scholarly journals Vaccination and herd immunity thresholds in heterogeneous populations

2021 ◽  
Author(s):  
Elamin H. Elbasha ◽  
Abba B. Gumel
Keyword(s):  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Heterogeneous Population ◽  
Relative Population ◽  
Homogeneous Population ◽  
Heterogeneous Populations ◽  
Contact Rates ◽  
Per Capita ◽  
Rigorous Mathematical Analysis

AbstractIt has been suggested, without rigorous mathematical analysis, that the classical vaccine-induced herd immunity threshold (HIT) assuming a homogeneous population can be substantially higher than the minimum HIT obtained when considering population heterogeneities. We investigated this claim by developing, and rigorously analyzing, a vaccination model that incorporates various forms of heterogeneity and compared it with a model of a homogeneous population. By employing a two-group vaccination model in heterogeneous populations, we theoretically established conditions under which heterogeneity leads to different HIT values, depending on the relative values of the contact rates for each group, the type of mixing between groups, relative vaccine efficacy, and the relative population size of each group. For example, under biased random mixing and when vaccinating a given group results in disproportionate prevention of higher transmission per capita, it is optimal to vaccinate that group before vaccinating other groups. We also found situations, under biased assortative mixing assumption, where it is optimal to vaccinate more than one group. We show that regardless of the form of mixing between groups, the HIT values assuming a heterogeneous population are always lower than the HIT values obtained from a corresponding model with a homogeneous population. Using realistic numerical examples and parametrization (e.g., assuming assortative mixing together with vaccine efficacy of 95% and basic reproduction number of 2.5), we demonstrate that the HIT value considering heterogeneity (e.g., biased assortative mixing) is significantly lower (40%) compared with a HIT value of (63%) assuming a homogeneous population.

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 Estimation of measles vaccine efficacy and critical vaccination coverage in a highly vaccinated population

2010 ◽  
Vol 7 (52) ◽  
pp. 1537-1544 ◽  
Author(s):  
Michiel van Boven ◽  
Mirjam Kretzschmar ◽  
Jacco Wallinga ◽  
Philip D O'Neill ◽  
Ole Wichmann ◽  
...  
Keyword(s):  
Public School ◽  
Vaccination Coverage ◽  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Herd Immunity ◽  
Credible Interval ◽  
Final Size ◽  
Measles Elimination ◽  
The Basic Reproduction Number

Measles is a highly infectious disease that has been targeted for elimination from four WHO regions. Whether and under which conditions this goal is feasible is, however, uncertain since outbreaks have been documented in populations with high vaccination coverage (more than 90%). Here, we use the example of a large outbreak in a German public school to show how estimates of key epidemiological parameters such as the basic reproduction number ( R 0 ), vaccine efficacy (VE S ) and critical vaccination coverage ( p c ) can be obtained from partially observed outbreaks in highly vaccinated populations. Our analyses rely on Bayesian methods of inference based on the final size distribution of outbreak size, and use data which are easily collected. For the German public school the analyses indicate that the basic reproduction number of measles is higher than previously thought ( , 95% credible interval: 23.6–40.4), that the vaccine is highly effective in preventing infection ( , 95% credible interval: 0.993–0.999), and that a vaccination coverage in excess of 95 per cent may be necessary to achieve herd immunity ( , 95% credible interval: 0.961–0.978). We discuss the implications for measles elimination from highly vaccinated populations.

Heterogeneity in epidemic models and its effect on the spread of infection

1998 ◽  
Vol 35 (3) ◽  
pp. 651-661 ◽  
Author(s):  
Håkan Andersson ◽  
Tom Britton
Keyword(s):  
Heterogeneous Population ◽  
Epidemic Models ◽  
Homogeneous Population ◽  
Epidemic Size ◽  
Infection Pressure ◽  
Group A ◽  
Final Epidemic Size ◽  
Spread Of Infection ◽  
Very High ◽  
High Infectivity

