Logistics of community smallpox control through contact tracing and ring vaccination: a stochastic network model

Testing to sustain hepatitis C elimination targets in people who inject drugs: A network-based model

Little is known about the level of testing required to sustain elimination of hepatitis C (HCV), once achieved. In this study, we model the testing coverage required to maintain HCV elimination in an injecting network of people who inject drugs (PWID). We test the hypothesis that network-based strategies are a superior approach to deliver testing. We created a dynamic injecting network structure connecting 689 PWID based on empirical data. The primary outcome was the testing coverage required per month to maintain prevalence at the elimination threshold over 5 years. We compared four testing strategies. Without any testing or treatment provision, the prevalence of HCV increased from the elimination threshold (11.68%) to a mean of 25.4% (SD 2.96%) over the 5-year period. To maintain elimination with random testing, on average, 4.96% (SD 0.83%) of the injecting network needs to be tested per month. However, with a 'bring your friends' strategy, this was reduced to 3.79% (SD 0.64%) of the network (p < .001). The addition of contact tracing improved the efficiency of both strategies. In conclusion, we report that network-based approaches to testing such as 'bring a friend' initiatives and contact tracing lower the level of testing coverage required to maintain elimination.

Stochastic optimization for vaccine and testing kit allocation for the COVID-19 pandemic

We present a formal mathematical modeling framework for a multi-agent sequential decision problem during an epidemic. The problem is formulated as a collaboration between a vaccination agent and learning agent to allocate stockpiles of vaccines and tests to a set of zones under various types of uncertainty. The model is able to capture passive information processes and maintain beliefs over the uncertain state of the world. We designed a parameterized direct lookahead approximation which is robust and scalable under different scenarios, resource scarcity, and beliefs about the environment. We design a test allocation policy designed to capture the value of information and demonstrate that it outperforms other learning policies when there is an extreme shortage of resources (information is scarce). We simulate the model with two scenarios including a resource allocation problem to each state in the United States and another for the nursing homes in Nevada. The US example demonstrates the scalability of the model and the nursing home example demonstrates the robustness under extreme resource shortages.

Monkeypox virus vaccine evolution and global preparedness for vaccination

The recent emergence of monkeypox (MPX) has created a global threat. The number of infected and suspected cases of MPX is increasing in different parts of the world, especially in non-African countries. However, vaccines are available to fight against this disease. It has been observed that smallpox vaccines can be used to protect against MPX. The present article highlights the significant points and various issues for vaccines and vaccinations that should be considered related to MPX. This paper illustrates current vaccines for smallpox that can be utilized to protect against MPX infection. The article also describes the different significant research on MPXV, especially smallpox vaccines, and its outcome in MPX infection. We have also tried to depict the smallpox vaccination eradication model through the statistical interface using smallpox eradication data from Central and West Africa between 1967 and 1972. We suggest that these models might be helpful for the eradication of MPX in the middle to low-economic countries. Simultaneously, we have also discussed vaccination preparedness in different countries like the USA, UK, Canada, Denmark, Germany, etc. Our report might be helpful to scientists and policymakers in understanding the vaccines and vaccination against MPX and formulating effective strategies to fight against the disease.

Challenges and Opportunities of Mass Vaccination Centers in COVID-19 Times: A Rapid Review of Literature

A mass vaccination center is a location, normally used for nonhealthcare activities, set up for high-volume and high-speed vaccinations during infectious disease emergencies. The high contagiousness and mortality of COVID-19 and the complete lack of population immunity posed an extraordinary threat for global health. The aim of our research was to collect and review previous experiences on mass vaccination centers. On 4 April 2021, we developed a rapid review searching four electronic databases: PubMed/Medline, Scopus, EMBASE, Google Scholar and medRxiv. From a total of 2312 papers, 15 of them were included in the current review. Among them, only one article described a COVID-19 vaccination center; all of the others referred to other vaccinations, in particular influenza. The majority were conducted in the United States, and were simulations or single-day experiences to practice a mass vaccination after bioterrorist attacks. Indeed, all of them were published after September 11 attacks. Regarding staff, timing and performance, the data were highly heterogenous. Several studies used as a model the Center for Disease Control and Prevention guidelines. Results highlighted the differences around the definition, layout and management of a mass vaccination center, but some aspects can be considered as a core aspect. In light of this, we suggested a potential definition. The current review answers to the urgency of organizing a mass vaccination center during the COVID-19 pandemic, highlighting the most important organizational aspects that should be considered in the planning.

