A comparative analysis of influenza vaccination programs

Influenza vaccine allocation in tropical settings under constrained resources

Influenza virus seasonality, synchronicity, and vaccine supply differ substantially between temperate and tropical settings, and optimal vaccination strategy may differ on this basis. Many national vaccine recommendations focus on high-risk groups, elderly populations, and healthcare workers despite previous analyses demonstrating broad benefits to vaccinating younger high-contact age groups. In this study, we parameterized an age-structured nonseasonal asynchronous epidemiological model of influenza virus transmission for a tropical low-income setting. We evaluated timing and age allocation of vaccines across vaccine supplies ranging from 10 to 90% using decade-based age groups. Year-round vaccination was beneficial when compared with more concentrated annual vaccine distribution. When targeting a single age group for vaccine prioritization, maximum vaccine allocation to the 10-19 high-contact age group minimized annual influenza mortality for all but one vaccine supply. When evaluating across all possible age allocations, optimal strategies always allocated a plurality of vaccines to school-age children (10-19). The converse, however, was not true as not all strategies allocating a plurality to children aged 10-19 minimized mortality. Allocating a high proportion of vaccine supply to the 10-19 age group is necessary but not sufficient to minimize annual mortality as distribution of remaining vaccine doses to other age groups also needs to be optimized. Strategies focusing on indirect benefits (vaccinating children) showed higher variance in mortality outcomes than strategies focusing on direct benefits (vaccinating the elderly). However, the indirect benefit approaches showed a lower mean mortality and a lower minimum mortality than vaccination focused on the elderly.

Influenza vaccination allocation in tropical settings under constrained resources

Influenza virus seasonality, synchronicity, and vaccine supply differ substantially between temperate and tropical settings, and optimal vaccination strategy may differ on this basis. Most national vaccine recommendations focus on high-risk groups, elderly populations, and healthcare workers despite previous analyses demonstrating broad benefits to vaccinating younger high-contact age groups. Here, we parameterized an age-structured non-seasonal asynchronous epidemiological model of influenza virus transmission for a tropical low-income setting. We evaluated timing and age allocation of vaccines across vaccine supplies ranging from 10% to 90% using decade-based age groups. Year-round vaccination was beneficial when comparing to vaccination strategies focused on a particular time of year. When targeting a single age-group for vaccine prioritization, maximum vaccine allocation to the 10-19 high-contact age group minimized annual influenza mortality for all but one vaccine supply. When evaluating across all possible age allocations, optimal strategies always allocated a plurality of vaccines to school-age children (10-19). The converse however was not true as not all strategies allocating a plurality to children aged 10-19 minimized mortality. Allocating a high proportion of vaccine supply to the 10-19 age group is necessary but not sufficient to minimize annual mortality as distribution of remaining vaccine doses to other age groups also needs to be optimized. Strategies focusing on indirect benefits (vaccinating children) showed higher variance in mortality outcomes than strategies focusing on direct benefits (vaccinating the elderly). However, the indirect benefit approaches showed lower mean mortality and lower minimum mortality than vaccination focused on the elderly.

Identification of dynamical changes of rabies transmission under quarantine: Community-based measures towards rabies elimination

Quarantine has been long used as a public health response to emerging infectious diseases, particularly at the onset of an epidemic when the infected proportion of a population remains identifiable and logistically tractable. In theory, the same logic should apply to low-incidence infections; however, the application and impact of quarantine in low prevalence settings appears less common and lacks a formal analysis. Here, we present a quantitative framework using a series of progressively more biologically realistic models of canine rabies in domestic dogs and from dogs to humans, a suitable example system to characterize dynamical changes under varying levels of dog quarantine. We explicitly incorporate health-seeking behaviour data to inform the modelling of contact-tracing and exclusion of rabies suspect and probable dogs that can be identified through bite-histories of patients presenting at anti-rabies clinics. We find that a temporary quarantine of rabies suspect and probable dogs provides a powerful tool to curtail rabies transmission, especially in settings where optimal vaccination coverage is yet to be achieved, providing a critical stopgap to reduce the number of human and animal deaths due to rabid bites. We conclude that whilst comprehensive measures including sensitive surveillance and large-scale vaccination of dogs will be required to achieve disease elimination and sustained freedom given the persistent risk of rabies re-introductions, quarantine offers a low-cost community driven solution to intersectoral health burden.

Sociodemographic Variables Can Guide Prioritized Testing Strategies for Epidemic Control in Resource-Limited Contexts

BACKGROUND

Targeted surveillance allows public health authorities to implement testing and isolation strategies when diagnostic resources are limited, and can be implemented via the consideration of social network topologies. However, it remains unclear how to implement such surveillance and control when network data are unavailable.

METHODS

We evaluated the ability of sociodemographic proxies of degree centrality to guide prioritized testing of infected individuals compared to known degree centrality. Proxies were estimated via readily available sociodemographic variables (age, gender, marital status, educational attainment, household size). We simulated severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemics via a susceptible-exposed-infected-recovered individual-based model on 2 contact networks from rural Madagascar to test applicability of these findings to low-resource contexts.

RESULTS

Targeted testing using sociodemographic proxies performed similarly to targeted testing using known degree centralities. At low testing capacity, using proxies reduced infection burden by 22%-33% while using 20% fewer tests, compared to random testing. By comparison, using known degree centrality reduced the infection burden by 31%-44% while using 26%-29% fewer tests.

CONCLUSIONS

We demonstrate that incorporating social network information into epidemic control strategies is an effective countermeasure to low testing capacity and can be implemented via sociodemographic proxies when social network data are unavailable.

Study of optimal vaccination strategies for early COVID-19 pandemic using an age-structured mathematical model: A case study of the USA

In this paper we study different vaccination strategies that could have been implemented for the early COVID-19 pandemic. We use a demographic epidemiological mathematical model based on differential equations in order to investigate the efficacy of a variety of vaccination strategies under limited vaccine supply. We use the number of deaths as the metric to measure the efficacy of each of these strategies. Finding the optimal strategy for the vaccination programs is a complex problem due to the large number of variables that affect the outcomes. The constructed mathematical model takes into account demographic risk factors such as age, comorbidity status and social contacts of the population. We perform simulations to assess the performance of more than three million vaccination strategies which vary depending on the vaccine priority of each group. This study focuses on the scenario corresponding to the early vaccination period in the USA, but can be extended to other countries. The results of this study show the importance of designing an optimal vaccination strategy in order to save human lives. The problem is extremely complex due to the large amount of factors, high dimensionality and nonlinearities. We found that for low/moderate transmission rates the optimal strategy prioritizes high transmission groups, but for high transmission rates, the optimal strategy focuses on groups with high CFRs. The results provide valuable information for the design of optimal vaccination programs. Moreover, the results help to design scientific vaccination guidelines for future pandemics.

Optimal vaccination at high reproductive numbers: sharp transitions and counterintuitive allocations

Optimization of vaccine allocations among different segments of a heterogeneous population is important for enhancing the effectiveness of vaccination campaigns in reducing the burden of epidemics. Intuitively, it would seem that allocations designed to minimize infections should prioritize those with the highest risk of being infected and infecting others. This prescription is well supported by vaccination theory, e.g. when the vaccination campaign aims to reach herd immunity. In this work, we show, however, that for vaccines providing partial protection (leaky vaccines) and for sufficiently high values of the basic reproduction number, intuition is overturned: the optimal allocation minimizing the number of infections prioritizes the vaccination of those who are least likely to be infected. The work combines numerical investigations, asymptotic analysis for a general model, and complete mathematical analysis in a two-group model. The results point to important considerations in managing vaccination campaigns for infections with high transmissibility.

