Final Attack Rate Research Articles

Examining the effects of voluntary avoidance behaviour and policy-mediated behaviour change on the dynamics of SARS-CoV-2: A mathematical model

BackgroundThroughout the SARS-CoV-2 pandemic, policymakers have had to navigate between recommending voluntary behaviour change and policy-driven behaviour change to mitigate the impact of the virus. While individuals will voluntarily engage in self-protective behaviour when there is an increasing infectious disease risk, the extent to which this occurs and its impact on an epidemic is not known. MethodsThis paper describes a deterministic disease transmission model exploring the impact of individual avoidance behaviour and policy-mediated avoidance behaviour on epidemic outcomes during the second wave of SARS-CoV-2 infections in Ontario, Canada (September 1, 2020 to February 28, 2021). The model incorporates an information feedback function based on empirically derived behaviour data describing the degree to which avoidance behaviour changed in response to the number of new daily cases COVID-19. ResultsVoluntary avoidance behaviour alone was estimated to reduce the final attack rate by 23.1%, the total number of hospitalizations by 26.2%, and cumulative deaths by 27.5% over 6 months compared to a counterfactual scenario in which there were no interventions or avoidance behaviour. A provincial shutdown order issued on December 26, 2020 was estimated to reduce the final attack rate by 66.7%, the total number of hospitalizations by 66.8%, and the total number of deaths by 67.2% compared to the counterfactual scenario. ConclusionGiven the dynamics of SARS-CoV-2 in a pre-vaccine era, individual avoidance behaviour in the absence of government action would have resulted in a moderate reduction in disease however, it would not have been sufficient to entirely mitigate transmission and the associated risk to the population in Ontario. Government action during the second wave of the COVID-19 pandemic in Ontario reduced infections, protected hospital capacity, and saved lives.

The minimal COVID-19 vaccination coverage and efficacy to compensate for a potential increase of transmission contacts, and increased transmission probability of the emerging strains

BackgroundMass immunization is a potentially effective approach to finally control the local outbreak and global spread of the COVID-19 pandemic. However, it can also lead to undesirable outcomes if mass vaccination results in increased transmission of effective contacts and relaxation of other public health interventions due to the perceived immunity from the vaccine.MethodsWe designed a mathematical model of COVID-19 transmission dynamics that takes into consideration the epidemiological status, public health intervention status (quarantined/isolated), immunity status of the population, and strain variations. Comparing the control reproduction numbers and the final epidemic sizes (attack rate) in the cases with and without vaccination, we quantified some key factors determining when vaccination in the population is beneficial for preventing and controlling future outbreaks.ResultsOur analyses predicted that there is a critical (minimal) vaccine efficacy rate (or a critical quarantine rate) below which the control reproduction number with vaccination is higher than that without vaccination, and the final attack rate in the population is also higher with the vaccination. We also predicted the worst case scenario occurs when a high vaccine coverage rate is achieved for a vaccine with a lower efficacy rate and when the vaccines increase the transmission efficient contacts.ConclusionsThe analyses show that an immunization program with a vaccine efficacy rate below the predicted critical values will not be as effective as simply investing in the contact tracing/quarantine/isolation implementation. We reached similar conclusions by considering the final epidemic size (or attack rates). This research then highlights the importance of monitoring the impact on transmissibility and vaccine efficacy of emerging strains.

Homophily impacts the success of vaccine roll-outs

Physical contacts do not occur randomly, rather, individuals with similar socio-demographic and behavioral characteristics are more likely to interact among them, a phenomenon known as homophily. Concurrently, the same characteristics correlate with the adoption of prophylactic tools. As a result, the latter do not unfold homogeneously in a population, affecting their ability to control the spread of infectious diseases. Focusing on the case of vaccines, we reveal that, provided an imperfect vaccine efficacy, three different dynamical regimes exist as a function of the mixing rate between vaccinated and not vaccinated individuals. Specifically, depending on the epidemic pressure, vaccine coverage and efficacy, we find the final attack rate to decrease, increase or vary non monotonously with respect to the mixing rate. We corroborate the phenomenology through Monte Carlo simulations on a temporal real-world contact network. Besides vaccines, our findings hold for any prophylactic tool that reduces but not suppress the probability of transmission, indicating a universal mechanism in spreading dynamics.

A model framework for projecting the prevalence and impact of Long-COVID in the UK.

