Effects of behavioral changes in a smallpox attack model

The impact of individual and community behavioral changes in response to an outbreak of a disease with high mortality is often not appreciated. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation of infectives, contact tracing, quarantine of contacts, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. Transmission parameters are estimated from data and an expression is derived for the effective reproduction number. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity rates and to the precautions that the population takes to reduce the transmission of the disease. Even gradual and mild behavioral changes can have a dramatic impact in slowing an epidemic. When behavioral changes are combined with other interventions, the epidemic is shortened and the number of smallpox cases is reduced. We conclude that for simulations of a smallpox outbreak to be useful, they must consider the impact of behavioral changes. This is especially true if the model predictions are being used to guide public health policy.     

An integral equation model for the control of a smallpox outbreak

An integral equation model of a smallpox epidemic is proposed. The model structures the incidence of infection among the household, the workplace, the wider community and a health-care facility; and incorporates a finite incubation period and plausible infectivity functions. Linearisation of the model is appropriate for small epidemics, and enables analytic expressions to be derived for the basic reproduction number and the size of the epidemic. The effects of control interventions (vaccination, isolation, quarantine and public education) are explored for a smallpox epidemic following an imported case. It is found that the rapid identification and isolation of cases, the quarantine of affected households and a public education campaign to reduce contact would be capable of bringing an epidemic under control. This could be used in conjunction with the vaccination of healthcare workers and contacts. Our results suggest that prior mass vaccination would be an inefficient method of containing an outbreak.     

Antiviral immunity following smallpox virus infection: a case-control study

Outbreaks of smallpox (i.e., caused by variola virus) resulted in up to 30% mortality, but those who survived smallpox infection were regarded as immune for life. Early studies described the levels of neutralizing antibodies induced after infection, but smallpox was eradicated before contemporary methods for quantifying T-cell memory were developed. To better understand the levels and duration of immunity after smallpox infection, we performed a case-control study comparing antiviral CD4(+) and CD8(+) T-cell responses and neutralizing antibody levels of 24 smallpox survivors with the antiviral immunity observed in 60 smallpox-vaccinated (i.e., vaccinia virus-immune) control subjects. We found that the duration of immunity following smallpox infection was remarkably similar to that observed after smallpox vaccination, with antiviral T-cell responses that declined slowly over time and antiviral antibody responses that remained stable for decades after recovery from infection. These results indicate that severe, potentially life-threatening disease is not required for the development of sustainable long-term immunity. This study shows that the levels of immunity induced following smallpox vaccination are comparable in magnitude to that achieved through natural variola virus infection, and this may explain the notable success of vaccination in eradicating smallpox, one of the world's most lethal diseases.     

Theory versus data: how to calculate R0?

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R(0)>1 the outbreak generates an epidemic, and if R(0)<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R(0)). Surprisingly, we find that this value of R(0) calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.     

The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda

Despite improved control measures, Ebola remains a serious public health risk in African regions where recurrent outbreaks have been observed since the initial epidemic in 1976. Using epidemic modeling and data from two well-documented Ebola outbreaks (Congo 1995 and Uganda 2000), we estimate the number of secondary cases generated by an index case in the absence of control interventions R0. Our estimate of R0 is 1.83 (SD 0.06) for Congo (1995) and 1.34 (SD 0.03) for Uganda (2000). We model the course of the outbreaks via an SEIR (susceptible-exposed-infectious-removed) epidemic model that includes a smooth transition in the transmission rate after control interventions are put in place. We perform an uncertainty analysis of the basic reproductive number R0 to quantify its sensitivity to other disease-related parameters. We also analyse the sensitivity of the final epidemic size to the time interventions begin and provide a distribution for the final epidemic size. The control measures implemented during these two outbreaks (including education and contact tracing followed by quarantine) reduce the final epidemic size by a factor of 2 relative the final size with a 2-week delay in their implementation.     

Detecting Differential Transmissibilities That Affect the Size of Self-Limited Outbreaks