It's worth a shot: urban density, endogenous vaccination decisions, and dynamics of infectious disease

We develop an agent-based model of vaccine decisions across a heterogeneous network model with urban and rural regions. In the model, agents make rational decisions to vaccinate or not, based on the relative private costs of vaccinations and infections as well as an estimated probability of infection if not vaccinated. The model is a methodological advance in that it provides an economic rationale for traditional threshold models of vaccine decision-making that are commonly used in agent-based network models of vaccine choice. In the model, more dense urban regions have more connections between agents than less dense rural regions. Higher density leads to higher levels of vaccine usage and lower rates of infection in urban regions within the model. This finding adds to the more commonly discussed socio-economic reasons for higher levels of vaccination usage in urban areas compared to rural areas. In addition to this direct contribution, the paper emphasizes the importance of endogenous decision-making in models of epidemiology. For instance, we find that networks that lead to larger epidemics in exogenous vaccination models lead to smaller epidemics in our model because agents use vaccinations to offset the additional risk introduced by these network structures. Endogenous agent responses to risk need to be incorporated into theoretical and empirical models of economic epidemiology.

Targeted vaccination and the speed of SARS-CoV-2 adaptation

The limited supply of vaccines against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) raises the question of targeted vaccination. Many countries have opted to vaccinate older and more sensitive hosts first to minimize the disease burden. However, what are the evolutionary consequences of targeted vaccination? We clarify the consequences of different vaccination strategies through the analysis of the speed of viral adaptation measured as the rate of change of the frequency of a vaccine-adapted variant. We show that such a variant is expected to spread faster if vaccination targets individuals who are likely to be involved in a higher number of contacts. We also discuss the pros and cons of dose-sparing strategies. Because delaying the second dose increases the proportion of the population vaccinated with a single dose, this strategy can both speed up the spread of the vaccine-adapted variant and reduce the cumulative number of deaths. Hence, strategies that are most effective at slowing viral adaptation may not always be epidemiologically optimal. A careful assessment of both the epidemiological and evolutionary consequences of alternative vaccination strategies is required to determine which individuals should be vaccinated first.

Optimal vaccine allocation for COVID-19 in the Netherlands: A data-driven prioritization

For the control of COVID-19, vaccination programmes provide a long-term solution. The amount of available vaccines is often limited, and thus it is crucial to determine the allocation strategy. While mathematical modelling approaches have been used to find an optimal distribution of vaccines, there is an excessively large number of possible allocation schemes to be simulated. Here, we propose an algorithm to find a near-optimal allocation scheme given an intervention objective such as minimization of new infections, hospitalizations, or deaths, where multiple vaccines are available. The proposed principle for allocating vaccines is to target subgroups with the largest reduction in the outcome of interest. We use an approximation method to reconstruct the age-specific transmission intensity (the next generation matrix), and express the expected impact of vaccinating each subgroup in terms of the observed incidence of infection and force of infection. The proposed approach is firstly evaluated with a simulated epidemic and then applied to the epidemiological data on COVID-19 in the Netherlands. Our results reveal how the optimal allocation depends on the objective of infection control. In the case of COVID-19, if we wish to minimize deaths, the optimal allocation strategy is not efficient for minimizing other outcomes, such as infections. In simulated epidemics, an allocation strategy optimized for an outcome outperforms other strategies such as the allocation from young to old, from old to young, and at random. Our simulations clarify that the current policy in the Netherlands (i.e., allocation from old to young) was concordant with the allocation scheme that minimizes deaths. The proposed method provides an optimal allocation scheme, given routine surveillance data that reflect ongoing transmissions. This approach to allocation is useful for providing plausible simulation scenarios for complex models, which give a more robust basis to determine intervention strategies.

Influenza vaccination should have no border: cost-effectiveness of cross-border subsidy

Background

Influenza is a substantial cause of morbidity and mortality for Israel and the Palestinian territory. Given the extensive interaction between the two populations, vaccination in one population may indirectly benefit the other via reduced transmission. Due to the mobility and extensive contacts, Palestinians employed in Israel could be a prime target for vaccination.

Methods

To evaluate the epidemiological and the economic benefits conferred by vaccinating Palestinians employed in Israel, we developed a model of influenza transmission within and between Israel and the West Bank. We parameterized the contact patterns underlying transmission by conducting a survey among Palestinians employed in Israel, and integrating survey results with traffic patterns and socio-demographic data.

Results

Vaccinating 50% of Palestinian workers is predicted to reduce the annual influenza burden by 28,745 cases (95% CI: 15,031-50,717) and 37.7 deaths (95% CI: 19·9–65·5) for the Israeli population, and by 32,9900 cases (95% CI: 14,379-51,531) and 20.2 deaths (CI 95%: 9·8–31·5) for the Palestinian population. Further, we found that as the indirect protection was so substantial, funding such a vaccination campaign would be cost-saving from the Israeli Ministry of Health perspective.

Conclusions

Offering influenza vaccination to Palestinians employed in Israel could efficiently reduce morbidity and mortality within both Israel and the Palestinian territory.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-021-11601-2.

Prioritising COVID-19 vaccination in changing social and epidemiological landscapes: a mathematical modelling study

BACKGROUND

During the COVID-19 pandemic, authorities must decide which groups to prioritise for vaccination in a shifting social-epidemiological landscape in which the success of large-scale non-pharmaceutical interventions requires broad social acceptance. We aimed to compare projected COVID-19 mortality under four different strategies for the prioritisation of SARS-CoV-2 vaccines.

METHODS

We developed a coupled social-epidemiological model of SARS-CoV-2 transmission in which social and epidemiological dynamics interact with one another. We modelled how population adherence to non-pharmaceutical interventions responds to case incidence. In the model, schools and workplaces are also closed and reopened on the basis of reported cases. The model was parameterised with data on COVID-19 cases and mortality, SARS-CoV-2 seroprevalence, population mobility, and demography from Ontario, Canada (population 14·5 million). Disease progression parameters came from the SARS-CoV-2 epidemiological literature. We assumed a vaccine with 75% efficacy against disease and transmissibility. We compared vaccinating those aged 60 years and older first (oldest-first strategy), vaccinating those younger than 20 years first (youngest-first strategy), vaccinating uniformly by age (uniform strategy), and a novel contact-based strategy. The latter three strategies interrupt transmission, whereas the first targets a vulnerable group to reduce disease. Vaccination rates ranged from 0·5% to 5% of the population per week, beginning on either Jan 1 or Sept 1, 2021.

FINDINGS

Case notifications, non-pharmaceutical intervention adherence, and lockdown undergo successive waves that interact with the timing of the vaccine programme to determine the relative effectiveness of the four strategies. Transmission-interrupting strategies become relatively more effective with time as herd immunity builds. The model predicts that, in the absence of vaccination, 72 000 deaths (95% credible interval 40 000-122 000) would occur in Ontario from Jan 1, 2021, to March 14, 2025, and at a vaccination rate of 1·5% of the population per week, the oldest-first strategy would reduce COVID-19 mortality by 90·8% on average (followed by 89·5% in the uniform, 88·9% in the contact-based, and 88·2% in the youngest-first strategies). 60 000 deaths (31 000-108 000) would occur from Sept 1, 2021, to March 14, 2025, in the absence of vaccination, and the contact-based strategy would reduce COVID-19 mortality by 92·6% on average (followed by 92·1% in the uniform, 91·0% in the oldest-first, and 88·3% in the youngest-first strategies) at a vaccination rate of 1·5% of the population per week.

