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Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity., Author Summary Both infectious diseases and behavioral traits can spread via social contacts. Using network-based mathematical models, our study addresses the interplay between these two processes, as disease spreads through a population and individuals copy their social contacts when making vaccination decisions. Imitation can produce clusters of non-vaccinating, susceptible individuals that facilitate relatively large outbreaks of infectious diseases despite high overall vaccination coverage. This may explain, for example, recent measles outbreaks observed in many countries with universal measles vaccination policies. Given that vaccine decisions are likely to be influenced by social contacts and that such imitation can have detrimental epidemiological effects, it is important that policy makers understand its causes, magnitude and implications for disease eradication.

Preprint of an article published in Journal of Biological Systems, Vol. 23, No. 03, 259-283 (2012) https://doi.org/10.1142/S0218339012500106. © World Scientific Publishing Company [https://www.worldscientific.com/worldscinet/jbs] In the last two decades, monkeypox outbreaks in human populations in Africa and North America have reminded us that smallpox is not the only poxvirus with potential to cause harm in human populations. Monkeypox transmission is sustained in animal reservoirs, and animal-human contacts are responsible for sporadic outbreaks in humans. Here, we develop and analyze a deterministic epizootic (animal-based) transmission model capturing disease dynamics in an animal population, disease dynamics in an age-structured human population, and their coupling through animal-human contacts. We develop a single-patch model as well as a two-patch meta-population extension. We derive mathematical expressions for the basic reproduction number, which governs the likelihood of a large outbreak. We also investigate the effectiveness of culling strategies and the impact of changes in the animal-human contact rate. Numerical analysis of the model suggests that, for some parameter values, culling can actually have the counter-productive outcome of increasing monkeypox infection in children, if animal reproduction is a density-dependent process. The likelihood of this happening, as well as the prevalence of monkeypox in humans, depends sensitively on the animal-human contact rate. We also find that ignoring age structure in human populations can lead to overestimating the transmissibility of monkeypox in humans. In conclusion, the effectiveness of monkeypox control strategies such as culling can strongly depend on the details of demography and epidemiology in the animal reservoirs that sustain it. Therefore, to better understand how to prevent and control monkeypox outbreaks in humans, better empirical data from wild animal populations where monkeypox is endemic must be collected, and these data must be incorporated into highly structured theoretical models.

Vaccination is a cornerstone of infectious disease prevention. However, individual vaccinating behaviour does not always result in population-level vaccine coverage patterns that are optimal for protecting public health. For example, vaccine coverage may fall below the elimination threshold due to nonvaccinators who “free-ride” on the herd immunity provided by vaccinators. Routine vaccination programs for many paediatric infectious diseases now have an almost worldwide coverage, but vaccine scares fuelled by such behaviours threaten eradication goals. This free-riding behaviour can be seen as a manifestation of policy resistance, where humans respond to an intervention in such a way that tends to undermine the intervention. However, policy resistance is only one such example of the types of dynamics that emerge from the interaction between vaccinating behaviour and disease incidence or prevalence. Here we explore four types of emergent dynamics of behaviour-incidence systems: policy resistance, policy reinforcement, outcome inelasticity, and outcome variability. We discuss examples of each of these dynamics in the behaviour-incidence modelling literature, and suggest potential implications for vaccination policy.

There is significant current interest in the application of media/psychosocial effects to problems in epidemiology. News reporting has the potential to reach and to modify the knowledge, attitudes, and behavior of a large proportion of the community. A susceptible-infected-hospitalized-recovered model with vital dynamics, where media coverage of disease incidence and disease prevalence can influence people to reduce their contact rates is formulated. The media function is incorporated into the model using an exponentially decreasing function. Qualitative analysis of the model reveals that the disease-free equilibrium is locally asymptotically stable when a certain threshold is less than unity. Numerical results show the potential short-term beneficial effect of media coverage.

We used the 'comet assay' to compare the amount of radiation-induced DNA damage in three tumour cell lines (MeWo, PECA 4451 and PECA 4197) and the extent of DNA repair in two of these lines (MeWo and PECA 4197). Tumour cells were irradiated with X-rays (0.1-10 Gy), embedded in agarose on slides, lysed with sodium dodecyl sulphate and exposed to an electric field. DNA migrated within the agarose and formed comets whose length depended on the amount of DNA damage. When the cells were incubated at 37 degrees C for various time intervals before electrophoresis started, the comets shrank in the course of time, indicating repair of DNA damage. All three cell lines showed the same extent of DNA damage after radiation exposure, despite the fact that in the colony-forming assay MeWo and PECA 4451 were much more sensitive to radiation exposure than PECA 4197. The repair characteristics, however, were markedly different for MeWo and PECA 4197 cells. PECA 4197 cells showed a much faster restoration of the original shape of the cell nucleus than MeWo cells.