A multi-stage stochastic programming approach to epidemic resource allocation with equity considerations

Existing compartmental models in epidemiology are limited in terms of optimizing the resource allocation to control an epidemic outbreak under disease growth uncertainty. In this study, we address this core limitation by presenting a multi-stage stochastic programming compartmental model, which integrates the uncertain disease progression and resource allocation to control an infectious disease outbreak. The proposed multi-stage stochastic program involves various disease growth scenarios and optimizes the distribution of treatment centers and resources while minimizing the total expected number of new infections and funerals. We define two new equity metrics, namely infection and capacity equity, and explicitly consider equity for allocating treatment funds and facilities over multiple time stages. We also study the multi-stage value of the stochastic solution (VSS), which demonstrates the superiority of the proposed stochastic programming model over its deterministic counterpart. We apply the proposed formulation to control the Ebola Virus Disease (EVD) in Guinea, Sierra Leone, and Liberia of West Africa to determine the optimal and fair resource-allocation strategies. Our model balances the proportion of infections over all regions, even without including the infection equity or prevalence equity constraints. Model results also show that allocating treatment resources proportional to population is sub-optimal, and enforcing such a resource allocation policy might adversely impact the total number of infections and deaths, and thus resulting in a high cost that we have to pay for the fairness. Our multi-stage stochastic epidemic-logistics model is practical and can be adapted to control other infectious diseases in meta-populations and dynamically evolving situations.

Modelling of optimal vaccination strategies in response to a bioterrorism associated smallpox outbreak

The reemergence of smallpox as a bioterrorism attack is now an increasing and legitimate concern. Advances in synthetic biology have now made it possible for the virus to be synthesized in a laboratory, with methods publicly available. Smallpox introduction into a susceptible population, with increased immunosuppression and an aging population, raises questions of how vaccination should be used in an epidemic situation when supply may be limited. We constructed three modified susceptible-latent-infectious-recovered (SEIR) models to simulate targeted, ring and mass vaccination in response to a smallpox outbreak in Sydney, Australia. We used age-specific distributions of susceptibility, infectivity, contact rates, and tested outputs under different assumptions. The number of doses needed of second- and third-generation vaccines are estimated, along with the total number of deaths at the end of the epidemic. We found a faster response is the key and ring vaccination of traced contacts is the most effective strategy and requires a smaller number of doses. However if public health authorities are unable to trace a high proportion of contacts, mass vaccination with at least 125,000 doses delivered per day is required. This study informs a better preparedness and response planning for vaccination in a case of a smallpox outbreak in a setting such as Sydney.

Postcode based participatory disease surveillance systems : a comparison with traditional risk-based surveillance and its application in the COVID-19 pandemic

BACKGROUND

Background: The SARS-Cov-2 infection has rapidly saturated health systems and traditional surveillance networks are finding hard to keep pace with its spread. We designed a participatory disease surveillance (PDS) system, to capture symptoms of Influenza-like illness (ILI) to estimate SARS-CoV-2 infection in the community. While data generated by these platforms can help public health organisations find community hotspots and effectively direct control measures, it has never been compared to traditional systems.

OBJECTIVE

Methods and Objectives: A completely anonymised web based PDS system, www.trackcovid-19.org was developed. We evaluated the symptomatic responses received form the PDS system to the traditional risk based surveillance carried out by the Bruhat Bengaluru Mahanagara Palike over a period of 45 days in the South Indian city of Bengaluru.

METHODS

Methods and Objectives: A completely anonymised web based PDS system, www.trackcovid-19.org was developed. We evaluated the symptomatic responses received form the PDS system to the traditional risk based surveillance carried out by the Bruhat Bengaluru Mahanagara Palike over a period of 45 days in the South Indian city of Bengaluru.

RESULTS

Results: The PDS system recorded 11062 entries from 106 Postal codes. A healthy response was obtained from 10863 users while 199 (1.8%) reported symptomatic. Subgroup analysis of a 14 day symptomatic window recorded 33 (0.29%) responses. Risk based surveillance was carried out covering a population of 605,284 with 209 (0.03%) individuals identified symptomatic.

CONCLUSIONS

Conclusion: Web PDS platforms provide better visualisation of community infection when compared to traditional risk based surveillance systems. They are extremely useful by providing real time information in the extended battle against this pandemic. When integrated into national disease surveillance systems, they can provide long term community surveillance adding an important cost-effective layer to already available data sources.

Maintaining efficient logistics and supply chain management operations during and after coronavirus (COVID-19) pandemic: learning from the past experiences

The outbreak of the novel coronavirus (COVID-19) forced the governing bodies across the world to ban all kinds of travel involving the movement of people. However, the policymakers have been working hard to mobilize the movement of essential goods and services considering its importance in containing the pandemic. It signifies how important the establishment and maintenance of logistics and supply chain management (LSCM) operations are, both during the containment and the successive periods. Motivated with the paramount importance of LSCM operations during the rapid spread of the novel coronavirus (COVID-19) across the globe, this paper critically reviews the existing literature closely related to it. The main aim is to identify and enhance the understanding of the logistical characteristics that play a vital role during pandemics. The selection of the literature was done using Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) methodology. The classification of the selected literature was done using a tripartite framework. Results show that researchers have focused mostly on "Post-event" (48.24%) management of logistical operations followed by the "Pre-event" (31.76%) and least in the "Integrated" (20%.) approaches. Furthermore, the analysis of the results provided useful insights that are discussed in detail. Also, twelve key areas have been identified that need due attention to improve the overall efficiency of the LSCM operations. We believe that the findings from this paper would be useful to the decision-makers and other stakeholders, as far as, maintaining efficient LSCM operations during as well after the pandemics are concerned.