INTERPRETATION

The most effective vaccination strategy for reducing mortality due to COVID-19 depends on the time course of the pandemic in the population. For later vaccination start dates, use of SARS-CoV-2 vaccines to interrupt transmission might prevent more deaths than prioritising vulnerable age groups.

FUNDING

Ontario Ministry of Colleges and Universities.

Optimal SARS-CoV-2 vaccine allocation using real-time attack-rate estimates in Rhode Island and Massachusetts

BACKGROUND

When three SARS-CoV-2 vaccines came to market in Europe and North America in the winter of 2020-2021, distribution networks were in a race against a major epidemiological wave of SARS-CoV-2 that began in autumn 2020. Rapid and optimized vaccine allocation was critical during this time. With 95% efficacy reported for two of the vaccines, near-term public health needs likely require that distribution is prioritized to the elderly, health care workers, teachers, essential workers, and individuals with comorbidities putting them at risk of severe clinical progression.

METHODS

We evaluate various age-based vaccine distributions using a validated mathematical model based on current epidemic trends in Rhode Island and Massachusetts. We allow for varying waning efficacy of vaccine-induced immunity, as this has not yet been measured. We account for the fact that known COVID-positive cases may not have been included in the first round of vaccination. And, we account for age-specific immune patterns in both states at the time of the start of the vaccination program. Our analysis assumes that health systems during winter 2020-2021 had equal staffing and capacity to previous phases of the SARS-CoV-2 epidemic; we do not consider the effects of understaffed hospitals or unvaccinated medical staff.

RESULTS

We find that allocating a substantial proportion (>75%) of vaccine supply to individuals over the age of 70 is optimal in terms of reducing total cumulative deaths through mid-2021. This result is robust to different profiles of waning vaccine efficacy and several different assumptions on age mixing during and after lockdown periods. As we do not explicitly model other high-mortality groups, our results on vaccine allocation apply to all groups at high risk of mortality if infected. A median of 327 to 340 deaths can be avoided in Rhode Island (3444 to 3647 in Massachusetts) by optimizing vaccine allocation and vaccinating the elderly first. The vaccination campaigns are expected to save a median of 639 to 664 lives in Rhode Island and 6278 to 6618 lives in Massachusetts in the first half of 2021 when compared to a scenario with no vaccine. A policy of vaccinating only seronegative individuals avoids redundancy in vaccine use on individuals that may already be immune, and would result in 0.5% to 1% reductions in cumulative hospitalizations and deaths by mid-2021.

CONCLUSIONS

Assuming high vaccination coverage (>28%) and no major changes in distancing, masking, gathering size, hygiene guidelines, and virus transmissibility between 1 January 2021 and 1 July 2021 a combination of vaccination and population immunity may lead to low or near-zero transmission levels by the second quarter of 2021.

Model-informed COVID-19 vaccine prioritization strategies by age and serostatus

Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.

Model-informed COVID-19 vaccine prioritization strategies by age and serostatus

Limited initial supply of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine raises the question of how to prioritize available doses. We used a mathematical model to compare five age-stratified prioritization strategies. A highly effective transmission-blocking vaccine prioritized to adults ages 20 to 49 years minimized cumulative incidence, but mortality and years of life lost were minimized in most scenarios when the vaccine was prioritized to adults greater than 60 years old. Use of individual-level serological tests to redirect doses to seronegative individuals improved the marginal impact of each dose while potentially reducing existing inequities in COVID-19 impact. Although maximum impact prioritization strategies were broadly consistent across countries, transmission rates, vaccination rollout speeds, and estimates of naturally acquired immunity, this framework can be used to compare impacts of prioritization strategies across contexts.

Optimal SARS-CoV-2 vaccine allocation using real-time seroprevalence estimates in Rhode Island and Massachusetts

As three SARS-CoV-2 vaccines come to market in Europe and North America in the winter of 2020-2021, distribution networks will be in a race against a major epidemiological wave of SARS-CoV-2 that began in autumn 2020. Rapid and optimized vaccine allocation is critical during this time. With 95% efficacy reported for two of the vaccines, near-term public health needs require that distribution is prioritized to the elderly, health-care workers, teachers, essential workers, and individuals with co-morbidities putting them at risk of severe clinical progression. Here, we evaluate various age-based vaccine distributions using a validated mathematical model based on current epidemic trends in Rhode Island and Massachusetts. We allow for varying waning efficacy of vaccine-induced immunity, as this has not yet been measured. We account for the fact that known COVID-positive cases may not be included in the first round of vaccination. And, we account for current age-specific immune patterns in both states. We find that allocating a substantial proportion ( > 75%) of vaccine supply to individuals over the age of 70 is optimal in terms of reducing total cumulative deaths through mid-2021. As we do not explicitly model other high mortality groups, this result on vaccine allocation applies to all groups at high risk of mortality if infected. Our analysis confirms that for an easily transmissible respiratory virus, allocating a large majority of vaccinations to groups with the highest mortality risk is optimal. Our analysis assumes that health systems during winter 2020-2021 have equal staffing and capacity to previous phases of the SARS-CoV-2 epidemic; we do not consider the effects of understaffed hospitals or unvaccinated medical staff. Vaccinating only seronegative individuals avoids redundancy in vaccine use on individuals that may already be immune, and will result in 1% to 2% reductions in cumulative hospitalizations and deaths by mid-2021. Assuming high vaccination coverage ( > 28%) and no major relaxations in distancing, masking, gathering size, or hygiene guidelines between now and spring 2021, our model predicts that a combination of vaccination and population immunity will lead to low or near-zero transmission levels by the second quarter of 2021.

How resource limitations and household economics may compromise efforts to safeguard children during outbreaks

Background

Epidemiological models have been employed with great success to explore the efficacy of alternative strategies at combating disease outbreaks. These models have often incorporated an understanding of age-based susceptibility and severity of outcome, considering how to limit the adverse outcomes or disease burden relative to an age structure. Such models frequently recommend the preferential treatment/vaccination of children or the elderly, demonstrating how prevention of serious disease within these etiological subgroups can provide both protection within the subgroup itself and indirect protection to the broader population. However, it is most frequently the case that these target populations are consumers, rather than providers, of household resources. In areas of the globe where continued health of household members relies on continued provision of resources, these models may fail to provide the most effective overall strategies for health outcomes in both target populations and overall. This is particularly important for tropical diseases impacting rural and low-income areas in which the disease may be endemic or newly emergent, particularly in the wake of natural disasters.

Methods

We propose a modified epidemiological model with targeted treatment in resource-limited populations. We evaluate the model over a broad parameter space.

Results

This model demonstrates how economic limitations may shift the optimal strategy. It may be advantageous to treat populations at lesser direct risk if they are responsible for providing secondary protection to higher-risk population(s) by producing household resources. Evaluation of this model over the parameter space reveals that, in some cases, targeting treatment towards consumers may result in greater numbers of consumer infections.

Conclusions

Our results demonstrate how household resource limitation can drastically affect the impact of targeted treatment strategies for limiting epidemics. Depending on the economic circumstances, it is possible that focusing treatment on consumers such as children can produce a counter-intuitive outcome in which more children contract the disease.

