are calibrated with the Philippines’ confirmed cases. Simulations show that vaccination has a significant effect in reducing future infections, with the vaccination rate being the dominant determining factor of the level of reduction. Moreover, depending on the vaccination rate and the vaccine-induced immunity duration, the system could reach a disease-free state but could not attain herd immunity. Simulations are also done to compare the effects of the various available vaccines. Results show that Pfizer-BioNTech has the most promising effect while Sinovac has the worst result relative to the others.

scholarly journals THE SCALE OF THE SPREAD OF COVID-19 IN GEORGIA AND EFFECTIVENESS OF PREVENTIVE MEASURES IMPLIMENTED BY THE GOVERNMENT – WHAT DO MODELS SAY?

2020 ◽  
pp. 49-57
Author(s):  
IURI ANANIASHVILI ◽  
LEVAN GAPRINDASHVILI
Keyword(s):  
Machine Learning ◽  
Preventive Measures ◽  
Herd Immunity ◽  
Optimal Level ◽  
Short Term ◽  
Machine Learning Methods ◽  
Data Limitations ◽  
The Government ◽  
Different Characteristics

. In this article we present forecasts of the spread of COVID-19 virus, obtained by econometric and machine learning methods. Furthermore, by employing modelling method, we estimate effectiveness of preventive measures implemented by the government. Each of the models discussed in this article is modelling different characteristics of the COVID-19 epidemic’s trajectory: peak and end date, number of daily infections over different forecasting horizons, total number of infection cases. All these provide quite clear picture to the interested reader of the future threats posed by COVID-19. In terms of existing models and data, our research indicates that phenomenological models do well in forecasting the trend, duration and total infections of the COVID- 19 epidemic, but make serious mistakes in forecasting the number of daily infections. Machine learning models, deliver more accurate short –term forecast of daily infections, but due to data limitations, they struggle to make long-term forecasts. Compartmental models are the best choice for modelling the measures implemented by the government for preventing the spread of COVID-19 and determining optimal level of restrictions. These models show that until achieving herd immunity (i.e. without any epidemiological or government implemented measures), approximate number of people infected with COVID-19 would be 3 million, but due to preventive measures, expected total number of infections has reduced to several thousand (1555-3189) people. This unequivocally indicates the effectiveness of the preventive measures.

scholarly journals Missed takes towards a pandemic of COVID-19? A systematic literature review of Coronavirus related diseases in Pakistan

2020 ◽  
Vol 14 (07) ◽  
pp. 726-731
Author(s):  
Wajiha Haq ◽  
Syed Hassan Raza ◽  
Muhammad Wasif Malik
Keyword(s):  
Health Care ◽  
Developing Countries ◽  
Literature Review ◽  
Health Care System ◽  
Respiratory Diseases ◽  
Systematic Approach ◽  
Preventive Measures ◽  
Herd Immunity ◽  
Scientific Investigation ◽  
Open Research

Pakistan is also seeing the profound effect of the outbreak of COVID-19, which demands an urgent investigation of literature and further scientific investigation for cure and prevention. This study has employed the systematic approach for searching the literature from the recently compiled database of researches namely COVID-19 Open Research Dataset (CORD-19) and related diseases. The literature on Pakistan has shown the evidence of human-to-human and animal-to-human transmission of viruses, the presence of antibodies of MERS-CoV in camels, and careless attitude towards preventive measures of such respiratory diseases. There is a lot of gap in the literature regarding coronaviruses and their antibodies creating herd immunity for another coronavirus and COVID-19. In particular to Pakistan, and in general, for other developing countries, a weak health-care system coupled with the trembling economy has many implications of COVID-19 which should be carefully thought-out to combat the spread.

scholarly journals Development of a Scale for Assessing the Meaning of Participation in Care Prevention Group Activities Provided by Local Governments in Japan

2020 ◽  
Vol 17 (12) ◽  
pp. 4499
Author(s):  
Ryu Sasaki ◽  
Michiyo Hirano
Keyword(s):  
Local Governments ◽  
Goodness Of Fit ◽  
Daily Life ◽  
Social Activity ◽  
Reliability And Validity ◽  
Satisfaction Scale ◽  
Group Activities ◽  
Scale Scores ◽  
Two Factors ◽  
Fit Index