The objective of this paper is to model lost Quality Adjusted Life Years (QALYs) from symptoms arising from COVID-19 disease in the UK population, including symptoms of 'long-COVID'. The scope includes QALYs lost to symptoms, but not deaths, due to acute COVID-19 and long-COVID. The prevalence of symptomatic COVID-19, encompassing acute symptoms and long-COVID symptoms, was modelled using a decay function. Permanent injury as a result of COVID-19 infection, was modelled as a fixed prevalence. Both parts were combined to calculate QALY loss due to COVID-19 symptoms. Assuming a 60% final attack rate for SARS-CoV-2 infection in the population, we modelled 299,730 QALYs lost within 1 year of infection (90% due to symptomatic COVID-19 and 10% permanent injury) and 557,764 QALYs lost within 10 years of infection (49% due to symptomatic COVID-19 and 51% due to permanent injury). The UK Government willingness-to-pay to avoid these QALY losses would be £17.9 billion and £32.2 billion, respectively. Additionally, 90,143 people were subject to permanent injury from COVID-19 (0.14% of the population). Given the ongoing development in information in this area, we present a model framework for calculating the health economic impacts of symptoms following SARS-CoV-2 infection. This model framework can aid in quantifying the adverse health impact of COVID-19, long-COVID and permanent injury following COVID-19 in society and assist the proactive management of risk posed to health. Further research is needed using standardised measures of patient reported outcomes relevant to long-COVID and applied at a population level.

Modelling testing and response strategies for COVID-19 outbreaks in remote Australian Aboriginal communities

BackgroundRemote Australian Aboriginal and Torres Strait Islander communities have potential to be severely impacted by COVID-19, with multiple factors predisposing to increased transmission and disease severity. Our modelling aims to inform optimal public health responses.MethodsAn individual-based simulation model represented SARS-CoV2 transmission in communities ranging from 100 to 3500 people, comprised of large, interconnected households. A range of strategies for case finding, quarantining of contacts, testing, and lockdown were examined, following the silent introduction of a case.ResultsMultiple secondary infections are likely present by the time the first case is identified. Quarantine of close contacts, defined by extended household membership, can reduce peak infection prevalence from 60 to 70% to around 10%, but subsequent waves may occur when community mixing resumes. Exit testing significantly reduces ongoing transmission. Concurrent lockdown of non-quarantined households for 14 days is highly effective for epidemic control and reduces overall testing requirements; peak prevalence of the initial outbreak can be constrained to less than 5%, and the final community attack rate to less than 10% in modelled scenarios. Lockdown also mitigates the effect of a delay in the initial response. Compliance with lockdown must be at least 80–90%, however, or epidemic control will be lost.ConclusionsA SARS-CoV-2 outbreak will spread rapidly in remote communities. Prompt case detection with quarantining of extended-household contacts and a 14 day lockdown for all other residents, combined with exit testing for all, is the most effective strategy for rapid containment. Compliance is crucial, underscoring the need for community supported, culturally sensitive responses.

Factors influencing SARS-CoV-2 transmission and outbreak control measures in densely populated settings

Starting with a handful of SARS-CoV-2 infections in dormitory residents in late March 2020, rapid transmission in their dense living environments ensued and by October 2020, more than 50,000 acute infections were identified across various dormitories in Singapore. The aim of the study is to identify combination of factors facilitating SARS-CoV-2 transmission and the impact of control measures in a dormitory through extensive epidemiological, serological and phylogenetic investigations, supported by simulation models. Our findings showed that asymptomatic cases and symptomatic cases who did not seek medical attention were major drivers of the outbreak. Furthermore, each resident had about 30 close contacts and each infected resident spread to 4.4 (IQR 3.5–5.3) others at the start of the outbreak. The final attack rate of the current outbreak was 76.2% (IQR 70.6–98.0%) and could be reduced by further 10% under a modified dormitory housing condition. These findings are important when designing living environments in a post COVID-19 future to reduce disease spread and facilitate rapid implementation of outbreak control measures.

Potential lethal outbreak of coronavirus disease (COVID-19) among the elderly in retirement homes and long-term facilities, France, March 2020.

Motivated by the potential devastating effect of a COVID-19 outbreak in retirement homes and long-term facilities for dependent elderly, we present the impact of worst-case scenarios in French institutions using a specific age structure and case–age fatality ratios. The death toll could equal the yearly death toll caused by seasonal influenza in those older than 65 years or could largely exceed that, depending on the final attack rate and proportion of infected institutions.