Disease spreading with social distancing: A prevention strategy in disordered multiplex networks

The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction q of shared individuals (overlap). We model the interactions through weighted networks, because person-to-person interactions are diverse (or disordered); weights represent the contact times of the interactions. Using branching theory supported by simulations, we analyze a social distancing strategy that reduces the average contact time in both layers, where the intensity of the distancing is related to the topology of the layers. We find that the critical values of the distancing intensities, above which an epidemic can be prevented, increase with the overlap q. Also we study the effect of the social distancing on the mutual giant component of susceptible individuals, which is crucial to keep the functionality of the system. In addition, we find that for relatively small values of the overlap q, social distancing policies might not be needed at all to maintain the functionality of the system.

Immunization strategies in networks with missing data

Network-based intervention strategies can be effective and cost-efficient approaches to curtailing harmful contagions in myriad settings. As studied, these strategies are often impractical to implement, as they typically assume complete knowledge of the network structure, which is unusual in practice. In this paper, we investigate how different immunization strategies perform under realistic conditions-where the strategies are informed by partially-observed network data. Our results suggest that global immunization strategies, like degree immunization, are optimal in most cases; the exception is at very high levels of missing data, where stochastic strategies, like acquaintance immunization, begin to outstrip them in minimizing outbreaks. Stochastic strategies are more robust in some cases due to the different ways in which they can be affected by missing data. In fact, one of our proposed variants of acquaintance immunization leverages a logistically-realistic ongoing survey-intervention process as a form of targeted data-recovery to improve with increasing levels of missing data. These results support the effectiveness of targeted immunization as a general practice. They also highlight the risks of considering networks as idealized mathematical objects: overestimating the accuracy of network data and foregoing the rewards of additional inquiry.

Efficient vaccination strategies for epidemic control using network information

BACKGROUND

Network-based interventions against epidemic spread are most powerful when the full network structure is known. However, in practice, resource constraints require decisions to be made based on partial network information. We investigated how the accuracy of network data available at individual and village levels affected network-based vaccination effectiveness.

METHODS

We simulated a Susceptible-Infected-Recovered process on static empirical social networks from 75 rural Indian villages. First, we used regression analysis to predict the percentage of individuals ever infected (cumulative incidence) based on village-level network properties for simulated datasets from 10 representative villages. Second, we simulated vaccinating 10% of each of the 75 empirical village networks at baseline, selecting vaccinees through one of five network-based approaches: random individuals (Random); random contacts of random individuals (Nomination); random high-degree individuals (High Degree); highest degree individuals (Highest Degree); or most central individuals (Central). The first three approaches require only sample data; the latter two require full network data. We also simulated imposing a limit on how many contacts an individual can nominate (Fixed Choice Design, FCD), which reduces the data collection burden but generates only partially observed networks.

RESULTS

In regression analysis, we found mean and standard deviation of the degree distribution to strongly predict cumulative incidence. In simulations, the Nomination method reduced cumulative incidence by one-sixth compared to Random vaccination; full network methods reduced infection by two-thirds. The High Degree approach had intermediate effectiveness. Somewhat surprisingly, FCD truncating individuals' degrees at three was as effective as using complete networks.

CONCLUSIONS

Using even partial network information to prioritize vaccines at either the village or individual level, i.e. determine the optimal order of communities or individuals within each village, substantially improved epidemic outcomes. Such approaches may be feasible and effective in outbreak settings, and full ascertainment of network structure may not be required.

An agent-based model of dengue virus transmission shows how uncertainty about breakthrough infections influences vaccination impact projections

Prophylactic vaccination is a powerful tool for reducing the burden of infectious diseases, due to a combination of direct protection of vaccinees and indirect protection of others via herd immunity. Computational models play an important role in devising strategies for vaccination by making projections of its impacts on public health. Such projections are subject to uncertainty about numerous factors, however. For example, many vaccine efficacy trials focus on measuring protection against disease rather than protection against infection, leaving the extent of breakthrough infections (i.e., disease ameliorated but infection unimpeded) among vaccinees unknown. Our goal in this study was to quantify the extent to which uncertainty about breakthrough infections results in uncertainty about vaccination impact, with a focus on vaccines for dengue. To realistically account for the many forms of heterogeneity in dengue virus (DENV) transmission, which could have implications for the dynamics of indirect protection, we used a stochastic, agent-based model for DENV transmission informed by more than a decade of empirical studies in the city of Iquitos, Peru. Following 20 years of routine vaccination of nine-year-old children at 80% coverage, projections of the proportion of disease episodes averted varied by a factor of 1.76 (95% CI: 1.54-2.06) across the range of uncertainty about breakthrough infections. This was equivalent to the range of vaccination impact projected across a range of uncertainty about vaccine efficacy of 0.268 (95% CI: 0.210-0.329). Until uncertainty about breakthrough infections can be addressed empirically, our results demonstrate the importance of accounting for it in models of vaccination impact.

A two-stage approach for estimating the parameters of an age-group epidemic model from incidence data

Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models are highly nonlinear and may have a large number of unknown parameters. Thus, parameter estimation of age-group models, while becoming a fundamental issue for both the scientific study and policy making in infectious diseases, is not a trivial task in practice. In this paper, we examine the estimation of the so-called next-generation matrix using incidence data of a single entire outbreak, and extend the approach to deal with recurring outbreaks. Unlike previous studies, we do not assume any constraints regarding the structure of the matrix. A novel two-stage approach is developed, which allows for efficient parameter estimation from both statistical and computational perspectives. Simulation studies corroborate the ability to estimate accurately the parameters of the model for several realistic scenarios. The model and estimation method are applied to real data of influenza-like-illness in Israel. The parameter estimates of the key relevant epidemiological parameters and the recovered structure of the estimated next-generation matrix are in line with results obtained in previous studies.

Model-based reconstruction of an epidemic using multiple datasets: understanding influenza A/H1N1 pandemic dynamics in Israel

Intensified surveillance during the 2009 A/H1N1 influenza pandemic in Israel resulted in large virological and serological datasets, presenting a unique opportunity for investigating the pandemic dynamics. We employ a conditional likelihood approach for fitting a disease transmission model to virological and serological data, conditional on clinical data. The model is used to reconstruct the temporal pattern of the pandemic in Israel in five age-groups and evaluate the factors that shaped it. We estimate the reproductive number at the beginning of the pandemic to beR= 1.4. We find that the combined effect of varying absolute humidity conditions and school vacations (SVs) is responsible for the infection pattern, characterized by three epidemic waves. Overall attack rate is estimated at 32% (28-35%) with a large variation among the age-groups: the highest attack rates within school children and the lowest within the elderly. This pattern of infection is explained by a combination of the age-group contact structure and increasing immunity with age. We assess that SVs increased the overall attack rates by prolonging the pandemic into the winter. Vaccinating school children would have been the optimal strategy for minimizing infection rates in all age-groups.