The meaning of participation in care prevention group activities may encourage continuous participation, making older adults active and healthy throughout their lives. This study developed a scale to assess the meaning of participation in care prevention group activities. It involved 427 participants in care prevention group activities (CPGAs) in Japan who filled out a self-administered questionnaire between October 2017 and February 2018. The meaning of participation was assessed using 15 items. In total, there were 379 valid responses. A factor analysis yielded two factors: “promotion of self-growth” and “enrichment of daily life”. The goodness of fit index (GFI), comparative fit index (CFI), and root mean square error of approximation (RMSEA) were satisfactory (GFI = 0.923; CFI = 0.960; RMSEA = 0.073). Cronbach’s α was 0.939 for the entire scale. The scale scores were significantly correlated with scores of the social activity-related daily life satisfaction scale and Ikigai-9. The scale’s reliability and validity were confirmed, indicating its usability for promoting care prevention efforts.

scholarly journals Investors’ Risk Preference Characteristics Based on Different Reference Point

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Fenghua Wen ◽  
Zhifang He ◽  
Xu Gong ◽  
Aiming Liu
Keyword(s):  
Stock Market ◽  
Risk Aversion ◽  
Empirical Evidence ◽  
Reference Point ◽  
Risk Preference ◽  
Reference Points ◽  
Time Varying ◽  
Explanatory Variables ◽  
House Money Effect ◽  
Two Factors

Taking the stock market as a whole object, we assume that prior losses and gains are two different factors that can influence risk preference separately. The two factors are introduced as separate explanatory variables into the time-varying GARCH-M (TVRA-GARCH-M) model. Then, we redefine prior losses and gains by selecting different reference point to study investors’ time-varying risk preference. The empirical evidence shows that investors’ risk preference is time varying and is influenced by previous outcomes; the stock market as a whole exhibits house money effect; that is, prior gains can decrease investors’ risk aversion while prior losses increase their risk aversion. Besides, different reference points selected by investors will cause different valuation of prior losses and gains, thus affecting investors’ risk preference.

scholarly journals Low SARS-CoV-2 seroprevalence but high perception of risk among healthcare workers at children’s hospital before second pandemic wave in Germany

2021 ◽  
Author(s):  
Marietta Neumann ◽  
Annette Aigner ◽  
Eileen Rossow ◽  
David Schwarz ◽  
Maria Marschallek ◽  
...  
Keyword(s):  
Confidence Interval ◽  
Perceived Risk ◽  
Odds Ratio ◽  
Healthcare Workers ◽  
Herd Immunity ◽  
High Risk Group ◽  
Children's Hospital ◽  
Significant Difference ◽  
Children’S Hospital ◽  
Epidemic Wave

Abstract Background Healthcare workers are considered a particularly high-risk group during the coronavirus disease 2019 (COVID-19) pandemic. Healthcare workers in paediatrics are a unique subgroup: they come into frequent contact with children, who often experience few or no symptoms when infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and, therefore, may transmit the disease to unprotected staff. In Germany, no studies exist evaluating the risk of COVID-19 to healthcare workers in paediatric institutions. Methods We tested the staff at a large children’s hospital in Germany for immunoglobulin (Ig) G antibodies against the nucleocapsid protein of SARS-CoV-2 in a period between the first and second epidemic wave in Germany. We used a questionnaire to assess each individual’s exposure risk and his/her own perception of having already been infected with SARS-CoV-2. Results We recruited 619 participants from all sectors, clinical and non-clinical, constituting 70% of the entire staff. The seroprevalence of SARS-CoV-2 antibodies was 0.325% (95% confidence interval 0.039–1.168). Self-perceived risk of a previous SARS-CoV-2 infection decreased with age (odds ratio, 0.81; 95% confidence interval, 0.70–0.93). Having experienced symptoms more than doubled the odds of a high self-perceived risk (odds ratio, 2.18; 95% confidence interval, 1.59–3.00). There was no significant difference in self-perceived risk between men and women. Conclusions Seroprevalence was low among healthcare workers at a large children’s hospital in Germany before the second epidemic wave, and it was far from a level that confers herd immunity. Self-perceived risk of infection is often overestimated.

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