Contact tracing - Old models and new challenges

Contact tracing is an effective method to control emerging infectious diseases. Since the 1980's, modellers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations, and to assess the effects of contact tracing on the spread of an infectious disease. Despite the progress made in the area, there remain important open questions. In addition, technological developments, especially in the field of molecular biology (genetic sequencing of pathogens) and modern communication (digital contact tracing), have posed new challenges for the modelling community. In the present paper, we discuss modelling approaches for contact tracing and identify some of the current challenges for the field.

Outbreak response intervention models of vaccine-preventable diseases in humans and foot-and-mouth disease in livestock: a protocol for a systematic review

INTRODUCTION

Outbreaks of vaccine-preventable diseases continue to threaten public health, despite the proven effectiveness of vaccines. Interventions such as vaccination, social distancing and palliative care are usually implemented, either individually or in combination, to control these outbreaks. Mathematical models are often used to assess the impact of these interventions and for supporting outbreak response decision making. The objectives of this systematic review, which covers all human vaccine-preventable diseases, are to determine the relative impact of vaccination compared with other outbreak interventions, and to ascertain the temporal trends in the use of modelling in outbreak response decision making. We will also identify gaps and opportunities for future research through a comparison with the foot-and-mouth disease outbreak response modelling literature, which has good examples of the use of modelling to inform outbreak response intervention decision making.

METHODS AND ANALYSIS

We searched on PubMed, Scopus, Web of Science, Google Scholar and some preprint servers from the start of indexing to 15 January 2020. Inclusion: modelling studies, published in English, that use a mechanistic approach to evaluate the impact of an outbreak intervention. Exclusion: reviews, and studies that do not describe or use mechanistic models or do not describe an outbreak. We will extract data from the included studies such as their objectives, model types and composition, and conclusions on the impact of the intervention. We will ascertain the impact of models on outbreak response decision making through visualisation of time trends in the use of the models. We will also present our results in narrative style.

ETHICS AND DISSEMINATION

This systematic review will not require any ethics approval since it only involves scientific articles. The review will be disseminated in a peer-reviewed journal and at various conferences fitting its scope.

PROSPERO REGISTRATION NUMBER

CRD42020160803.

Digital Contact tracing in the COVID-19 Pandemic: A tool far from reality

Digital contact tracing applications are being developed by governments across the world, to track and trace contacts. With little evidence, citizens are being forced and made to believe that it is an important step in pandemic control. We discuss briefly if contact tracing will be successful in the control of the Corona virus pandemic or is it just a tool governments are using to cover their helplessness.

Vaccines against Ebola virus

We have just witnessed the largest and most devastating outbreak of Ebola virus disease, which highlighted the urgent need for development of an efficacious vaccine that could be used to curtail future outbreaks. Prior to 2014, there had been limited impetus worldwide to develop a vaccine since the virus was first discovered in 1976. Though too many lives were lost during this outbreak, it resulted in the significantly accelerated clinical development of a number of candidate vaccines through an extraordinary collaborative global effort coordinated by the World Health Organisation (WHO) and involving a number of companies, trial centres, funders, global stakeholders and agencies. We have acquired substantial safety and immunogenicity data on a number of vaccines in Caucasian and African populations. The rapid pace of events led to the initiation of the landmark efficacy trial testing the rVSV-vectored vaccine, which showed high level efficacy in an outbreak setting when deployed using an innovative ring vaccination strategy. Though the Public Health Emergency of International Concern (PHEIC) declared by the WHO has now been lifted, the global scientific community faces numerous challenges ahead to ensure that there is a licensed, deployable vaccine available for use in future outbreaks for at least the Zaire and Sudan strains of Ebola virus. There remain several unanswered questions on the durability of protection, mechanistic immunological correlates and preferred deployment strategies. This review outlines a brief history of the development of Ebola vaccines, the significant progress made since the scale of the outbreak became apparent, some lessons learnt and how they could shape future development of vaccines and the management of similar outbreaks.

The Effect of Contact Investigations and Public Health Interventions in the Control and Prevention of Measles Transmission: A Simulation Study

BACKGROUND

Measles cases continue to occur despite its elimination status in the United States. To control transmission, public health officials confirm the measles diagnosis, identify close contacts of infectious cases, deliver public health interventions (i.e., post-exposure prophylaxis) among those who are eligible, and follow-up with the close contacts to determine overall health outcomes. A stochastic network simulation of measles contact tracing was conducted using existing agent-based modeling software and a synthetic population with high levels of immunity in order to estimate the impact of different interventions in controlling measles transmission.

METHODS AND FINDINGS

The synthetic population was created to simulate California`s population in terms of population demographics, household, workplace, school, and neighborhood characteristics using California Department of Finance 2010 census data. Parameters for the model were obtained from a review of the literature, California measles case surveillance data, and expert opinion. Eight different scenarios defined by the use of three different public health interventions were evaluated: (a) post-exposure measles, mumps, and rubella (MMR) vaccine, (b) post-exposure immune globulin (IG), and (c) voluntary isolation and home quarantine in the presence or absence of public health response delays. Voluntary isolation and home quarantine coupled with one or two other interventions had the greatest reduction in the number of secondary cases infected by the index case and the probability of escape situations (i.e., the outbreak continues after 90 days).