Efficient Vaccine Distribution Based on a Hybrid Compartmental Model

To effectively and efficiently reduce the morbidity and mortality that may be caused by outbreaks of emerging infectious diseases, it is very important for public health agencies to make informed decisions for controlling the spread of the disease. Such decisions must incorporate various kinds of intervention strategies, such as vaccinations, school closures and border restrictions. Recently, researchers have paid increased attention to searching for effective vaccine distribution strategies for reducing the effects of pandemic outbreaks when resources are limited. Most of the existing research work has been focused on how to design an effective age-structured epidemic model and to select a suitable vaccine distribution strategy to prevent the propagation of an infectious virus. Models that evaluate age structure effects are common, but models that additionally evaluate geographical effects are less common. In this paper, we propose a new SEIR (susceptible-exposed-infectious šC recovered) model, named the hybrid SEIR-V model (HSEIR-V), which considers not only the dynamics of infection prevalence in several age-specific host populations, but also seeks to characterize the dynamics by which a virus spreads in various geographic districts. Several vaccination strategies such as different kinds of vaccine coverage, different vaccine releasing times and different vaccine deployment methods are incorporated into the HSEIR-V compartmental model. We also design four hybrid vaccination distribution strategies (based on population size, contact pattern matrix, infection rate and infectious risk) for controlling the spread of viral infections. Based on data from the 2009-2010 H1N1 influenza epidemic, we evaluate the effectiveness of our proposed HSEIR-V model and study the effects of different types of human behaviour in responding to epidemics.

Increasing herd immunity with influenza revaccination

Seasonal influenza is a significant public health concern globally. While influenza vaccines are the single most effective intervention to reduce influenza morbidity and mortality, there is considerable debate surrounding the merits and consequences of repeated seasonal vaccination. Here, we describe a two-season influenza epidemic contact network model and use it to demonstrate that increasing the level of continuity in vaccination across seasons reduces the burden on public health. We show that revaccination reduces the influenza attack rate not only because it reduces the overall number of susceptible individuals, but also because it better protects highly connected individuals, who would otherwise make a disproportionately large contribution to influenza transmission. We also demonstrate that our results hold on an empirical contact network, in the presence of assortativity in vaccination status, and are robust for a range of vaccine coverage and efficacy levels. Our work contributes a population-level perspective to debates about the merits of repeated influenza vaccination and advocates for public health policy to incorporate individual vaccine histories.

Network position and health care worker infections

We use a newly collected data set coupled with an agent-based model to study the spread of infectious disease in hospitals. We estimate the average and marginal infections created by various worker groups in a hospital as a function of their network position in order to identify groups most crucial in a hospital-based epidemic. Surprisingly, we find that many groups with primary patient care responsibilities play a small role in spreading an infectious disease within our hospital data set. We also demonstrate that the effect of different network positions can be as important as the effect of different transmission rates for some categories of workers.

Flexible Modeling of Epidemics with an Empirical Bayes Framework

Seasonal influenza epidemics cause consistent, considerable, widespread loss annually in terms of economic burden, morbidity, and mortality. With access to accurate and reliable forecasts of a current or upcoming influenza epidemic’s behavior, policy makers can design and implement more effective countermeasures. This past year, the Centers for Disease Control and Prevention hosted the “Predict the Influenza Season Challenge”, with the task of predicting key epidemiological measures for the 2013–2014 U.S. influenza season with the help of digital surveillance data. We developed a framework for in-season forecasts of epidemics using a semiparametric Empirical Bayes framework, and applied it to predict the weekly percentage of outpatient doctors visits for influenza-like illness, and the season onset, duration, peak time, and peak height, with and without using Google Flu Trends data. Previous work on epidemic modeling has focused on developing mechanistic models of disease behavior and applying time series tools to explain historical data. However, tailoring these models to certain types of surveillance data can be challenging, and overly complex models with many parameters can compromise forecasting ability. Our approach instead produces possibilities for the epidemic curve of the season of interest using modified versions of data from previous seasons, allowing for reasonable variations in the timing, pace, and intensity of the seasonal epidemics, as well as noise in observations. Since the framework does not make strict domain-specific assumptions, it can easily be applied to some other diseases with seasonal epidemics. This method produces a complete posterior distribution over epidemic curves, rather than, for example, solely point predictions of forecasting targets. We report prospective influenza-like-illness forecasts made for the 2013–2014 U.S. influenza season, and compare the framework’s cross-validated prediction error on historical data to that of a variety of simpler baseline predictors.

Influenza epidemics occur annually, and incur significant losses in terms of lost productivity, sickness, and death. Policy makers employ countermeasures, such as vaccination campaigns, to combat the occurrence and spread of infectious diseases, but epidemics exhibit a wide range of behavior, which makes designing and planning these efforts difficult. Accurate and reliable numerical forecasts of how an epidemic will behave, as well as advance notice of key events, could enable policy makers to further specialize countermeasures for a particular season. While a large amount of work already exists on modeling epidemics in past seasons, work on forecasting is relatively sparse. Specially tailored models for historical data may be overly strict and fail to produce behavior similar to the current season. We designed a framework for predicting epidemics without making strong assumptions about how the disease propagates by relying on slightly modified versions of past epidemics to form possibilities for the current season. We report forecasts generated for the 2013–2014 Centers for Disease Control and Prevention (CDC) “Predict the Influenza Season Challenge”, and assess its accuracy retrospectively.

Infectious disease transmission and contact networks in wildlife and livestock

The use of social and contact networks to answer basic and applied questions about infectious disease transmission in wildlife and livestock is receiving increased attention. Through social network analysis, we understand that wild animal and livestock populations, including farmed fish and poultry, often have a heterogeneous contact structure owing to social structure or trade networks. Network modelling is a flexible tool used to capture the heterogeneous contacts of a population in order to test hypotheses about the mechanisms of disease transmission, simulate and predict disease spread, and test disease control strategies. This review highlights how to use animal contact data, including social networks, for network modelling, and emphasizes that researchers should have a pathogen of interest in mind before collecting or using contact data. This paper describes the rising popularity of network approaches for understanding transmission dynamics in wild animal and livestock populations; discusses the common mismatch between contact networks as measured in animal behaviour and relevant parasites to match those networks; and highlights knowledge gaps in how to collect and analyse contact data. Opportunities for the future include increased attention to experiments, pathogen genetic markers and novel computational tools.

A marginal benefit approach for vaccinating influenza "superspreaders"

BACKGROUND

There is widespread recognition that interventions targeting "superspreaders" are more effective at containing epidemics than strategies aimed at the broader

POPULATION

However, little attention has been devoted to determining optimal levels of coverage for targeted vaccination strategies, given the nonlinear relationship between program scale and the costs and benefits of identifying and successfully administering vaccination to potential superspreaders.

METHODS

We developed a framework for such an assessment derived from a transmission model of seasonal influenza parameterized to emulate typical seasonal influenza epidemics in the US. We used this framework to estimate how the marginal benefit of expanded targeted vaccination changes with the proportion of the target population already vaccinated.

RESULTS

The benefit of targeting additional superspreaders varies considerably as a function of both the baseline vaccination coverage and proximity to the herd immunity threshold. The general form of the marginal benefit function starts low, particularly for severe epidemics, increases monotonically until its peak at the point of herd immunity, and then plummets rapidly. We present a simplified transmission model, primarily designed to convey qualitative insight rather than quantitative precision. With appropriate contact data, future work could address more complex population structures, such as age structure and assortative mixing patterns. Our illustrative example highlights the general economic and epidemiological findings of our method but does not address intervention design, policy, and resource allocation issues related to practical implementation of this particular scenario.

CONCLUSIONS

Our approach offers a means of estimating willingness to pay for search costs associated with targeted vaccination of superspreaders, which can inform policies regarding whether a targeted intervention should be implemented and, if so, up to what levels.

Responding to vaccine safety signals during pandemic influenza: a modeling study

Background

Managing emerging vaccine safety signals during an influenza pandemic is challenging. Federal regulators must balance vaccine risks against benefits while maintaining public confidence in the public health system.

