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.     

Analyzing bioterror response logistics: the case of smallpox

To evaluate existing and alternative proposals for emergency response to a deliberate smallpox attack, we embed the key operational features of such interventions into a smallpox disease transmission model. We use probabilistic reasoning within an otherwise deterministic epidemic framework to model the 'race to trace', i.e., attempting to trace (via the infector) and vaccinate an infected person while (s)he is still vaccine-sensitive. Our model explicitly incorporates a tracing/vaccination queue, and hence can be used as a capacity planning tool. An approximate analysis of this large (16 ODE) system yields closed-form estimates for the total number of deaths and the maximum queue length. The former estimate delineates the efficacy (i.e., accuracy) and efficiency (i.e., speed) of contact tracing, while the latter estimate reveals how congestion makes the race to trace more difficult to win, thereby causing more deaths. A probabilistic analysis is also used to find an approximate closed-form expression for the total number of deaths under mass vaccination, in terms of both the basic reproductive ratio and the vaccination capacity. We also derive approximate thresholds for initially controlling the epidemic for more general interventions that include imperfect vaccination and quarantine.     

Confidence in crisis? Understanding trust in government and public attitudes toward mandatory state health powers

In response to the possibility of a bioterror attack using smallpox, many states have updated and revised their current public health laws in line with the Model Act, which would effectively give states the right to invoke mandatory state health powers, such as quarantine or vaccine. Previous studies have supported the importance of allying with the public in creating and implementing effective bioterror response policies. Historical case studies and recent research suggest that when the public is not supportive of government health policies, they may be less willing to comply. In this study we analyze a recent survey to determine the effects of a set of variables, including aspects of trust in government that have been found in previous studies to influence public opposition to compulsory government health policies, on opinions about compulsory vaccination and quarantine.     

A model of bovine tuberculosis control in domesticated cattle herds.

A typical strategy for disease control in domesticated animals involves regular field tests and quarantine of infected herds. This prevents disease spread beyond the herd, while slaughter of diseased animals removes the infection from within the herd. A model of bovine tuberculosis (Tb) control in cattle is examined, which includes ''test and slaughter'' combined with herd isolation and vaccination. Herd status is represented by an integral equation expressing the duration of herd isolation. The current Tb situation in New Zealand is used as an example, and vaccination strategy discussed. Extrapolation of existing management strategies indicate that a vaccine of efficacy greater than 96% would be required, reaching 95% of target Tb levels within six years. These results suggest that a complementary strategy of vaccination and vector control may be more promising than vaccination alone.     

Harnessing Case Isolation and Ring Vaccination to Control Ebola

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts.     

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.     

Convincing the “Herd” of immunity: Lessons from smallpox vaccination in 19th century Germany

Although vaccination is a cost-effective way to control infectious diseases, it is often met with popular resistance. Studying smallpox in 19th century Germany, this paper explores how economic incentives contribute to this phenomenon. The paper adds to the literature by combining mathematical epidemiology and unpublished archival evidence from two German states - Baden and Wurttemberg. The two states are an intriguing case because their initial conditions and vaccination laws were similar. Despite this, Baden experienced lower smallpox prevalence and higher vaccination uptake than Wurttemberg. The epidemiological model predicts that incentives to vaccinate decline rapidly when immunization reduces prevalence. The archival evidence reveals that Baden offset this decline by creating a public vaccination system which reduced costs for vaccinees and vaccinators alike. This suggests that the high fixed costs of centralized immunization policies can be compensated by economies of scale and popular acceptance.     

Variability order of the latent and the infectious periods in a deterministic SEIR epidemic model and evaluation of control effectiveness

We use distribution theory and ordering of non-negative random variables to study the Susceptible-Exposed-Infectious-Removed (SEIR) model with two control measures, quarantine and isolation, to reduce the spread of an infectious disease. We identify that the probability distributions of the latent period and the infectious period are primary features of the SEIR model to formulate the epidemic threshold and to evaluate the effectiveness of the intervention measures. If the primary features are changed, the conclusions will be altered in an importantly different way. For the latent and infectious periods with known mean values, it is the dilation, a generalization of variance, of their distributions that ranks the effectiveness of these control measures. We further propose ways to set quarantine and isolation targets to reduce the controlled reproduction number below the threshold using observed initial growth rate from outbreak data. If both quarantine and isolation are 100% effective, one can directly use the observed growth rate for setting control targets. If they are not 100% effective, some further knowledge of the distributions is required.     

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。     

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.     