Our ability to respond appropriately to infectious diseases is enhanced by identifying differences in the potential for transmitting infection between individuals. Here, we identify epidemiological traits of self-limited infections (i.e. infections with an effective reproduction number satisfying ) that correlate with transmissibility. Our analysis is based on a branching process model that permits statistical comparison of both the strength and heterogeneity of transmission for two distinct types of cases. Our approach provides insight into a variety of scenarios, including the transmission of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the Arabian peninsula, measles in North America, pre-eradication smallpox in Europe, and human monkeypox in the Democratic Republic of the Congo. When applied to chain size data for MERS-CoV transmission before 2014, our method indicates that despite an apparent trend towards improved control, there is not enough statistical evidence to indicate that has declined with time. Meanwhile, chain size data for measles in the United States and Canada reveal statistically significant geographic variation in , suggesting that the timing and coverage of national vaccination programs, as well as contact tracing procedures, may shape the size distribution of observed infection clusters. Infection source data for smallpox suggests that primary cases transmitted more than secondary cases, and provides a quantitative assessment of the effectiveness of control interventions. Human monkeypox, on the other hand, does not show evidence of differential transmission between animals in contact with humans, primary cases, or secondary cases, which assuages the concern that social mixing can amplify transmission by secondary cases. Lastly, we evaluate surveillance requirements for detecting a change in the human-to-human transmission of monkeypox since the cessation of cross-protective smallpox vaccination. Our studies lay the foundation for future investigations regarding how infection source, vaccination status or other putative transmissibility traits may affect self-limited transmission.     

Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes

This paper treats a stochastic model for an SIR (susceptible-->infective-->removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinates the fewest among all vaccination schemes that reduce the threshold parameter below 1. This is done for the situation where all model parameters are known and also for the case where parameters are estimated from an outbreak in the community prior to vaccination. It is shown that the algorithm which chooses vaccines sequentially, at each step selecting the individual which reduces the threshold parameter the most, is not in general an optimal scheme. As a consequence, explicit characterisation of the optimal scheme is only possible in certain special cases. Two different types of vaccine responses, leaky and all-or-nothing, are considered and compared for the problems mentioned above. The methods are illustrated with some numerical examples.     

The smallpox vaccine: a multidimensional model of choice

Following September 11, 2001, the U.S. government increased its efforts to prepare for future attacks, including those using dangerous biological agents such as smallpox. The smallpox vaccination program called for vaccinating military personnel and smallpox response teams, including healthcare workers and other first responders. The program of vaccinating healthcare workers was largely unsuccessful; few individuals volunteered to be vaccinated, highlighting the importance of understanding the factors that influence choice regarding this complex medical decision. This study examined stated choice and how it was associated with risk perceptions, knowledge, psychological distress, and general vaccine beliefs using a five-dimensional choice model. The model used multivariable modeling strategies in a sample of 256 undergraduate, graduate, and medical students. Sixty-three percent of the sample stated that they would elect to receive the smallpox vaccination. Multiple factors were related to stated choice in multivariable models, including perceived risk/worry, general vaccine beliefs, decisional conflict, and gender. However, the models were more successful at predicting acceptance of the vaccination than vaccine refusal. Although support was obtained for a multidimensional model of choice, several questions were raised by our results, including (a) whether refusal of smallpox vaccination can be more effectively characterized, possibly with additional questions; (b) whether the model translates to actual vaccination behavior; and (c) whether the model describes choice in more at-risk samples (e.g., first responders, healthcare workers). A multidimensional modeling approach should facilitate these and other studies of choice.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

An SIRVS epidemic model with pulse vaccination strategy

The aim of this paper is to analyze an SIRVS epidemic model in which pulse vaccination strategy (PVS) is included. We are interested in finding the basic reproductive number of the model which determine whether or not the disease dies out. The global attractivity of the disease-free periodic solution (DFPS for short) is obtained when the basic reproductive number is less than unity. The disease is permanent when the basic reproductive number is greater than unity, i.e., the epidemic will turn out to endemic. Our results indicate that the disease will go to extinction when the vaccination rate reaches some critical value.     

天花预防接种面临的挑战与DNA痘苗

介绍美国重新启动种痘的动因,LIR、A27L、A33R、B5R基因痘苗建立、修饰的Ankara痘苗和Lister基因缺失痘苗动物保护力、安全试验、临床研究现状及预防天花、人类猴痘的前景。     

Stability properties of pulse vaccination strategy in SEIR epidemic model

The problem of the applicability of the pulse vaccination strategy (PVS) for the stable eradication of some relevant general class of infectious diseases is analyzed in terms of study of local asymptotic stability (LAS) and global asymptotic stability (GAS) of the periodic eradication solution for the SEIR epidemic model in which is included the PVS. Demographic variations due or not to diseased-related fatalities are also considered. Due to the non-triviality of the Floquet's matrix associate to the studied model, the LAS is studied numerically and in this way it is found a simple approximate (but analytical) sufficient criterion which is an extension of the LAS constraint for the stability of the trivial equilibrium in SEIR model without vaccination. The numerical simulations also seem to suggest that the PVS is slightly more efficient than the continuous vaccination strategy. Analytically, the GAS of the eradication solutions is studied and it is demonstrated that the above criteria for the LAS guarantee also the GAS.     