Methods

We developed a multi-criteria decision analysis model to explore regulatory decision-making in the context of emerging vaccine safety signals during a pandemic. We simulated vaccine safety surveillance system capabilities and used an age-structured compartmental model to develop potential pandemic scenarios. We used an expert-derived multi-attribute utility function to evaluate potential regulatory responses by combining four outcome measures into a single measure of interest: 1) expected vaccination benefit from averted influenza; 2) expected vaccination risk from vaccine-associated febrile seizures; 3) expected vaccination risk from vaccine-associated Guillain-Barre Syndrome; and 4) expected change in vaccine-seeking behavior in future influenza seasons.

Results

Over multiple scenarios, risk communication, with or without suspension of vaccination of high-risk persons, were the consistently preferred regulatory responses over no action or general suspension when safety signals were detected during a pandemic influenza. On average, the expert panel valued near-term vaccine-related outcomes relative to long-term projected outcomes by 3∶1. However, when decision-makers had minimal ability to influence near-term outcomes, the response was selected primarily by projected impacts on future vaccine-seeking behavior.

Conclusions

The selected regulatory response depends on how quickly a vaccine safety signal is identified relative to the peak of the pandemic and the initiation of vaccination. Our analysis suggested two areas for future investment: efforts to improve the size and timeliness of the surveillance system and behavioral research to understand changes in vaccine-seeking behavior.

Assessing the use of antiviral treatment to control influenza

Vaccines are the cornerstone of influenza control policy, but can suffer from several drawbacks. Seasonal influenza vaccines are prone to production problems and low efficacies, while pandemic vaccines are unlikely to be available in time to slow a rapidly spreading global outbreak. Antiviral therapy was found to be beneficial during the influenza A(H1N1)pdm09 pandemic even with limited use; however, antiviral use has decreased further since then. We sought to determine the role antiviral therapy can play in pandemic and seasonal influenza control using conservative estimates of antiviral efficacy, and to assess if conservative but targeted strategies could be employed to optimize the use of antivirals. Using an age-structured contact network model for an urban population, we compared the transmission-blocking ability of a conservative antiviral therapy strategy to the susceptibility-reducing effects of a robust influenza vaccine. Our results show that while antiviral therapy cannot replace a robust influenza vaccine, it can play a role in reducing attack rates and eliminating outbreaks, and could significantly reduce public health burden when vaccine is either unavailable or ineffective. We also found that antiviral therapy, by treating those who are infected, is naturally a highly optimized strategy, and need not be improved upon with expensive targeted campaigns.

Eight challenges for network epidemic models

Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host-pathogen biology (e.g. waning immunity) have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.

Incidence of influenza virus infections in children in Hong Kong in a 3-year randomized placebo-controlled vaccine study, 2009-2012

BACKGROUND

School-aged children suffer high rates of influenza virus infections and associated illnesses each year, and are a major source of transmission in the community. However, information on the cumulative incidence of infection in specific epidemics is scarce, and there are limited studies with sufficient follow-up to identify the strength and duration of protection against reinfection.

METHODS

We randomly allocated children 5-17 years of age to receive trivalent inactivated influenza vaccine (TIV) or placebo from September 2009 through January 2010, and then conducted follow-up for 3 years including regular collection of sera, symptom diaries, and collection of nose and throat swabs during illness episodes in participants or their household members.

RESULTS

Of 796 children initially randomized, 484 continued to participate for all 3 years. In unvaccinated children, cumulative incidence of infection was estimated to be 59% in the first wave of H1N1pdm09 in 2009-2010, and 7%, 14%, 20%, and 31% in subsequent epidemics of H3N2 (2010), H1N1pdm09 (2011), B (2012), and H3N2 (2012), respectively. Infection with H1N1pdm09 in 2009-2010 and H3N2 in 2010 was associated with protection against infection with subsequent epidemics of the same subtype in 2011 and 2012, respectively, but we found no evidence of heterotypic or heterosubtypic protection against infection.

CONCLUSIONS

We identified substantial incidence of influenza virus infections in children in Hong Kong in 5 major epidemics over a 3-year period, and evidence of homosubtypic but not heterosubtypic protection following infection.

CLINICAL TRIALS REGISTRATION

NCT00792051.

Sampling Networks from Their Posterior Predictive Distribution

Recent research indicates that knowledge about social networks can be leveraged to increase efficiency of interventions (Valente, 2012). However, in many settings, there exists considerable uncertainty regarding the structure of the network. This can render the estimation of potential effects of network-based interventions difficult, as providing appropriate guidance to select interventions often requires a representation of the whole network. In order to make use of the network property estimates to simulate the effect of interventions, it may be beneficial to sample networks from an estimated posterior predictive distribution, which can be specified using a wide range of models. Sampling networks from a posterior predictive distribution of network properties ensures that the uncertainty about network property parameters is adequately captured. The tendency for relationships among network properties to exhibit sharp thresholds has important implications for understanding global network topology in the presence of uncertainty; therefore, it is essential to account for uncertainty. We provide detail needed to sample networks for the specific network properties of degree distribution, mixing frequency, and clustering. Our methods to generate networks are demonstrated using simulated data and data from the National Longitudinal Study of Adolescent Health.

Evaluating roles of nodes in optimal allocation of vaccines with economic considerations

Since the allocation of vaccines is often constrained by limited resources, designing an economical vaccination strategy is a fundamental goal of the epidemiological modelling. In this study, with the objective of reducing costs, we determine the optimal allocation of vaccines for a general class of infectious diseases that spread mainly via contact. We use an optimization routine to identify the roles of nodes with distinct degrees as depending on the cost of treatment to that of vaccination (relative cost of treatment). The optimal allocation drives vaccination priority to medium-degree nodes at a low relative cost of treatment or to high-degree nodes at a high relative cost of treatment. According to the presented results, we may adjust the vaccination priority in the face of an endemic situation.

The importance of contact network topology for the success of vaccination strategies

The effects of a number of vaccination strategies on the spread of an SIR type disease are numerically investigated for several common network topologies including random, scale-free, small world, and meta-random networks. These strategies, namely, prioritized, random, follow links and contact tracing, are compared across networks using extensive simulations with disease parameters relevant for viruses such as pandemic influenza H1N1/09. Two scenarios for a network SIR model are considered. First, a model with a given transmission rate is studied. Second, a model with a given initial growth rate is considered, because the initial growth rate is commonly used to impute the transmission rate from incidence curves and to predict the course of an epidemic. Since a vaccine may not be readily available for a new virus, the case of a delay in the start of vaccination is also considered in addition to the case of no delay. It is found that network topology can have a larger impact on the spread of the disease than the choice of vaccination strategy. Simulations also show that the network structure has a large effect on both the course of an epidemic and the determination of the transmission rate from the initial growth rate. The effect of delay in the vaccination start time varies tremendously with network topology. Results show that, without the knowledge of network topology, predictions on the peak and the final size of an epidemic cannot be made solely based on the initial exponential growth rate or transmission rate. This demonstrates the importance of understanding the topology of realistic contact networks when evaluating vaccination strategies.