We first study an epidemic amongst a population consisting of individuals with the same infectivity but with varying susceptibilities to the disease. The asymptotic final epidemic size is compared with the corresponding size for a homogeneous population. Then we group a heterogeneous population into households, assuming very high infectivity within households, and investigate how the global infection pressure is affected by rearranging individuals between the households. In both situations considered, it turns out that whether or not homogenizing the individuals or households will result in an increased spread of infection actually depends on the infectiousness of the disease.

scholarly journals Estimating the impact of reopening schools on the reproduction number of SARS-CoV-2 in England, using weekly contact survey data

BMC Medicine ◽  
2021 ◽  
Vol 19 (1) ◽  
Author(s):  
James D. Munday ◽  
Christopher I. Jarvis ◽  
Amy Gimma ◽  
Kerry L. M. Wong ◽  
Kevin van Zandvoort ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Transmission Rate ◽  
Transmission Risk ◽  
Individual Level ◽  
Face To Face ◽  
School Settings ◽  
Contact Rates ◽  
Contact Survey ◽  
The Uk ◽  
The Impact

Abstract Background Schools were closed in England on 4 January 2021 as part of increased national restrictions to curb transmission of SARS-CoV-2. The UK government reopened schools on 8 March. Although there was evidence of lower individual-level transmission risk amongst children compared to adults, the combined effects of this with increased contact rates in school settings and the resulting impact on the overall transmission rate in the population were not clear. Methods We measured social contacts of > 5000 participants weekly from March 2020, including periods when schools were both open and closed, amongst other restrictions. We combined these data with estimates of the susceptibility and infectiousness of children compared with adults to estimate the impact of reopening schools on the reproduction number. Results Our analysis indicates that reopening all schools under the same measures as previous periods that combined lockdown with face-to-face schooling would be likely to increase the reproduction number substantially. Assuming a baseline of 0.8, we estimated a likely increase to between 1.0 and 1.5 with the reopening of all schools or to between 0.9 and 1.2 reopening primary or secondary schools alone. Conclusion Our results suggest that reopening schools would likely halt the fall in cases observed between January and March 2021 and would risk a return to rising infections, but these estimates relied heavily on the latest estimates or reproduction number and the validity of the susceptibility and infectiousness profiles we used at the time of reopening.

scholarly journals Will the Large-scale Vaccination Succeed in Containing the COVID-19 Epidemic and How Soon?

2021 ◽  
Author(s):  
Shilei Zhao ◽  
Tong Sha ◽  
Yongbiao Xue ◽  
Chung-I Wu ◽  
Hua Chen
Keyword(s):  
United States Of America ◽  
Vaccine Efficacy ◽  
Large Scale ◽  
Herd Immunity ◽  
Vaccination Rate ◽  
Epidemic Dynamics ◽  
Intervention Measures ◽  
Vaccination Scheme ◽  
Mutant Strains ◽  
Promising Solution

The availability of vaccines provides a promising solution to containing the COVID-19 pandemic. Here, we develop an epidemiological model to quantitatively analyze and predict the epidemic dynamics of COVID-19 under vaccination. The model is applied to the daily released numbers of confirmed cases of Israel and United States of America to explore and predict the trend under vaccination based on their current epidemic status and intervention measures. For Israel, of which 53.83% of the population was fully vaccinated, under the current intensity of NPIs and vaccination scheme, the pandemic is predicted to end between May 14, 2021 to May 16, 2021 depending on an immunity duration between 180 days and 365 days; Assuming no NPIs after March 24, 2021, the pandemic will ends later, between July 4, 2021 to August 26, 2021. For USA, if we assume the current vaccination rate (0.268% per day) and intensity of NPIs, the pandemic will end between February 3, 2022 and August 17, 2029 depending on an immunity duration between 180 days and 365 days. However, assuming an immunity duration of 180 days and with no NPIs, the pandemic will not end, and instead reach an equilibrium state with a proportion of the population remaining actively infected. Overall the daily vaccination rate should be chosen according to the vaccine efficacy and the immunity duration to achieve herd immunity. In some situations, vaccination alone cannot stop the pandemic, and NPIs are necessary both to supplement vaccination and accelerate the end of the pandemic. Considering that vaccine efficacy and duration of immunity may be reduced for new mutant strains, it is necessary to remain cautiously optimistic about the prospect of the pandemic under vaccination.