Covasim: An agent-based model of COVID-19 dynamics and interventions

The COVID-19 pandemic has created an urgent need for models that can project epidemic trends, explore intervention scenarios, and estimate resource needs. Here we describe the methodology of Covasim (COVID-19 Agent-based Simulator), an open-source model developed to help address these questions. Covasim includes country-specific demographic information on age structure and population size; realistic transmission networks in different social layers, including households, schools, workplaces, long-term care facilities, and communities; age-specific disease outcomes; and intrahost viral dynamics, including viral-load-based transmissibility. Covasim also supports an extensive set of interventions, including non-pharmaceutical interventions, such as physical distancing and protective equipment; pharmaceutical interventions, including vaccination; and testing interventions, such as symptomatic and asymptomatic testing, isolation, contact tracing, and quarantine. These interventions can incorporate the effects of delays, loss-to-follow-up, micro-targeting, and other factors. Implemented in pure Python, Covasim has been designed with equal emphasis on performance, ease of use, and flexibility: realistic and highly customized scenarios can be run on a standard laptop in under a minute. In collaboration with local health agencies and policymakers, Covasim has already been applied to examine epidemic dynamics and inform policy decisions in more than a dozen countries in Africa, Asia-Pacific, Europe, and North America.     

An Optimal Cost Effectiveness Study on Zimbabwe Cholera Seasonal Data from 2008–2011

Incidence of cholera outbreak is a serious issue in underdeveloped and developing countries. In Zimbabwe, after the massive outbreak in 2008–09, cholera cases and deaths are reported every year from some provinces. Substantial number of reported cholera cases in some provinces during and after the epidemic in 2008–09 indicates a plausible presence of seasonality in cholera incidence in those regions. We formulate a compartmental mathematical model with periodic slow-fast transmission rate to study such recurrent occurrences and fitted the model to cumulative cholera cases and deaths for different provinces of Zimbabwe from the beginning of cholera outbreak in 2008–09 to June 2011. Daily and weekly reported cholera incidence data were collected from Zimbabwe epidemiological bulletin, Zimbabwe Daily cholera updates and Office for the Coordination of Humanitarian Affairs Zimbabwe (OCHA, Zimbabwe). For each province, the basic reproduction number () in periodic environment is estimated. To the best of our knowledge, this is probably a pioneering attempt to estimate in periodic environment using real-life data set of cholera epidemic for Zimbabwe. Our estimates of agree with the previous estimate for some provinces but differ significantly for Bulawayo, Mashonaland West, Manicaland, Matabeleland South and Matabeleland North. Seasonal trend in cholera incidence is observed in Harare, Mashonaland West, Mashonaland East, Manicaland and Matabeleland South. Our result suggests that, slow transmission is a dominating factor for cholera transmission in most of these provinces. Our model projects cholera cases and cholera deaths during the end of the epidemic in 2008–09 to January 1, 2012. We also determine an optimal cost-effective control strategy among the four government undertaken interventions namely promoting hand-hygiene & clean water distribution, vaccination, treatment and sanitation for each province.     

Age-structured non-pharmaceutical interventions for optimal control of COVID-19 epidemic

In an epidemic, individuals can widely differ in the way they spread the infection depending on their age or on the number of days they have been infected for. In the absence of pharmaceutical interventions such as a vaccine or treatment, non-pharmaceutical interventions (e.g. physical or social distancing) are essential to mitigate the pandemic. We develop an original approach to identify the optimal age-stratified control strategy to implement as a function of the time since the onset of the epidemic. This is based on a model with a double continuous structure in terms of host age and time since infection. By applying optimal control theory to this model, we identify a solution that minimizes deaths and costs associated with the implementation of the control strategy itself. We also implement this strategy for three countries with contrasted age distributions (Burkina-Faso, France, and Vietnam). Overall, the optimal strategy varies throughout the epidemic, with a more intense control early on, and depending on host age, with a stronger control for the older population, except in the scenario where the cost associated with the control is low. In the latter scenario, we find strong differences across countries because the control extends to the younger population for France and Vietnam 2 to 3 months after the onset of the epidemic, but not for Burkina Faso. Finally, we show that the optimal control strategy strongly outperforms a constant uniform control exerted over the whole population or over its younger fraction. This improved understanding of the effect of age-based control interventions opens new perspectives for the field, especially for age-based contact tracing.     

Patterns of smallpox mortality in London,England, over three centuries

Smallpox is unique among infectious diseases in the degree to which it devastated human populations, its long history of control interventions, and the fact that it has been successfully eradicated. Mortality from smallpox in London, England was carefully documented, weekly, for nearly 300 years, providing a rare and valuable source for the study of ecology and evolution of infectious disease. We describe and analyze smallpox mortality in London from 1664 to 1930. We digitized the weekly records published in the London Bills of Mortality (LBoM) and the Registrar General’s Weekly Returns (RGWRs). We annotated the resulting time series with a sequence of historical events that might have influenced smallpox dynamics in London. We present a spectral analysis that reveals how periodicities in reported smallpox mortality changed over decades and centuries; many of these changes in epidemic patterns are correlated with changes in control interventions and public health policies. We also examine how the seasonality of reported smallpox mortality changed from the 17th to 20th centuries in London.