Background The potential benefits of coordinating infectious disease eradication programs that use campaigns such as supplementary immunization activities (SIAs) should not be over-looked. One example of a coordinated approach is an adaptive "sequential strategy": first, all annual SIA budget is dedicated to the eradication of a single infectious disease; once that disease is eradicated, the annual SIA budget is re-focussed on eradicating a second disease, etc. Herd immunity suggests that a sequential strategy may eradicate several infectious diseases faster than a non-adaptive "simultaneous strategy" of dividing annual budget equally among eradication programs for those diseases. However, mathematical modeling is required to understand the potential extent of this effect. Methods Our objective was to illustrate how budget allocation strategies can interact with the nonlinear nature of disease transmission to determine time to eradication of several infectious diseases under different budget allocation strategies. Using a mathematical transmission model, we analyzed three hypothetical vaccine-preventable infectious diseases in three different countries. A central decision-maker can distribute funding among SIA programs for these three diseases according to either a sequential strategy or a simultaneous strategy. We explored the time to eradication under these two strategies under a range of scenarios. Results For a certain range of annual budgets, all three diseases can be eradicated relatively quickly under the sequential strategy, whereas eradication never occurs under the simultaneous strategy. However, moderate changes to total SIA budget, SIA frequency, order of eradication, or funding disruptions can create disproportionately large differences in the time and budget required for eradication under the sequential strategy. We find that the predicted time to eradication can be very sensitive to small differences in the rate of case importation between the countries. We also find that the time to eradication of all three diseases is not necessarily lowest when the least transmissible disease is targeted first. Conclusions Relatively modest differences in budget allocation strategies in the near-term can result in surprisingly large long-term differences in time required to eradicate, as a result of the amplifying effects of herd immunity and the nonlinearities of disease transmission. More sophisticated versions of such models may be useful to large international donors or other organizations as a planning or portfolio optimization tool, where choices must be made regarding how much funding to dedicate to different infectious disease eradication efforts.

Immunization programs have often been impeded by vaccine scares, as evidenced by the measles-mumps-rubella (MMR) autism vaccine scare in Britain. A “free rider” effect may be partly responsible: vaccine-generated herd immunity can reduce disease incidence to such low levels that real or imagined vaccine risks appear large in comparison, causing individuals to cease vaccinating. This implies a feedback loop between disease prevalence and strategic individual vaccinating behavior. Here, we analyze a model based on evolutionary game theory that captures this feedback in the context of vaccine scares, and that also includes social learning. Vaccine risk perception evolves over time according to an exogenously imposed curve. We test the model against vaccine coverage data and disease incidence data from two vaccine scares in England & Wales: the whole cell pertussis vaccine scare and the MMR vaccine scare. The model fits vaccine coverage data from both vaccine scares relatively well. Moreover, the model can explain the vaccine coverage data more parsimoniously than most competing models without social learning and/or feedback (hence, adding social learning and feedback to a vaccine scare model improves model fit with little or no parsimony penalty). Under some circumstances, the model can predict future vaccine coverage and disease incidence—up to 10 years in advance in the case of pertussis—including specific qualitative features of the dynamics, such as future incidence peaks and undulations in vaccine coverage due to the population's response to changing disease incidence. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. Such models could help us predict how vaccine scares might unfold and assist mitigation efforts., Author Summary “Herd immunity” is a phenomenon whereby an entire population—including unvaccinated individuals—can be protected from infection by vaccinating only a certain percentage of the population. This suggests that immunization programs can be victims of their own success: past vaccinations can drive disease incidence to such low levels that as-yet unvaccinated individuals feel no incentive to get vaccinated, which creates conditions for future outbreaks. “Behavior-incidence” models capture this interplay between disease dynamics and vaccinating behavior. However, the predictive and explanatory value of these models is rarely tested against empirical data, and it is not clear whether the implied strategic interaction between individuals drives vaccinating behavior in real populations. Here we develop a behavior-incidence model based on evolutionary game theory and social learning. We show it often explains vaccine coverage data during a vaccine scare better than most competing models without strategic interactions and/or social learning. It can also predict future vaccine coverage and disease incidence peaks to a significant extent. Thus, strategic interactions between individuals via herd immunity appear to be a significant driver of behavior during a vaccine scare. It may be possible to harness behavior-incidence models to predict how future vaccine scares might unfold and possibly also to mitigate them.