Is West Africa Approaching a Catastrophic Phase or is the 2014 Ebola Epidemic Slowing Down? Different Models Yield Different Answers for Liberia.

An unprecedented epidemic of Zaire ebolavirus (EBOV) has affected West Africa since approximately December 2013, with intense transmission on-going in Guinea, Sierra Leone and Liberia and increasingly important international repercussions. Mathematical models are proving instrumental to forecast the expected number of infections and deaths and quantify the intensity of interventions required to control transmission; however, calibrating mechanistic transmission models to an on-going outbreak is a challenging task owing to limited availability of epidemiological data and rapidly changing interventions. Here we project the trajectory of the EBOV epidemic in Liberia by fitting logistic growth models to the cumulative number of cases. Our model predictions align well with the latest epidemiological reports available as of October 23, and indicates that the exponential growth phase is over in Liberia, with an expected final attack rate of ~0.1-0.12%. Our results indicate that simple phenomenological models can provide complementary insights into the dynamics of an outbreak and capture early signs of changes in population behavior and interventions. In particular, our results underscore the need to treat the effective size of the susceptible population as a dynamic variable rather than a fixed quantity, due to reactive changes in transmission throughout the outbreak. We show that predictions from the logistic model are more variable in the earlier stages of an epidemic (such as the EBOV epidemics in Sierra Leone and Guinea). More research is warranted to compare the performances of mechanistic and phenomenological approaches for disease forecasts, before such predictions can be fully used by public health authorities.

The role of schools in the spread of mumps among unvaccinated children: a retrospective cohort study.

BackgroundIn the Netherlands, epidemics of vaccine preventable diseases are largely confined to an orthodox protestant minority with religious objections to vaccination. The clustering of unvaccinated children in orthodox protestant schools can foster the spread of epidemics. School closure has nevertheless not been practiced up until now. A mumps epidemic in 2007-2008 gave us an opportunity to study the role of schools in the spread of a vaccine preventable disease in a village with low vaccination coverage.MethodsA retrospective cohort study was conducted among the students in four elementary schools and their siblings. The following information was collected for each child: having had the mumps or not and when, school, age, MMR vaccination status, household size, presence of high school students in the household, religious denomination, and home village. The spread of mumps among unvaccinated children was compared for the four schools in a Kaplan-Meier analysis using a log-rank test. Cox proportional hazard analyses were performed to test for the influence of other factors. To correct for confounding, a univariate Cox regression model with only school included as a determinant was compared to a multivariate regression model containing all possible confounders.ResultsOut of 650 households with children at the schools, 54% completed a questionnaire, which provided information on 1191 children. For the unvaccinated children (N = 769), the Kaplan-Meier curves showed significant differences among the schools in their cumulative attack rates. After correction for confounding, the Cox regression analysis showed the hazard of mumps to be higher in one orthodox protestant school compared to the other (hazard ratio 1.43, p < 0.001). Household size independently influenced the hazard of mumps (hazard ratio 1.44, p < 0.005) with children in larger households running a greater risk.ConclusionIf and when unvaccinated children got mumps was determined by the particular school the children and their siblings attended, and by the household size. This finding suggests that school closure can influence the spread of an epidemic among orthodox protestant populations, provided that social distancing is adhered to as well. Further research on the effects of school closure on the final attack rate is nevertheless recommended.

Analysis of the effectiveness of interventions used during the 2009 A/H1N1 influenza pandemic

BackgroundFollowing the emergence of the A/H1N1 2009 influenza pandemic, public health interventions were activated to lessen its potential impact. Computer modelling and simulation can be used to determine the potential effectiveness of the social distancing and antiviral drug therapy interventions that were used at the early stages of the pandemic, providing guidance to public health policy makers as to intervention strategies in future pandemics involving a highly pathogenic influenza strain.MethodsAn individual-based model of a real community with a population of approximately 30,000 was used to determine the impact of alternative interventions strategies, including those used in the initial stages of the 2009 pandemic. Different interventions, namely school closure and antiviral strategies, were simulated in isolation and in combination to form different plausible scenarios. We simulated epidemics with reproduction numbers R0of 1.5, which aligns with estimates in the range 1.4-1.6 determined from the initial outbreak in Mexico.ResultsSchool closure of 1 week was determined to have minimal effect on reducing overall illness attack rate. Antiviral drug treatment of 50% of symptomatic cases reduced the attack rate by 6.5%, from an unmitigated rate of 32.5% to 26%. Treatment of diagnosed individuals combined with additional household prophylaxis reduced the final attack rate to 19%. Further extension of prophylaxis to close contacts (in schools and workplaces) further reduced the overall attack rate to 13% and reduced the peak daily illness rate from 120 to 22 per 10,000 individuals. We determined the size of antiviral stockpile required; the ratio of the required number of antiviral courses to population was 13% for the treatment-only strategy, 25% for treatment and household prophylaxis and 40% for treatment, household and extended prophylaxis. Additional simulations suggest that coupling school closure with the antiviral strategies further reduces epidemic impact.ConclusionsThese results suggest that the aggressive use of antiviral drugs together with extended school closure may substantially slow the rate of influenza epidemic development. These strategies are more rigorous than those actually used during the early stages of the relatively mild 2009 pandemic, and are appropriate for future pandemics that have high morbidity and mortality rates.