CONCLUSIONS

Interrupting contact patterns via voluntary isolation and home quarantine are particularly important in reducing the number of secondary cases infected by the index case and the probability of uncontrolled outbreaks.

Genomic Analysis of Viral Outbreaks

Genomic analysis is a powerful tool for understanding viral disease outbreaks. Sequencing of viral samples is now easier and cheaper than ever before and can supplement epidemiological methods by providing nucleotide-level resolution of outbreak-causing pathogens. In this review, we describe methods used to answer crucial questions about outbreaks, such as how they began and how a disease is transmitted. More specifically, we explain current techniques for viral sequencing, phylogenetic analysis, transmission reconstruction, and evolutionary investigation of viral pathogens. By detailing the ways in which genomic data can help us understand viral disease outbreaks, we aim to provide a resource that will facilitate the response to future outbreaks.

The role of vaccination coverage, individual behaviors, and the public health response in the control of measles epidemics: an agent-based simulation for California

BACKGROUND

Measles cases continue to occur among susceptible individuals despite the elimination of endemic measles transmission in the United States. Clustering of disease susceptibility can threaten herd immunity and impact the likelihood of disease outbreaks in a highly vaccinated population. Previous studies have examined the role of contact tracing to control infectious diseases among clustered populations, but have not explicitly modeled the public health response using an agent-based model.

METHODS

We developed an agent-based simulation model of measles transmission using the Framework for Reconstructing Epidemiological Dynamics (FRED) and the Synthetic Population Database maintained by RTI International. The simulation of measles transmission was based on interactions among individuals in different places: households, schools, daycares, workplaces, and neighborhoods. The model simulated different levels of immunity clustering, vaccination coverage, and contact investigations with delays caused by individuals' behaviors and/or the delay in a health department's response. We examined the effects of these characteristics on the probability of uncontrolled measles outbreaks and the outbreak size in 365 days after the introduction of one index case into a synthetic population.

RESULTS

We found that large measles outbreaks can be prevented with contact investigations and moderate contact rates by having (1) a very high vaccination coverage (≥ 95%) with a moderate to low level of immunity clustering (≤ 0.5) for individuals aged less than or equal to 18 years, or (2) a moderate vaccination coverage (85% or 90%) with no immunity clustering for individuals (≤ 18 years of age), a short intervention delay, and a high probability that a contact can be traced. Without contact investigations, measles outbreaks may be prevented by the highest vaccination coverage with no immunity clustering for individuals (≤ 18 years of age) with moderate contact rates; but for the highest contact rates, even the highest coverage with no immunity clustering for individuals (≤ 18 years of age) cannot completely prevent measles outbreaks.

CONCLUSIONS

The simulation results demonstrated the importance of vaccination coverage, clustering of immunity, and contact investigations in preventing uncontrolled measles outbreaks.

Conflicts of interest during contact investigations: a game-theoretic analysis

The goal of contact tracing is to reduce the likelihood of transmission, particularly to individuals who are at greatest risk for developing complications of infection, as well as identifying individuals who are in need of medical treatment of other interventions. In this paper, we develop a simple mathematical model of contact investigations among a small group of individuals and apply game theory to explore conflicts of interest that may arise in the context of perceived costs of disclosure. Using analytic Kolmogorov equations, we determine whether or not it is possible for individual incentives to drive noncooperation, even though cooperation would yield a better group outcome. We found that if all individuals have a cost of disclosure, then the optimal individual decision is to simply not disclose each other. With further analysis of (1) completely offsetting the costs of disclosure and (2) partially offsetting the costs of disclosure, we found that all individuals disclose all contacts, resulting in a smaller basic reproductive number and an alignment of individual and group optimality. More data are needed to understand decision making during outbreak investigations and what the real and perceived costs are.

Effect of the one-child policy on influenza transmission in China: a stochastic transmission model

BACKGROUND

China's one-child-per-couple policy, introduced in 1979, led to profound demographic changes for nearly a quarter of the world's population. Several decades later, the consequences include decreased fertility rates, population aging, decreased household sizes, changes in family structure, and imbalanced sex ratios. The epidemiology of communicable diseases may have been affected by these changes since the transmission dynamics of infectious diseases depend on demographic characteristics of the population. Of particular interest is influenza because China and Southeast Asia lie at the center of a global transmission network of influenza. Moreover, changes in household structure may affect influenza transmission. Is it possible that the pronounced demographic changes that have occurred in China have affected influenza transmission?

METHODS AND FINDINGS

To address this question, we developed a continuous-time, stochastic, individual-based simulation model for influenza transmission. With this model, we simulated 30 years of influenza transmission and compared influenza transmission rates in populations with and without the one-child policy control. We found that the average annual attack rate is reduced by 6.08% (SD 2.21%) in the presence of the one-child policy compared to a population in which no demographic changes occurred. There was no discernible difference in the secondary attack rate, -0.15% (SD 1.85%), between the populations with and without a one-child policy. We also forecasted influenza transmission over a ten-year time period in a population with a two-child policy under a hypothesis that a two-child-per-couple policy will be carried out in 2015, and found a negligible difference in the average annual attack rate compared to the population with the one-child policy.