Background Measles control has succeeded worldwide, and many countries have substantially reduced incidence and mortality. This has led to consideration of the feasibility of measles elimination in Uganda within the context of global eradication. Before an elimination program is initiated, it is important to consider its potential economic impact, including its cost-effectiveness. Methods Incremental cost-effectiveness ratios (ICERs) were estimated for measles mortality reduction and measles elimination in Uganda. A dynamic age-structured compartmental model of measles transmission was used to simulate scenarios and estimate health outcomes and costs. The main outcome measures were costs, measles cases, measles deaths, disability-adjusted life-years (DALYs), and ICERs measured as cost per DALY averted through either the year 2030 or 2050. Results Measles elimination by 2020 averted 130,232 measles cases, 3520 measles deaths, and 106,330 DALYs through the year 2030, compared with the next best scenario (95% mortality reduction by 2015), and it was the most cost-effective strategy, with ICERs of $556 per DALY averted (2030 time horizon) and $284 per DALY averted (2050 time horizon). Conclusions Measles elimination in Uganda, as part of a global eradication program, is projected to be highly cost-effective and should be considered among the available policy options for dealing with the disease.

Background Several potential measles vaccine innovations are in development to address the shortcomings of the current vaccine. Funders need to prioritize their scarce research and development resources. This article demonstrates the usefulness of cost-effectiveness analysis to support these decisions. Methods This study had 4 major components: (1) identifying potential innovations, (2) developing transmission models to assess mortality and morbidity impacts, (3) estimating the unit cost impacts, and (4) assessing aggregate cost-effectiveness in United Nations Children's Fund countries through 2049. Results Four promising technologies were evaluated: aerosol delivery, needle-free injection, inhalable dry powder, and early administration DNA vaccine. They are projected to have a small absolute impact in terms of reducing the number of measles cases in most scenarios because of already improving vaccine coverage. Three are projected to reduce unit cost per dose by $0.024 to $0.170 and would improve overall cost-effectiveness. Each will require additional investments to reach the market. Over the next 40 years, the aggregate cost savings could be substantial, ranging from $98.4 million to $689.4 million. Conclusions Cost-effectiveness analysis can help to inform research and development portfolio prioritization decisions. Three new measles vaccination technologies under development hold promise to be cost-saving from a global perspective over the long-term, even after considering additional investment costs.

Vaccination can delay the peak of a pandemic influenza wave by reducing the number of individuals initially susceptible to influenza infection. Emerging evidence indicates that susceptibility to severe secondary bacterial infections following a primary influenza infection may vary seasonally, with peak susceptibility occurring in winter. Taken together, these two observations suggest that vaccinating to prevent a fall pandemic wave might delay it long enough to inadvertently increase influenza infections in winter, when primary influenza infection is more likely to cause severe outcomes. This could potentially cause a net increase in severe outcomes. Most pandemic models implicitly assume that the probability of severe outcomes does not vary seasonally and hence cannot capture this effect. Here we show that the probability of intensive care unit (ICU) admission per influenza infection in the 2009 H1N1 pandemic followed a seasonal pattern. We combine this with an influenza transmission model to investigate conditions under which a vaccination program could inadvertently shift influenza susceptibility to months where the risk of ICU admission due to influenza is higher. We find that vaccination in advance of a fall pandemic wave can actually increase the number of ICU admissions in situations where antigenic drift is sufficiently rapid or where importation of a cross-reactive strain is possible. Moreover, this effect is stronger for vaccination programs that prevent more primary influenza infections. Sensitivity analysis indicates several mechanisms that may cause this effect. We also find that the predicted number of ICU admissions changes dramatically depending on whether the probability of ICU admission varies seasonally, or whether it is held constant. These results suggest that pandemic planning should explore the potential interactions between seasonally varying susceptibility to severe influenza outcomes and the timing of vaccine-altered pandemic influenza waves.

Ring vaccination can be a highly effective control strategy for an emerging disease or in the final phase of disease eradication, as witnessed in the eradication of smallpox. However, the impact of behavioural dynamics on the effectiveness of ring vaccination has not been explored in mathematical models. Here, we analyze a series of stochastic models of voluntary ring vaccination. Contacts of an index case base vaccinating decisions on their own individual payoffs to vaccinate or not vaccinate, and they can also imitate the behaviour of other contacts of the index case. We find that including imitation changes the probability of containment through ring vaccination considerably. Imitation can cause a strong majority of contacts to choose vaccination in some cases, or to choose non-vaccination in other cases—even when the equivalent solution under perfectly rational (non-imitative) behaviour yields mixed choices. Moreover, imitation processes can result in very different outcomes in different stochastic realizations sampled from the same parameter distributions, by magnifying moderate tendencies toward one behaviour or the other: in some realizations, imitation causes a strong majority of contacts not to vaccinate, while in others, imitation promotes vaccination and reduces the number of secondary infections. Hence, the effectiveness of ring vaccination can depend significantly and unpredictably on imitation processes. Therefore, our results suggest that risk communication efforts should be initiated early in an outbreak when ring vaccination is to be applied, especially among subpopulations that are heavily influenced by peer opinions.