Spontaneous behavioural changes in response to epidemics

We study how spontaneous reduction in the number of contacts could develop, as a defensive response, during an epidemic and affect the course of infection events. A model is proposed which couples an SIR model with selection of behaviours driven by imitation dynamics. Therefore, infection transmission and population behaviour become dynamical variables that influence each other. In particular, time scales of behavioural changes and epidemic transmission can be different. We provide a full qualitative characterization of the solutions when the dynamics of behavioural changes is either much faster or much slower than that of epidemic transmission. The model accounts for multiple outbreaks occurring within the same epidemic episode. Moreover, the model can explain “asymmetric waves”, i.e., infection waves whose rising and decaying phases differ in slope. Finally, we prove that introduction of behavioural dynamics results in the reduction of the final attack rate.

Simulation suggests that rapid activation of social distancing can arrest epidemic development due to a novel strain of influenza

BackgroundSocial distancing interventions such as school closure and prohibition of public gatherings are present in pandemic influenza preparedness plans. Predicting the effectiveness of intervention strategies in a pandemic is difficult. In the absence of other evidence, computer simulation can be used to help policy makers plan for a potential future influenza pandemic. We conducted simulations of a small community to determine the magnitude and timing of activation that would be necessary for social distancing interventions to arrest a future pandemic.MethodsWe used a detailed, individual-based model of a real community with a population of approximately 30,000. We simulated the effect of four social distancing interventions: school closure, increased isolation of symptomatic individuals in their household, workplace nonattendance, and reduction of contact in the wider community. We simulated each of the intervention measures in isolation and in several combinations; and examined the effect of delays in the activation of interventions on the final and daily attack rates.ResultsFor an epidemic with an R0 value of 1.5, a combination of all four social distancing measures could reduce the final attack rate from 33% to below 10% if introduced within 6 weeks from the introduction of the first case. In contrast, for an R0 of 2.5 these measures must be introduced within 2 weeks of the first case to achieve a similar reduction; delays of 2, 3 and 4 weeks resulted in final attack rates of 7%, 21% and 45% respectively. For an R0 of 3.5 the combination of all four measures could reduce the final attack rate from 73% to 16%, but only if introduced without delay; delays of 1, 2 or 3 weeks resulted in final attack rates of 19%, 35% or 63% respectively. For the higher R0 values no single measure has a significant impact on attack rates.ConclusionOur results suggest a critical role of social distancing in the potential control of a future pandemic and indicate that such interventions are capable of arresting influenza epidemic development, but only if they are used in combination, activated without delay and maintained for a relatively long period.

Basic reproduction number for equine-2 influenza virus a (H3N8) epidemic in racehorse facilities in Japan, 1971

Characterizing the epidemiologic determinants of equine influenza to facilitate effective control measures, including determining the critical proportion of the population that must be immunized to achieve containment, is critical. Through the use of counting process and martingale method, the basic reproduction number ( R 0; a measure of transmission potential) of equine-2 influenza A virus (H3N8) infection was estimated based on outbreak data recorded in 1971. The final attack rate ranged from 81.9% to 99.4%. Our estimate of R 0 was in the order of 2 to 5, which was smaller than the previously suggested estimate. Numerical analysis supported airborne spread as the major mode of transmission. Given that simple threshold vaccination coverage might not be realistic within racing stables, the combination of movement restrictions, isolation, and other countermeasures alongside vaccination is recommended to contain outbreaks of equine influenza.