CONCLUSIONS

This study found that the average annual attack rate is slightly lowered in a population with a one-child policy, which may have resulted from a decrease in household size and the proportion of children in the population.

Hepatitis C transmission and treatment in contact networks of people who inject drugs

Hepatitis C virus (HCV) chronically infects over 180 million people worldwide, with over 350,000 estimated deaths attributed yearly to HCV-related liver diseases. It disproportionally affects people who inject drugs (PWID). Currently there is no preventative vaccine and interventions feature long treatment durations with severe side-effects. Upcoming treatments will improve this situation, making possible large-scale treatment interventions. How these strategies should target HCV-infected PWID remains an important unanswered question. Previous models of HCV have lacked empirically grounded contact models of PWID. Here we report results on HCV transmission and treatment using simulated contact networks generated from an empirically grounded network model using recently developed statistical approaches in social network analysis. Our HCV transmission model is a detailed, stochastic, individual-based model including spontaneously clearing nodes. On transmission we investigate the role of number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. On treatment we investigate the effect of nine network-based treatment strategies on chronic prevalence and incidence rates of primary infection and re-infection. Both numbers of contacts and injecting frequency play key roles in reducing time to primary infection. The change from "less-" to "more-frequent" injector is roughly similar to having one additional network contact. Nodes that spontaneously clear their HCV infection have a local effect on infection risk and the total number of such nodes (but not their locations) has a network wide effect on the incidence of both primary and re-infection with HCV. Re-infection plays a large role in the effectiveness of treatment interventions. Strategies that choose PWID and treat all their contacts (analogous to ring vaccination) are most effective in reducing the incidence rates of re-infection and combined infection. A strategy targeting infected PWID with the most contacts (analogous to targeted vaccination) is the least effective.

The contribution of residents who cooperate with ring-vaccination measures against smallpox epidemic

OBJECTIVES

Establishing containment measures against the potential spread of the smallpox virus has become a major issue in the public health field since the 2001 anthrax attacks in the United States. The primary objective of the study was to investigate the relationship between the level of activity of public health agencies and the voluntary cooperation of residents with ring-vaccination measures against a smallpox epidemic.

METHODS

A discrete-time, stochastic, individual-based model was used to simulate the spread of a smallpox epidemic that has become a more pressing topic due to 9/11 and to assess the effectiveness of and required resources for ring-vaccination measures in a closed community. In the simulation, we related sensitive tracing to the level of activity of the public health agency and strict isolation to the level of voluntary cooperation from residents.

RESULTS

Our results suggest that early and intensive case detection and contact tracing by public health agencies can reduce the scale of an epidemic and use fewer total resources. In contrast, voluntary reporting by the traced contacts of symptom onset after vaccination had little impact on the scale of epidemic in our model. However, it reduced the total required resources, indicating that citizens' voluntary cooperation would contribute to reducing the burden on public health agencies.

CONCLUSIONS

We conclude that a combined effort on the part of public health agencies and residents in performing containment measures is essential to quickly ending a smallpox epidemic.

Stamping Out Fires! Controlling Smallpox with Targeted Mass Vaccination

Background. More than 30 years have now passed since the last naturally occurring case of smallpox; however, the variola virus still exists in at least 2 locations. The possibility that any clandestine stocks could be used for bioterrorism is a continuing concern for the public health community. Objective. Mathematical modeling is used to assess the impact of mass vaccination following a smallpox release when either standard public health controls are failing or political/public opinion is urging more comprehensive methods. Two mass vaccination strategies are considered: a blanket nationwide campaign v. an approach targeted only at those geographic areas that experience smallpox cases. The study evaluates which intervention strategy results in the fewest combined disease and vaccine-related deaths. Results. Outbreaks that go unnoticed until up to 50 cases have occurred are optimally controlled with targeted mass vaccination of the affected administrative districts in the majority of scenarios considered. The number of people vaccinated is approximately two thirds fewer than when implementing a nationwide campaign. Similar results arise when contact tracing is either highly unsuccessful or reduced in favor of reallocating limited resources for a policy of mass vaccination. Conclusions. Reactive nationwide mass vaccination remains a suboptimal strategy for controlling an expanding smallpox outbreak in all but the most extreme circumstances. Rather, targeted mass vaccination of affected areas is likely to result in fewer deaths. The vaccines administered are also likely to be much fewer because they would probably be distributed to a much smaller number of districts, thus relieving pressure on potentially stretched public health systems.

Contingency planning for a deliberate release of smallpox in Great Britain--the role of geographical scale and contact structure

Background

In the event of a release of a pathogen such as smallpox, which is human-to-human transmissible and has high associated mortality, a key question is how best to deploy containment and control strategies. Given the general uncertainty surrounding this issue, mathematical modelling has played an important role in informing the likely optimal response, in particular defining the conditions under which mass-vaccination would be appropriate. In this paper, we consider two key questions currently unanswered in the literature: firstly, what is the optimal spatial scale for intervention; and secondly, how sensitive are results to the modelling assumptions made about the pattern of human contacts?