This study presents the complete historical weekly record of smallpox mortality in London over more than 250 years (1664-1930), describes it using spectral analyses, and discusses it in the context of events and interventions that might have influenced infectious disease dynamics.     

Real-time investigation of measles epidemics with estimate of vaccine efficacy

As part of measles elimination effort, evaluation of the vaccination program and real-time assessment of the epidemic dynamics constitute two important tasks to improve and strengthen the control. The present study aimed to develop an epidemiological modeling method which can be applied to estimating the vaccine efficacy at an individual level while conducting the timely investigation of the epidemic. The multivariate renewal process model was employed to describe the temporal evolution of infection by vaccination history, jointly estimating the time-dependent reproduction number and the vaccine efficacy. Analyzing the enhanced surveillance data of measles in Aichi prefecture, Japan from 2007-08, the vaccine efficacy was estimated at 96.7% (95% confidence interval: 95.8, 97.4). Using an age structured model, the vaccine efficacy among those aged from 5-19 years was shown to be smaller than that among those from 0-4 years. The age-dependent vaccine efficacy estimate informs the age-groups to be targeted for revaccination. Because the estimation method can rest on readily available epidemiological data, the proposed model has a potential to be integrated with routine surveillance.     

Quantification of the effect of control strategies on classical swine fever epidemics

Emergency vaccination during an epidemic of classical swine fever virus (CSFV) has become a serious option because of the ethical problems of strategies with massive culling and the availability of a marker vaccine that reduces virus transmission. Here we present a model of between-herd CSFV transmission, which quantifies the effect of control strategies with and without vaccination. We estimate the model parameters from data of the Dutch CSFV epidemic of 1997/1998. With the model, a set of control strategies is compared, consisting of five control measures in several combinations. Consequently, the following general requirements of successful strategies can be formulated. First, to achieve extinction of a CSFV epidemic, transmission through transport should be prevented and the indirect virus transmission, i.e. all transmission not through animal contacts, should at least be halved, either by vaccination or by culling of the susceptible pig population. Second, to minimize the size and duration of an epidemic, the extinction requirements should be met quickly and indirect virus transmission should be reduced by far more than a half. Although the origin of the model parameters let the requirements in fact be only applicable for the south-eastern part of the Netherlands, it is argued that epidemics in other areas will not need stricter control strategies.     

Smallpox: A Retrospect

Smallpox has been known as a disease of man since the earliest times. However, its severity increased greatly during the eighteenth century, stimulating physicians and others to find methods of protection against it. Variolation (the inoculation of smallpox material into the skin) was tried, and for a while found general approval, although its practice was not without danger. In 1796, Edward Jenner began his investigations into the use of cow-pox material (vaccination) as a prophylactic against smallpox, and later showed that vaccination could confer protection. Although vaccination centres were first set up in Canada early in the nineteenth century, the disease on occasion assumed epidemic proportions, such as occurred in Montreal in 1885. Sporadic outbreaks have occurred since then, including the recent case in Toronto. From the public health point of view, maintenance of a high level of immunity to smallpox throughout the general population is necessary if serious epidemics are to be avoided.     

猴痘的流行现状及防控

猴痘(monkeypox)是由猴痘病毒感染所致的人兽共患病,主要发生在非洲中部、西部地区。猴痘病毒可感染多种哺乳类动物,主要在动物中流行,人接触感染动物后可被传染。猴痘的临床表现与天花相似(发热、皮疹等),但症状较轻。天花疫苗接种可提供预防猴痘的免疫保护力。然而,因全球天花被消灭而停止接种天花疫苗后,猴痘成为最可能威胁人类的正痘病毒性疾病。近期,其散发病例在欧洲多地出现。2022年5月7日英国报道了猴痘疫情。随后,欧洲报道猴痘确诊和疑似病例超过100例。猴痘主要传播途径包括接触感染动物、与患者直接接触或间接接触。2022年5月20日,世界卫生组织就此次猴痘疫情召开了紧急会议,旨在提高对猴痘的认识,做好防范应对准备。世界卫生组织、美国疾病预防控制中心、英国卫生部门报告了相关疫情并制定了相应的防控措施。截至2022年5月28日我国尚无输入性猴痘报道,但因国际交往频繁等仍须提高警惕。本文介绍了猴痘流行现状及有关防控信息,以供借鉴。