Optimal targeting of seasonal influenza vaccination toward younger ages is robust to parameter uncertainty

Identification of the optimal vaccine allocation for the control of influenza requires consideration of uncertainty arising from numerous unpredictable factors, including viral evolution and diversity within the human population's immunity as well as variation in vaccine efficacy. The best policy must account for diverse potential outcomes based on these uncertainties. Here we used a mathematical model parametrized with survey-based contact data, demographic, and epidemiological data from seasonal influenza in the United States to determine the optimal vaccine allocation for five outcome measures: infections, hospitalizations, deaths, years of life loss, and contingent valuation. We incorporated uncertainty of epidemiological parameters and derive probability distributions of optimal age- and risk-specific allocation of vaccine. Our analysis demonstrated that previous recommendations of targeting schoolchildren (ages 5-17 years) and young adults (18-44 years) are generally robust in the face of uncertainty. However, when the outcome measure is to minimize deaths, years of life loss, or contingent valuation, uncertainty analysis identified scenarios under which it is optimal to target people at high risk for complications, even when vaccine are in abundance.

Towards multiscale modeling of influenza infection

Aided by recent advances in computational power, algorithms, and higher fidelity data, increasingly detailed theoretical models of infection with influenza A virus are being developed. We review single scale models as they describe influenza infection from intracellular to global scales, and, in particular, we consider those models that capture details specific to influenza and can be used to link different scales. We discuss the few multiscale models of influenza infection that have been developed in this emerging field. In addition to discussing modeling approaches, we also survey biological data on influenza infection and transmission that is relevant for constructing influenza infection models. We envision that, in the future, multiscale models that capitalize on technical advances in experimental biology and high performance computing could be used to describe the large spatial scale epidemiology of influenza infection, evolution of the virus, and transmission between hosts more accurately.

Epidemiological effects of group size variation in social species

Contact patterns in group-structured populations determine the course of infectious disease outbreaks. Network-based models have revealed important connections between group-level contact patterns and the dynamics of epidemics, but these models typically ignore heterogeneities in within-group composition. Here, we analyse a flexible mathematical model of disease transmission in a hierarchically structured wildlife population, and find that increased variation in group size reduces the epidemic threshold, making social animal populations susceptible to a broader range of pathogens. Variation in group size also increases the likelihood of an epidemic for mildly transmissible diseases, but can reduce the likelihood and expected size of an epidemic for highly transmissible diseases. Further, we introduce the concept of epidemiological effective group size, which we define to be the group size of a hypothetical population containing groups of identical size that has the same epidemic threshold as an observed population. Using data from the Serengeti Lion Project, we find that pride-living Serengeti lions are epidemiologically comparable to a homogeneous population with up to 20 per cent larger prides.

Optimal vaccine allocation for the early mitigation of pandemic influenza

With new cases of avian influenza H5N1 (H5N1AV) arising frequently, the threat of a new influenza pandemic remains a challenge for public health. Several vaccines have been developed specifically targeting H5N1AV, but their production is limited and only a few million doses are readily available. Because there is an important time lag between the emergence of new pandemic strain and the development and distribution of a vaccine, shortage of vaccine is very likely at the beginning of a pandemic. We coupled a mathematical model with a genetic algorithm to optimally and dynamically distribute vaccine in a network of cities, connected by the airline transportation network. By minimizing the illness attack rate (i.e., the percentage of people in the population who become infected and ill), we focus on optimizing vaccine allocation in a network of 16 cities in Southeast Asia when only a few million doses are available. In our base case, we assume the vaccine is well-matched and vaccination occurs 5 to 10 days after the beginning of the epidemic. The effectiveness of all the vaccination strategies drops off as the timing is delayed or the vaccine is less well-matched. Under the best assumptions, optimal vaccination strategies substantially reduced the illness attack rate, with a maximal reduction in the attack rate of 85%. Furthermore, our results suggest that cooperative strategies where the resources are optimally distributed among the cities perform much better than the strategies where the vaccine is equally distributed among the network, yielding an illness attack rate 17% lower. We show that it is possible to significantly mitigate a more global epidemic with limited quantities of vaccine, provided that the vaccination campaign is extremely fast and it occurs within the first weeks of transmission.

An approximation of herd effect due to vaccinating children against seasonal influenza - a potential solution to the incorporation of indirect effects into static models

Background

Indirect herd effect from vaccination of children offers potential for improving the effectiveness of influenza prevention in the remaining unvaccinated population. Static models used in cost-effectiveness analyses cannot dynamically capture herd effects. The objective of this study was to develop a methodology to allow herd effect associated with vaccinating children against seasonal influenza to be incorporated into static models evaluating the cost-effectiveness of influenza vaccination.

Methods

Two previously published linear equations for approximation of herd effects in general were compared with the results of a structured literature review undertaken using PubMed searches to identify data on herd effects specific to influenza vaccination. A linear function was fitted to point estimates from the literature using the sum of squared residuals.

Results

The literature review identified 21 publications on 20 studies for inclusion. Six studies provided data on a mathematical relationship between effective vaccine coverage in subgroups and reduction of influenza infection in a larger unvaccinated population. These supported a linear relationship when effective vaccine coverage in a subgroup population was between 20% and 80%. Three studies evaluating herd effect at a community level, specifically induced by vaccinating children, provided point estimates for fitting linear equations. The fitted linear equation for herd protection in the target population for vaccination (children) was slightly less conservative than a previously published equation for herd effects in general. The fitted linear equation for herd protection in the non-target population was considerably less conservative than the previously published equation.

Conclusions

This method of approximating herd effect requires simple adjustments to the annual baseline risk of influenza in static models: (1) for the age group targeted by the childhood vaccination strategy (i.e. children); and (2) for other age groups not targeted (e.g. adults and/or elderly). Two approximations provide a linear relationship between effective coverage and reduction in the risk of infection. The first is a conservative approximation, recommended as a base-case for cost-effectiveness evaluations. The second, fitted to data extracted from a structured literature review, provides a less conservative estimate of herd effect, recommended for sensitivity analyses.

H3N2v and other influenza epidemic risk based on age-specific estimates of sero-protection and contact network interactions

Cases of a novel swine-origin influenza A(H3N2) variant (H3N2v) have recently been identified in the US, primarily among children. We estimated potential epidemic attack rates (ARs) based on age-specific estimates of sero-susceptibility and social interactions. A contact network model previously established for the Greater Vancouver Area (GVA), Canada was used to estimate average epidemic (infection) ARs for the emerging H3N2v and comparator viruses (H1N1pdm09 and an extinguished H3N2 seasonal strain) based on typical influenza characteristics, basic reproduction number (R(0)), and effective contacts taking into account age-specific sero-protection rates (SPRs). SPRs were assessed in sera collected from the GVA in 2009 or earlier (pre-H1N1pdm09) and fall 2010 (post-H1N1pdm09, seasonal A/Brisbane/10/2007(H3N2), and H3N2v) by hemagglutination inhibition (HI) assay. SPR was assigned per convention based on proportion with HI antibody titre ≥40 (SPR40). Recognizing that the HI titre ≥40 was established as the 50%sero-protective threshold we also explored for ½SPR40, SPR80 and a blended gradient defined as: ¼SPR20, ½SPR40, ¾SPR80, SPR160. Base case analysis assumed R(0) = 1.40, but we also explored R(0) as high as 1.80. With R(0) = 1.40 and SPR40, simulated ARs were well aligned with field observations for H1N1pdm09 incidence (AR: 32%), sporadic detections without a third epidemic wave post-H1N1pdm09 (negligible AR<0.1%) as well as A/Brisbane/10/2007(H3N2) seasonal strain extinction and antigenic drift replacement (negligible AR<0.1%). Simulated AR for the novel swine-origin H3N2v was 6%, highest in children 6-11years (16%). However, with modification to SPR thresholds per above, H3N2v AR ≥20% became possible. At SPR40, H3N2v AR ≥10%, ≥15% or ≥30%, occur if R(0)≥1.48, ≥1.56 or ≥1.86, respectively. Based on conventional assumptions, the novel swine-origin H3N2v does not currently pose a substantial pandemic threat. If H3N2v epidemics do occur, overall community ARs are unlikely to exceed typical seasonal influenza experience. However risk assessment may change with time and depends crucially upon the validation of epidemiological features of influenza, notably the serologic correlate of protection and R(0).