Methods

Here we develop a novel mathematical model for smallpox that incorporates both information on individual contact structure (which is important if the effects of contact tracing are to be captured accurately) and large-scale patterns of movement across a range of spatial scales in Great Britain.

Results

Analysis of this model confirms previous work suggesting that a locally targeted 'ring' vaccination strategy is optimal, and that this conclusion is actually quite robust for different socio-demographic and epidemiological assumptions.

Conclusions

Our method allows for intuitive understanding of the reasons why national mass vaccination is typically predicted to be suboptimal. As such, we present a general framework for fast calculation of expected outcomes during the attempted control of diverse emerging infections; this is particularly important given that parameters would need to be interactively estimated and modelled in any release scenario.

Recommendations for modeling disaster responses in public health and medicine: a position paper of the society for medical decision making

PURPOSE

Mathematical and simulation models are increasingly used to plan for and evaluate health sector responses to disasters, yet no clear consensus exists regarding best practices for the design, conduct, and reporting of such models. The authors examined a large selection of published health sector disaster response models to generate a set of best practice guidelines for such models.

METHODS

. The authors reviewed a spectrum of published disaster response models addressing public health or health care delivery, focusing in particular on the type of disaster and response decisions considered, decision makers targeted, choice of outcomes evaluated, modeling methodology, and reporting format. They developed initial recommendations for best practices for creating and reporting such models and refined these guidelines after soliciting feedback from response modeling experts and from members of the Society for Medical Decision Making.

RESULTS

. The authors propose 6 recommendations for model construction and reporting, inspired by the most exemplary models: health sector disaster response models should address real-world problems, be designed for maximum usability by response planners, strike the appropriate balance between simplicity and complexity, include appropriate outcomes that extend beyond those considered in traditional cost-effectiveness analyses, and be designed to evaluate the many uncertainties inherent in disaster response. Finally, good model reporting is particularly critical for disaster response models.

CONCLUSIONS

. Quantitative models are critical tools for planning effective health sector responses to disasters. The proposed recommendations can increase the applicability and interpretability of future models, thereby improving strategic, tactical, and operational aspects of preparedness planning and response.

The state-reproduction number for a multistate class age structured epidemic system and its application to the asymptomatic transmission model

In this paper, we develop the theory of a state-reproduction number for a multistate class age structured epidemic system and apply it to examine the asymptomatic transmission model. We formulate a renewal integral equation system to describe the invasion of infectious diseases into a multistate class age structured host population. We define the state-reproduction number for a class age structured system, which is the net reproduction number of a specific host type and which plays an analogous role to the type-reproduction number [M.G. Roberts, J.A.P. Heesterbeek, A new method for estimating the effort required to control an infectious disease, Proc. R. Soc. Lond. B 270 (2003) 1359; J.A.P. Heesterbeek, M.G. Roberts, The type-reproduction number T in models for infectious disease control, Math. Biosci. 206 (2007) 3] in discussing the critical level of public health intervention. The renewal equation formulation permits computations not only of the state-reproduction number, but also of the generation time and the intrinsic growth rate of infectious diseases. Subsequently, the basic theory is applied to capture the dynamics of a directly transmitted disease within two types of infected populations, i.e., asymptomatic and symptomatic individuals, in which the symptomatic class is observable and hence a target host of the majority of interventions. The state-reproduction number of the symptomatic host is derived and expressed as a measurable quantity, leading to discussion on the critical level of case isolation. The serial interval and other epidemiologic indices are computed, clarifying the parameters on which these indices depend. As a practical example, we illustrate the eradication threshold for case isolation of smallpox. The generation time and serial interval are comparatively examined for pandemic influenza.

Extracting key information from historical data to quantify the transmission dynamics of smallpox

Background

Quantification of the transmission dynamics of smallpox is crucial for optimizing intervention strategies in the event of a bioterrorist attack. This article reviews basic methods and findings in mathematical and statistical studies of smallpox which estimate key transmission parameters from historical data.

Main findings

First, critically important aspects in extracting key information from historical data are briefly summarized. We mention different sources of heterogeneity and potential pitfalls in utilizing historical records. Second, we discuss how smallpox spreads in the absence of interventions and how the optimal timing of quarantine and isolation measures can be determined. Case studies demonstrate the following. (1) The upper confidence limit of the 99th percentile of the incubation period is 22.2 days, suggesting that quarantine should last 23 days. (2) The highest frequency (61.8%) of secondary transmissions occurs 3–5 days after onset of fever so that infected individuals should be isolated before the appearance of rash. (3) The U-shaped age-specific case fatality implies a vulnerability of infants and elderly among non-immune individuals. Estimates of the transmission potential are subsequently reviewed, followed by an assessment of vaccination effects and of the expected effectiveness of interventions.