Predicting and Evaluating the Epidemic Trend of Ebola Virus Disease in the 2014-2015 Outbreak and the Effects of Intervention Measures

We constructed dynamic Ebola virus disease (EVD) transmission models to predict epidemic trends and evaluate intervention measure efficacy following the 2014 EVD epidemic in West Africa. We estimated the effective vaccination rate for the population, with basic reproduction number (R₀) as the intermediate variable. Periodic EVD fluctuation was analyzed by solving a Jacobian matrix of differential equations based on a SIR (susceptible, infective, and removed) model. A comprehensive compartment model was constructed to fit and predict EVD transmission patterns, and to evaluate the effects of control and prevention measures. Effective EVD vaccination rates were estimated to be 42% (31–50%), 45% (42–48%), and 51% (44–56%) among susceptible individuals in Guinea, Liberia and Sierra Leone, respectively. In the absence of control measures, there would be rapid mortality in these three countries, and an EVD epidemic would be likely recur in 2035, and then again 8~9 years later. Oscillation intervals would shorten and outbreak severity would decrease until the periodicity reached ~5.3 years. Measures that reduced the spread of EVD included: early diagnosis, treatment in isolation, isolating/monitoring close contacts, timely corpse removal, post-recovery condom use, and preventing or quarantining imported cases. EVD may re-emerge within two decades without control and prevention measures. Mass vaccination campaigns and control and prevention measures should be instituted to prevent future EVD epidemics.     

Optimal control of epidemics with limited resources

We extend the existing work on the time-optimal control of the basic SIR epidemic model with mass action contact rate. Previous results have focused on minimizing an objective function that is a linear combination of the cost associated with using control and either the outbreak size or the infectious burden. We instead, provide analytic solutions for the control that minimizes the outbreak size (or infectious burden) under the assumption that there are limited control resources. We provide optimal control policies for an isolation only model, a vaccination only model and a combined isolation–vaccination model (or mixed model). The optimal policies described here contain many interesting features especially when compared to previous analyses. For example, under certain circumstances the optimal isolation only policy is not unique. Furthermore the optimal mixed policy is not simply a combination of the optimal isolation only policy and the optimal vaccination only policy. The results presented here also highlight a number of areas that warrant further study and emphasize that time-optimal control of the basic SIR model is still not fully understood.     

When measles came to class: a look back at the 1989 Kent State University measles epidemic

BackgroundMeasles was eliminated from the United States in 2000, following a change from a single dose of measles vaccine to two doses after an epidemic 1989–1991. Several college campuses experienced outbreaks, including Kent State University (KSU) in Ohio.MethodsLocal news media from 1988 to 1989 were searched in August 2019. Interventions taken by the university were recorded, and an epidemic curve constructed.ResultsThe first measles cases were reported in October 1988. The outbreak diminished over winter break. New cases were confirmed in February 1989. Infected students were instructed to vacate the dorms. Vaccines were mandated for student groups. The epidemic grew rapidly in March but slowed after spring break. By April, 380 cases had been reported and 7000 students vaccinated.ConclusionsKSU was one of the hardest-hit universities during the 1989 measles epidemic. A combination of vaccination, isolation, quarantine, and elimination of public events helped to curtail the epidemic.     

Should Persons Detained During Public Health Crises Receive Compensation?

One of the ways in which public health officials control outbreaks of epidemic disease is by attempting to control the situations in which the infectious agent can spread. This may include isolation of infected persons, quarantine of persons who may be infected and detention of persons who are present in or have entered premises where infected persons are being treated. Most who have analysed such measures think that the restrictions in liberty they entail and the detriments in welfare they impose can be justified and this paper proceeds from the assumption that detention measures are justifiable in some circumstances. Such measures are often implemented without any compensation being given to the persons who are detained. This raises the question: What do we owe to those whose liberty is justifiably restricted (e.g. through isolation, quarantine or detention) as a public health measure during a public health emergency? More specifically, do we owe them compensation for any losses they experience? The paper falls in four main sections. The first section provides examples of the current regulatory state of affairs from the US, Canada and WHO. The second section lays out the liberal, welfarist and pragmatic arguments for providing compensation. The third section discusses the arguments against compensation and the fourth and final section provides the conclusion. It is argued that the arguments for providing compensation clearly outweigh the counterarguments and that the default public policy therefore should be that compensation is provided.     

Progression of pathogenic events in cynomolgus macaques infected with variola virus

Smallpox, caused by variola virus (VARV), is a devastating human disease that affected millions worldwide until the virus was eradicated in the 1970 s. Subsequent cessation of vaccination has resulted in an immunologically naive human population that would be at risk should VARV be used as an agent of bioterrorism. The development of antivirals and improved vaccines to counter this threat would be facilitated by the development of animal models using authentic VARV. Towards this end, cynomolgus macaques were identified as adequate hosts for VARV, developing ordinary or hemorrhagic smallpox in a dose-dependent fashion. To further refine this model, we performed a serial sampling study on macaques exposed to doses of VARV strain Harper calibrated to induce ordinary or hemorrhagic disease. Several key differences were noted between these models. In the ordinary smallpox model, lymphoid and myeloid hyperplasias were consistently found whereas lymphocytolysis and hematopoietic necrosis developed in hemorrhagic smallpox. Viral antigen accumulation, as assessed immunohistochemically, was mild and transient in the ordinary smallpox model. In contrast, in the hemorrhagic model antigen distribution was widespread and included tissues and cells not involved in the ordinary model. Hemorrhagic smallpox developed only in the presence of secondary bacterial infections - an observation also commonly noted in historical reports of human smallpox. Together, our results support the macaque model as an excellent surrogate for human smallpox in terms of disease onset, acute disease course, and gross and histopathological lesions.     