scholarly journals A window of opportunity for intensifying testing and tracing efforts to prevent new COVID-19 outbreaks due to more transmissible variants

2021 ◽  
Vol 47 (7/8) ◽  
pp. 329-338
Author(s):  
Jianhong Wu ◽  
Francesca Scarabel ◽  
Zachary McCarthy ◽  
Yanyu Xiao ◽  
Nicholas H Ogden
Keyword(s):  
Public Health ◽  
Reproduction Number ◽  
Health Interventions ◽  
Contact Tracing ◽  
Window Of Opportunity ◽  
New Wave ◽  
Public Health Interventions ◽  
Contact Rates ◽  
Large Outbreak ◽  
Restrictive Measures

Background: When public health interventions are being loosened after several days of decline in the number of coronavirus disease 2019 (COVID-19) cases, it is of critical importance to identify potential strategies to ease restrictions while mitigating a new wave of more transmissible variants of concern (VOCs). We estimated the necessary enhancements to public health interventions for a partial reopening of the economy while avoiding the worst consequences of a new outbreak, associated with more transmissible VOCs. Methods: We used a transmission dynamics model to quantify conditions that combined public health interventions must meet to reopen the economy without a large outbreak. These conditions are those that maintain the control reproduction number below unity, while accounting for an increase in transmissibility due to VOC. Results: We identified combinations of the proportion of individuals exposed to the virus who are traced and quarantined before becoming infectious, the proportion of symptomatic individuals confirmed and isolated, and individual daily contact rates needed to ensure the control reproduction number remains below unity. Conclusion: Our analysis indicates that the success of restrictive measures including lockdown and stay-at-home orders, as reflected by a reduction in number of cases, provides a narrow window of opportunity to intensify case detection and contact tracing efforts to prevent a new wave associated with circulation of more transmissible VOCs.

scholarly journals Demographics, perceptions, and socioeconomic factors affecting influenza vaccination among adults in the United States

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e5171 ◽  
Author(s):  
Kaja M. Abbas ◽  
Gloria J. Kang ◽  
Daniel Chen ◽  
Stephen R. Werre ◽  
Achla Marathe
Keyword(s):  
United States ◽  
Health Insurance ◽  
Influenza Vaccination ◽  
Vaccine Efficacy ◽  
Herd Immunity ◽  
The United States ◽  
Vaccine Cost ◽  
Factors Affecting ◽  
Vaccination Rates ◽  
Healthy People 2020

Objective The study objective is to analyze influenza vaccination status by demographic factors, perceived vaccine efficacy, social influence, herd immunity, vaccine cost, health insurance status, and barriers to influenza vaccination among adults 18 years and older in the United States. Background Influenza vaccination coverage among adults 18 years and older was 41% during 2010–2011 and has increased and plateaued at 43% during 2016–2017. This is below the target of 70% influenza vaccination coverage among adults, which is an objective of the Healthy People 2020 initiative. Methods We conducted a survey of a nationally representative sample of adults 18 years and older in the United States on factors affecting influenza vaccination. We conducted bivariate analysis using Rao-Scott chi-square test and multivariate analysis using weighted multinomial logistic regression of this survey data to determine the effect of demographics, perceived vaccine efficacy, social influence, herd immunity, vaccine cost, health insurance, and barriers associated with influenza vaccination uptake among adults in the United States. Results Influenza vaccination rates are relatively high among adults in older age groups (73.3% among 75 + year old), adults with education levels of bachelor’s degree or higher (45.1%), non-Hispanic Whites (41.8%), adults with higher incomes (52.8% among adults with income of over $150,000), partnered adults (43.2%), non-working adults (46.2%), and adults with internet access (39.9%). Influenza vaccine is taken every year by 76% of adults who perceive that the vaccine is very effective, 64.2% of adults who are socially influenced by others, and 41.8% of adults with health insurance, while 72.3% of adults without health insurance never get vaccinated. Facilitators for adults getting vaccinated every year in comparison to only some years include older age, perception of high vaccine effectiveness, higher income and no out-of-pocket payments. Barriers for adults never getting vaccinated in comparison to only some years include lack of health insurance, disliking of shots, perception of low vaccine effectiveness, low perception of risk for influenza infection, and perception of risky side effects. Conclusion Influenza vaccination rates among adults in the United States can be improved towards the Healthy People 2020 target of 70% by increasing awareness of the safety, efficacy and need for influenza vaccination, leveraging the practices and principles of commercial and social marketing to improve vaccine trust, confidence and acceptance, and lowering out-of-pocket expenses and covering influenza vaccination costs through health insurance.