A mathematical model for predicting the geographic spread of new infectious agents

A mathematical model for the temporal and geographic spread of an epidemic in a network of populations is presented. The model is formulated on a continuous state space in discrete time for an infectious disease that confers immunity following infection. The model allows for a general distribution of both the latent and infectious periods. An epidemic threshold theorem is given along with methods for finding the final attack rate when a single closed population is modeled. The model is first applied to analyzing the spread of influenza in single, closed populations in England and Wales and Greater London for the years 1958–1973. Then the model is used to predict the spread of Hong Kong influenza in 1968–1969 among 52 of the world's major cities. The prediction for the whole network of cities is based on air-transport data and on the estimated parameters from the ascending limb of the reported epidemic curve in Hong Kong, the first city to experience a major influenza epidemic in 1968. Finally, extensions and future uses of a model for temporal-geographic spread of infectious agents is discussed.

A mathematical model for predicting the geographic spread of new infectious agents

A mathematical model for the temporal and geographic spread of an epidemic in a network of populations is presented. The model is formulated on a continuous state space in discrete time for an infectious disease that confers immunity following infection. The model allows for a general distribution of both the latent and infectious periods. An epidemic threshold theorem is given along with methods for finding the final attack rate when a single closed population is modeled. The model is first applied to analyzing the spread of influenza in single, closed populations in England and Wales and Greater London for the years 1958–1973. Then the model is used to predict the spread of Hong Kong influenza in 1968–1969 among 52 of the world's major cities. The prediction for the whole network of cities is based on air-transport data and on the estimated parameters from the ascending limb of the reported epidemic curve in Hong Kong, the first city to experience a major influenza epidemic in 1968. Finally, extensions and future uses of a model for temporal-geographic spread of infectious agents is discussed.

The generalized discrete-time epidemic model with immunity: a synthesis

A general formulation of the discrete-time epidemic model with permanent immunity is presented, following the general format of a model developed in the Soviet Union. This paper presents a stochastic form of the model on a discrete state space and a deterministic form on a continuous state space. An epidemic threshold theorem is derived for the deterministic form. Bounds are found for the final infection attack rate, and the relative error of these bounds is investigated for varying parameter values. A number of discrete-time epidemic models proposed by others are shown to be special cases of the general model formulated. Methods for parameter estimation are given for small populations when the data are in either sequential or final value form and for large populations when the data are in sequential form. Examples are given of analysis of epidemic influenza data from small and large populations.

Streptococcal infections among children in a residential home. IV. Outbreaks of infection.

In a residential home for children, 367 cases of streptococcal illness were observed in a period of 30 months. The children lived in groups of about twelve in separate cottages. There were 194 occasions on which a streptococcus was thought to have been newly introduced into and produced illness in a cottage; on 132 of these 194 occasions there were no secondary cases of illness. The remaining 62 cottage introductions were followed by one or more secondary cases.In 27% of the 194 introductions, the primary case of illness seemed to have been infected from a healthy person in the cottage. In all, 30% of introductions of a new streptococcus into a cottage could be attributed to recognized contacts with one or more known infected children.The most important factor determining spread within the cottage seemed to be the carrier state of the primary case, spread following more often when the primary case had streptococci in the nose either on admission to hospital, or in convalescence.There was no evidence that spread within cottage bedrooms was of great importance.In about 35% of the incidents with spread, the initial spread to secondary cases seemed to be from the incubation-stage carriage of the introducer; in 42% it was from his or her convalescent carriage.The carrier rate in the healthy cottage-contacts was generally higher in cottages experiencing clinical spread of infection than in those that had single-case introductions. There was a strong correlation between the carrier rate in the first week after an introduction and the final bacteriological attack rate, and a weaker correlation with the final clinical attack rate.Continued spread of infection in a cottage was commonly due to the arrival of new children and was almost always associated with the presence of nasal carriers of streptococci.The 194 cottage introductions could be grouped into sixty-three overlapping Village epidemics, each apparently derving from a new importation of the particular type into the Village, although the evidence for this was often merely the absence of known infections within the previous few months. Only 13% of the introductions resulted in more than 10 cases, and some 80% had 5 or fewer. Introductions were more frequent in the cottages receiving children new to the homes than in those for the more permanent residents.The principal factor found as determining the spread from the first cottage to others was the attack rate in the first cottage. Introductions in cottages for school-age children, and especially those in which a child attending the school in the Village grounds was the first to be attacked, also seemed to lead to spread more often than others.The interval between successive Village introductions of one type did not appear to affect the extent of spread at the second; but the number of cases occurring in the first of two introductions had a notable effect: in no case did two successive introductions both result in a large number of cases of illness.