Conclusion

Current debates on bio-terrorism preparedness indicate that public health decision making must account for the complex interplay and balance between vaccination strategies and other public health measures (e.g. case isolation and contact tracing) taking into account the frequency of adverse events to vaccination. In this review, we summarize what has already been clarified and point out needs to analyze previous smallpox outbreaks systematically.

Contact tracing to control infectious disease: when enough is enough

Contact tracing (also known as partner notification) is a primary means of controlling infectious diseases such as tuberculosis (TB), human immunodeficiency virus (HIV), and sexually transmitted diseases (STDs). However, little work has been done to determine the optimal level of investment in contact tracing. In this paper, we present a methodology for evaluating the appropriate level of investment in contact tracing. We develop and apply a simulation model of contact tracing and the spread of an infectious disease among a network of individuals in order to evaluate the cost and effectiveness of different levels of contact tracing. We show that contact tracing is likely to have diminishing returns to scale in investment: incremental investments in contact tracing yield diminishing reductions in disease prevalence. In conjunction with a cost-effectiveness threshold, we then determine the optimal amount that should be invested in contact tracing. We first assume that the only incremental disease control is contact tracing. We then extend the analysis to consider the optimal allocation of a budget between contact tracing and screening for exogenous infection, and between contact tracing and screening for endogenous infection. We discuss how a simulation model of this type, appropriately tailored, could be used as a policy tool for determining the appropriate level of investment in contact tracing for a specific disease in a specific population. We present an example application to contact tracing for chlamydia control.

Optimal mix of screening and contact tracing for endemic diseases

Two common means of controlling infectious diseases are screening and contact tracing. Which should be used, and when? We consider the problem of determining the cheapest mix of screening and contact tracing necessary to achieve a desired endemic prevalence of a disease or to identify a specified number of cases. We perform a partial equilibrium analysis of small-scale interventions, assuming that prevalence is unaffected by the intervention; we develop a full equilibrium analysis where we compare the long-term cost of various combinations of screening and contact tracing needed to achieve a given equilibrium prevalence; and we solve the problem of minimizing the total costs of identifying and treating disease cases plus the cost of untreated disease cases. Our analysis provides several insights. First, contact tracing is only cost effective when prevalence is below a threshold value. This threshold depends on the relative cost per case found by screening versus contact tracing. Second, for a given contact tracing policy, the screening rate needed to achieve a given prevalence or identify a specified number of cases is a decreasing function of disease prevalence. As prevalence increases above the threshold (and contact tracing is discontinued), the screening rate jumps discontinuously to a higher level. Third, these qualitative results hold when we consider unchanged or changed prevalence, and short-term or long-term costs.

Interpreting the epidemiology of postexposure vaccination against smallpox

Six historical studies were investigated to clarify the obtainable information on postexposure vaccination against smallpox. Using the distribution of incubation period, the frequency of cases by time from exposure to vaccination was obtained. More than half of all failures happened within 7d after exposure in all six records investigated. Based on two studies (n=36 and 28), the probability of escaping severe smallpox was further analyzed using logistic regression, showing an inverse association between severe smallpox and time from vaccination to onset (p<0.01 and p=0.04, respectively). Whereas the relationship between the probability of developing severe disease and the time from vaccination to onset could be analyzed with the available information, our findings indicate that previous epidemiologic records showing cases alone, rather than also showing individuals probably protected, are not useful for clarifying the effectiveness of postexposure vaccination by time after exposure.

The effectiveness of contact tracing in emerging epidemics

Background

Contact tracing plays an important role in the control of emerging infectious diseases, but little is known yet about its effectiveness. Here we deduce from a generic mathematical model how effectiveness of tracing relates to various aspects of time, such as the course of individual infectivity, the (variability in) time between infection and symptom-based detection, and delays in the tracing process. In addition, the possibility of iteratively tracing of yet asymptomatic infecteds is considered. With these insights we explain why contact tracing was and will be effective for control of smallpox and SARS, only partially effective for foot-and-mouth disease, and likely not effective for influenza.

Methods and Findings

We investigate contact tracing in a model of an emerging epidemic that is flexible enough to use for most infections. We consider isolation of symptomatic infecteds as the basic scenario, and express effectiveness as the proportion of contacts that need to be traced for a reproduction ratio smaller than 1. We obtain general results for special cases, which are interpreted with respect to the likely success of tracing for influenza, smallpox, SARS, and foot-and-mouth disease epidemics.

Conclusions

We conclude that (1) there is no general predictive formula for the proportion to be traced as there is for the proportion to be vaccinated; (2) variability in time to detection is favourable for effective tracing; (3) tracing effectiveness need not be sensitive to the duration of the latent period and tracing delays; (4) iterative tracing primarily improves effectiveness when single-step tracing is on the brink of being effective.