Heterogeneity in epidemic models and its effect on the spread of infection

1998 ◽  
Vol 35 (03) ◽  
pp. 651-661 ◽  
Author(s):  
Håkan Andersson ◽  
Tom Britton
Keyword(s):  
Heterogeneous Population ◽  
Epidemic Models ◽  
Homogeneous Population ◽  
Epidemic Size ◽  
Infection Pressure ◽  
Group A ◽  
Final Epidemic Size ◽  
Spread Of Infection ◽  
Very High ◽  
High Infectivity

We first study an epidemic amongst a population consisting of individuals with the same infectivity but with varying susceptibilities to the disease. The asymptotic final epidemic size is compared with the corresponding size for a homogeneous population. Then we group a heterogeneous population into households, assuming very high infectivity within households, and investigate how the global infection pressure is affected by rearranging individuals between the households. In both situations considered, it turns out that whether or not homogenizing the individuals or households will result in an increased spread of infection actually depends on the infectiousness of the disease.

Trends in Health and Healthcare Utilization in Manitoba

2002 ◽  
Vol 15 (4_suppl) ◽  
pp. 35-38 ◽  
Author(s):  
Lisa M. Lix ◽  
Christine V. Newburn-Cook ◽  
Noralou P. Roos ◽  
Shelley Derksen
Keyword(s):  
Health Status ◽  
Mortality Rate ◽  
Healthcare Utilization ◽  
Hospital Admissions ◽  
Premature Mortality ◽  
Contact Rates ◽  
Physician Contact ◽  
Per Capita ◽  
The Difference ◽  
Hospital Days

Trends in health status and healthcare utilization were examined for regions of Manitoba from 1985 to 2000. While the provincial premature mortality rate decreased, the difference between the northern and southern regions increased. Hospital admissions remained stable despite major bed closures and an aging population; a decrease in hospital days per capita was observed in all regions. Physician contact rates also remained constant despite a 40% increase in the number of seniors.

scholarly journals A prototype vaccination model for endemic Covid-19 under waning immunity and imperfect vaccine take-up

2021 ◽  
Author(s):  
John S Dagpunar ◽  
ChenChen Wu
Keyword(s):  
Basic Reproduction Number ◽  
Vaccine Efficacy ◽  
Reproduction Number ◽  
Vaccine Coverage ◽  
Infection Prevalence ◽  
State Variables ◽  
Susceptible Population ◽  
Waning Immunity ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, for an infectious disease such as Covid-19, we present a SIR model which examines the impact of waning immunity, vaccination rates, vaccine efficacy, and the proportion of the susceptible population who aspire to be vaccinated. Under an assumed constant control reproduction number, we provide simple conditions for the disease to be eliminated, and conversely for it to exhibit the more likely endemic behaviour. With regard to Covid-19, it is shown that if the control reproduction number is set to the basic reproduction number (say 6) of the dominant delta (B1.617.2) variant, vaccination alone, even under the most optimistic of assumptions about vaccine efficacy and high vaccine coverage, is very unlikely to lead to elimination of the disease. The model is not intended to be predictive but more an aid to understanding the relative importance of various biological and control parameters. For example, from a long-term perspective, it may be found that in the UK, through changes in societal behaviour (such as mask use, ventilation, and level of homeworking), without formal government interventions such as on-off lockdowns, the control reproduction number can still be maintained at a level significantly below the basic reproduction number. Even so, our simulations show that endemic behaviour ensues. The model obtains equilibrium values of the state variables such as the infection prevalence and mortality rate under various scenarios.

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