Modeling the Impact of Behavior Changes on the Spread of Pandemic Influenza

We use mathematical models to assess the impact of behavioral changes in response to an emerging epidemic. Evaluating the quantitative and qualitative impact of public health interventions on the spread of infectious diseases is a crucial public health objective. The recent avian influenza (H5N1) outbreaks and the 2009 H1N1 pandemic have raised significant global concerns about the emergence of a deadly influenza virus causing a pandemic of catastrophic proportions. Mitigation strategies based on behavior changes are some of the only options available in the early stages of an emerging epidemic when vaccines are unlikely to be available and there are only limited stockpiles of antiviral medications. Mathematical models that capture these behavior changes can quantify the relative impact of different mitigation strategies, such as closing schools, in slowing the spread of an infectious disease. Including behavior changes in mathematical models increases complexity and is often left out of the analysis. We present a simple differential equation model which allows for people changing their behavior to decrease their probability of infection. We also describe a large-scale agent-based model that can be used to analyze the impact of isolation scenarios such as school closures and fear-based home isolation during a pandemic. The agent-based model captures realistic individual-level mixing patterns and coordinated reactive changes in human behavior in order to better predict the transmission dynamics of an epidemic. Both models confirm that changes in behavior can be effective in reducing the spread of disease. For example, our model predicts that if school closures are implemented for the duration of the pandemic, the clinical attack rate could be reduced by more than 50%. We also verify that when interventions are stopped too soon, a second wave of infection can occur.

Geographic prioritization of distributing pandemic influenza vaccines

Pandemic influenza is an international public health concern. In light of the persistent threat of H5N1 avian influenza and the recent pandemic of A/H1N1swine influenza outbreak, public health agencies around the globe are continuously revising their preparedness plans. The A/H1N1 pandemic of 2009 demonstrated that influenza activity and severity might vary considerably among age groups and locations, and the distribution of an effective influenza vaccine may be significantly delayed and staggered. Thus, pandemic influenza vaccine distribution policies should be tailored to the demographic and spatial structures of communities. Here, we introduce a bi-criteria decision-making framework for vaccine distribution policies that is based on a geospatial and demographically-structured model of pandemic influenza transmission within and between counties of Arizona in the Unites States. Based on data from the 2009-2010 H1N1 pandemic, the policy predicted to reduce overall attack rate most effectively is prioritizing counties expected to experience the latest epidemic waves (a policy that may be politically untenable). However, when we consider reductions in both the attack rate and the waiting period for those seeking vaccines, the widely adopted pro rata policy (distributing according to population size) is also predicted to be an effective strategy.

Optimal but unequitable prophylactic distribution of vaccine

The final epidemic size (R(∞)) remains one of the fundamental outcomes of an epidemic, and measures the total number of individuals infected during a "free-fall" epidemic when no additional control action is taken. As such, it provides an idealised measure for optimising control policies before an epidemic arises. Although the generality of formulae for calculating the final epidemic size have been discussed previously, we offer an alternative probabilistic argument and then use this formula to consider the optimal deployment of vaccine in spatially segregated populations that minimises the total number of cases. We show that for a limited stockpile of vaccine, the optimal policy is often to immunise one population to the exclusion of others. However, as greater realism is included, this extreme and arguably unethical policy, is replaced by an optimal strategy where vaccine supply is more evenly spatially distributed.

EpiFire: An open source C++ library and application for contact network epidemiology

BACKGROUND

Contact network models have become increasingly common in epidemiology, but we lack a flexible programming framework for the generation and analysis of epidemiological contact networks and for the simulation of disease transmission through such networks.

RESULTS

Here we present EpiFire, an applications programming interface and graphical user interface implemented in C++, which includes a fast and efficient library for generating, analyzing and manipulating networks. Network-based percolation and chain-binomial simulations of susceptible-infected-recovered disease transmission, as well as traditional non-network mass-action simulations, can be performed using EpiFire.

CONCLUSIONS

EpiFire provides an open-source programming interface for the rapid development of network models with a focus in contact network epidemiology. EpiFire also provides a point-and-click interface for generating networks, conducting epidemic simulations, and creating figures. This interface is particularly useful as a pedagogical tool.

Vaccination against 2009 pandemic H1N1 in a population dynamical model of Vancouver, Canada: timing is everything

BACKGROUND

Much remains unknown about the effect of timing and prioritization of vaccination against pandemic (pH1N1) 2009 virus on health outcomes. We adapted a city-level contact network model to study different campaigns on influenza morbidity and mortality.

METHODS

We modeled different distribution strategies initiated between July and November 2009 using a compartmental epidemic model that includes age structure and transmission network dynamics. The model represents the Greater Vancouver Regional District, a major North American city and surrounding suburbs with a population of 2 million, and is parameterized using data from the British Columbia Ministry of Health, published studies, and expert opinion. Outcomes are expressed as the number of infections and deaths averted due to vaccination.

RESULTS

The model output was consistent with provincial surveillance data. Assuming a basic reproduction number = 1.4, an 8-week vaccination campaign initiated 2 weeks before the epidemic onset reduced morbidity and mortality by 79-91% and 80-87%, respectively, compared to no vaccination. Prioritizing children and parents for vaccination may have reduced transmission compared to actual practice, but the mortality benefit of this strategy appears highly sensitive to campaign timing. Modeling the actual late October start date resulted in modest reductions in morbidity and mortality (13-25% and 16-20%, respectively) with little variation by prioritization scheme.

CONCLUSION

Delays in vaccine production due to technological or logistical barriers may reduce potential benefits of vaccination for pandemic influenza, and these temporal effects can outweigh any additional theoretical benefits from population targeting. Careful modeling may provide decision makers with estimates of these effects before the epidemic peak to guide production goals and inform policy. Integration of real-time surveillance data with mathematical models holds the promise of enabling public health planners to optimize the community benefits from proposed interventions before the pandemic peak.

Disease transmission in territorial populations: the small-world network of Serengeti lions

Territoriality in animal populations creates spatial structure that is thought to naturally buffer disease invasion. Often, however, territorial populations also include highly mobile, non-residential individuals that potentially serve as disease superspreaders. Using long-term data from the Serengeti Lion Project, we characterize the contact network structure of a territorial wildlife population and address the epidemiological impact of nomadic individuals. As expected, pride contacts are dominated by interactions with neighbouring prides and interspersed by encounters with nomads as they wander throughout the ecosystem. Yet the pride-pride network also includes occasional long-range contacts between prides, making it surprisingly small world and vulnerable to epidemics, even without nomads. While nomads increase both the local and global connectivity of the network, their epidemiological impact is marginal, particularly for diseases with short infectious periods like canine distemper virus. Thus, territoriality in Serengeti lions may be less protective and non-residents less important for disease transmission than previously considered.