Frequency of adverse events after vaccination with different vaccinia strains

BACKGROUND

Large quantities of smallpox vaccine have been stockpiled to protect entire nations against a possible reintroduction of smallpox. Planning for an appropriate use of these stockpiled vaccines in response to a smallpox outbreak requires a rational assessment of the risks of vaccination-related adverse events, compared to the risk of contracting an infection. Although considerable effort has been made to understand the dynamics of smallpox transmission in modern societies, little attention has been paid to estimating the frequency of adverse events due to smallpox vaccination. Studies exploring the consequences of smallpox vaccination strategies have commonly used a frequency of approximately one death per million vaccinations, which is based on a study of vaccination with the New York City Board of Health (NYCBH) strain of vaccinia virus. However, a multitude of historical studies of smallpox vaccination with other vaccinia strains suggest that there are strain-related differences in the frequency of adverse events after vaccination. Because many countries have stockpiled vaccine based on the Lister strain of vaccinia virus, a quantitative evaluation of the adverse effects of such vaccines is essential for emergency response planning. We conducted a systematic review and statistical analysis of historical data concerning vaccination against smallpox with different strains of vaccinia virus.

METHODS AND FINDINGS

We analyzed historical vaccination data extracted from the literature. We extracted data on the frequency of postvaccinal encephalitis and death with respect to vaccinia strain and age of vaccinees. Using a hierarchical Bayesian approach for meta-analysis, we estimated the expected frequencies of postvaccinal encephalitis and death with respect to age at vaccination for smallpox vaccines based on the NYCBH and Lister vaccinia strains. We found large heterogeneity between findings from different studies and a time-period effect that showed decreasing incidences of adverse events over several decades. To estimate death rates, we then restricted our analysis to more-recent studies. We estimated that vaccination with the NYCBH strain leads to an average of 1.4 deaths per million vaccinations (95% credible interval, 0-6) and that vaccination with Lister vaccine leads to an average of 8.4 deaths per million vaccinations (95% credible interval, 0-31). We combined age-dependent estimates of the frequency of death after vaccination and revaccination with demographic data to obtain estimates of the expected number of deaths in present societies due to vaccination with the NYCBH and Lister vaccinia strains.

CONCLUSIONS

Previous analyses of smallpox vaccination policies, which rely on the commonly assumed value of one death per million vaccinations, may give serious underestimates of the number of deaths resulting from vaccination. Moreover, because there are large, strain-dependent differences in the frequency of adverse events due to smallpox vaccination, it is difficult to extrapolate from predictions for the NYCBH-derived vaccines (stockpiled in countries such as the US) to predictions for the Lister-derived vaccines (stockpiled in countries such as Germany). In planning for an effective response to a possible smallpox outbreak, public-health decision makers should reconsider their strategies of when to opt for ring vaccination and when to opt for mass vaccination.

Dark Winter and the Spring of 1972: Deflecting the Social Lessons of Smallpox

This article examines how the master status of bioterrorism has distracted professional and political attention from the social lessons of smallpox. I illustrate this by comparing an influential bioterrorism simulation known as Dark Winter with the social history surrounding the Yugoslavian smallpox epidemic of 1972. Dark Winter's epidemiological premises were largely based upon what was learned from the Yugoslavian outbreak. Yet, although this epidemic was non-deliberate, the exercise did not attend to the social conditions within which it developed. Most notably, it did not consider that this epidemic was mainly borne by marginalized communities of Kosovan Albanians and that difficulties in controlling it were linked to the relative lack of pre-existing public health infrastructure among these people; instead, the Dark Winter exercise mainly focused upon the proximate determinants of violence and its immediate management. This distraction from the social dynamics of infectious diseases has major implications for the prevention and management of future outbreaks, regardless of whether or not they are deliberately initiated.

Mass vaccination and surveillance/containment in the eradication of smallpox

The Smallpox Eradication Program, initiated by the WHO in 1966, was originally based on mass vaccination. The program emphasized surveillance from the beginning, largely to track the success of the program and further our understanding of the epidemiology of the disease. Early observations in West Africa, bolstered by later data from Indonesia and the Asian subcontinent, showed that smallpox did not spread rapidly, and outbreaks could be quickly controlled by isolation of patients and vaccination of their contacts. Contacts were usually easy to find because transmission of smallpox usually required prolonged face-to-face contact. The emphasis therefore shifted to active searches to find cases, coupled with contact tracing, rigorous isolation of patients, and vaccination and surveillance of contacts to contain outbreaks. This shift away from mass vaccination resulted in an acceleration of the program's success.

The effect of treatment on pathogen virulence

The optimal virulence of a pathogen is determined by a trade-off between maximizing the rate of transmission and maximizing the duration of infectivity. Treatment measures such as curative therapy and case isolation exert selective pressure by reducing the duration of infectivity, reducing the value of duration-increasing strategies to the pathogen and favoring pathogen strategies that maximize the rate of transmission. We extend the trade-off models of previous authors, and represents the reproduction number of the pathogen as a function of the transmissibility, host contact rate, disease-induced mortality, recovery rate, and treatment rate, each of which may be influenced by the virulence. We find that when virulence is subject to a transmissibility-mortality trade-off, treatment can lead to an increase in optimal virulence, but that in other scenarios (such as the activity-recovery trade-off) treatment decreases the optimal virulence. Paradoxically, when levels of treatment rise with pathogen virulence, increasing control efforts may raise predicted levels of optimal virulence. Thus we show that conflict can arise between the epidemiological benefits of treatment and the evolutionary risks of heightened virulence.