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.     

Coadministration of Cidofovir and Smallpox Vaccine Reduced Vaccination Side Effects but Interfered with Vaccine-Elicited Immune Responses and Immunity to Monkeypox

While the smallpox vaccine, Dryvax or Dryvax-derived ACAM2000, holds potential for public immunization against the spread of smallpox by bioterror, there is serious concern about Dryvax-mediated side effects. Here, we report that a single-dose vaccination regimen comprised of Dryvax and an antiviral agent, cidofovir, could reduce vaccinia viral loads after vaccination and significantly control Dryvax vaccination side effects. However, coadministration of cidofovir and Dryvax also reduced vaccine-elicited immune responses of antibody and T effector cells despite the fact that the reduced priming could be boosted as a recall response after monkeypox virus challenge. Evaluations of four different aspects of vaccine efficacy showed that coadministration of cidofovir and Dryvax compromised the Dryvax-induced immunity against monkeypox, although the covaccinated monkeys exhibited measurable protection against monkeypox compared to that of naïve controls. Thus, the single-dose coadministration of cidofovir and Dryvax effectively controlled vaccination side effects but significantly compromised vaccine-elicited immune responses and vaccine-induced immunity to monkeypox.     

Mapping perceptions related to acceptance of smallpox vaccination by hospital emergency room personnel

Emergency department personnel would be first responders in the event of a bioterror smallpox outbreak, yet few were willing to be vaccinated during the 2002 federal campaign. To better understand vaccination concerns, perceptual mapping methods were used to create multidimensional models of how emergency department personnel (N= 73) in the Philadelphia area perceive the risks and benefits of smallpox vaccination under 4 levels of threat: (1) today; (2) if another terrorist attack happened anywhere in the U.S.; (3) if a smallpox attack happened somewhere in the U.S.; (4) if a smallpox attack happened locally. The perceptual maps show significant shifts in factors that are important for motivating respondents to accept vaccination under increasingly higher levels of threat. In the today scenario, endorsement of vaccination from a credible source, such as a major hospital in the area, was a very important factor (mean =7.10 on a 0-10 scale).However, endorsement was not as important under the 2 higher levels of threat. Under these conditions, respondents'sense of wanting to help in a disaster emerged as an important element the closer the hypothetical attack was to the respondent,ranging in importance from 3.87 under the least threat to 7.35 under the greatest threat scenario. The perceptual maps yield information that would assist planners in designing more effective risk communication strategies tailored to particular audiences and levels of threat. Such communications are important to prepare for a smallpox event or other uncertain outbreak, where it is essential to rapidly vaccinate a critical mass of healthcare workers.     

Establishment of the black-tailed prairie dog (Cynomys ludovicianus) as a novel animal model for comparing smallpox vaccines administered preexposure in both high- and low-dose monkeypox virus challenges

The 2003 monkeypox virus (MPXV) outbreak and subsequent laboratory studies demonstrated that the black-tailed prairie dog is susceptible to MPXV infection and that the ensuing rash illness is similar to human systemic orthopoxvirus (OPXV) infection, including a 7- to 9-day incubation period and, likely, in some cases a respiratory route of infection; these features distinguish this model from others. The need for safe and efficacious vaccines for OPVX in areas where it is endemic or epidemic is important to protect an increasingly OPXV-naïve population. In this study, we tested current and investigational smallpox vaccines for safety, induction of anti-OPXV antibodies, and protection against mortality and morbidity in two MPXV challenges. None of the smallpox vaccines caused illness in this model, and all vaccinated animals showed anti-OPXV antibody responses and neutralizing antibody. We tested vaccine efficacy by challenging the animals with 10⁵ or 10⁶ PFU Congo Basin MPXV 30 days postvaccination and evaluating morbidity and mortality. Our results demonstrated that vaccination with either Dryvax or Acambis2000 protected the animals from death with no rash illness. Vaccination with IMVAMUNE also protected the animals from death, albeit with (modified) rash illness. Based on the results of this study, we believe prairie dogs offer a novel and potentially useful small animal model for the safety and efficacy testing of smallpox vaccines in pre- and postexposure vaccine testing, which is important for public health planning.     

Control of emerging infectious diseases using responsive imperfect vaccination and isolation

This paper is concerned with a stochastic model for the spread of an SEIR (susceptible --> exposed (= latent) --> infective --> removed) epidemic among a population partitioned into households, featuring different rates of infection for within and between households. The model incorporates responsive vaccination and isolation policies, based upon the appearance of diagnosed cases in households. Different models for imperfect vaccine response are considered. A threshold parameter R*, which determines whether or not a major epidemic can occur, and the probability of a major epidemic are obtained for different infectious and latent period distributions. Simpler expressions for these quantities are obtained in the limiting case of infinite within-household infection rate. Numerical studies suggest that the choice of infectious period distribution and whether or not latent individuals are vaccine-sensitive have a material influence on the spread of the epidemic, while, for given vaccine efficacy, the choice of vaccine action model is less influential. They also suggest that an effective isolation policy has a more significant impact than vaccination. The results show that R* alone is not sufficient to summarise the potential for an epidemic.