Many jurisdictions have implemented universal human papillomavirus (HPV) immunization programs in preadolescent females. However, the cost-effectiveness of modified cervical screening guidelines and/or catch-up immunization in older females in Canada has not been evaluated. We conducted a cost-utility analysis of screening and immunization with the bivalent vaccine for the Canadian setting from the Ministry of Health perspective. We used a dynamic model to capture herd immunity and included cross-protection against strains not included in the vaccine. We found that adding catch-up immunization to the current program would be cost-effective, and that combining catch-up immunization with delaying the age at which screening is first initiated could result in cost savings and net health gains.

During the 2009 H1N1 pandemic, many individuals did not seek vaccination immediately but rather decided to "wait and see" until further information was available on vaccination costs. This behaviour implies two sources of strategic interaction: as more individuals become vaccinated, both the perceived vaccination cost and the probability that susceptible individuals become infected decline. Here we analyze the outcome of these two strategic interactions by combining game theory with a disease transmission model during an outbreak of a novel influenza strain. The model exhibits a "wait and see" Nash equilibrium strategy, with vaccine delayers relying on herd immunity and vaccine safety information generated by early vaccinators. This strategic behaviour causes the timing of the epidemic peak to be strongly conserved across a broad range of plausible transmission rates, in contrast to models without such adaptive behaviour. The model exhibits not only feedback mechanisms but also a feed-forward mechanism: a high initial perceived vaccination cost perpetuates high perceived vaccine costs (and lower vaccine coverage) throughout the remainder of the outbreak. This suggests that any effect of risk communication at the start of a pandemic outbreak will be amplified compared to the same amount of risk communication effort distributed throughout the outbreak.

We describe the application of mathematical models in the study of disease epidemics with particular focus on pandemic influenza. We outline the general mathematical approach and the complications arising from attempts to apply it for disease outbreak management in a real public health context.

In response to the pandemic H1N1 influenza 2009 outbreak, many jurisdictions undertook mass immunization programs that were among the largest in recent history. The objective of this study was to determine the cost-effectiveness of the mass H1N1 immunization program in Ontario, Canada's most populous province (population 13,000,000). This analysis suggests that a mass immunization program as carried out in Ontario and many other high-income health care systems in response to H1N1 2009 was effective in preventing influenza cases and health care resource use and was also highly cost-effective despite the substantial program cost.

Several studies have found that some parents delay the age at which their children receive pediatric vaccines due to perception of higher vaccine risk at the recommended age of vaccination. This has been particularly apparently during the Measles-Mumps-Rubella scare in the United Kingdom. Under a voluntary vaccination policy, vaccine coverage in certain age groups is a potentially complex interplay between vaccinating behaviour, disease dynamics, and age-specific risk factors. Here, we construct an age-structured game dynamic model, where individuals decide whether to vaccinate according to imitation dynamics depending on age-dependent disease prevalence and perceived risk of vaccination. Individuals may be timely vaccinators, delayers, or non-vaccinators. The model exhibits multiple equilibria and a broad range of possible dynamics. For certain parameter regimes, the proportion of timely vaccinators and delayers oscillate in an anti-phase fashion in response to oscillations in infection prevalence. Under an exogenous change to the perceived risk of vaccination as might occur during a vaccine scare, the model can also capture an increase in delayer strategists similar in magnitude to that observed during the Measles-Mumps-Rubella vaccine scare in the United Kingdom. Our model also shows that number of delayers steadily increases with increasing severity of the scare, whereas it saturates to specific value with increases in duration of the scare. Finally, by comparing the model dynamics with and without the option of a delayer strategy, we show that adding a third delayer strategy can have a stabilizing effect on model dynamics. In an era where individual choice--rather than accessibility--is becoming an increasingly important determinant of vaccine uptake, more infectious disease models may need to use game theory or related techniques to determine vaccine uptake.

Background Dynamic models of infection transmission can project future disease burden within a population. Few dynamic measles models have been developed for low-income countries, where measles disease burden is highest. Our objective was to review the literature on measles epidemiology in low-income countries, with a particular focus on data that are needed to parameterize dynamic models. Methods We included age-stratified case reporting and seroprevalence studies with fair to good sample sizes for mostly urban African and Indian populations. We emphasized studies conducted before widespread immunization. We summarized age-stratified attack rates and seroprevalence profiles across these populations. Using the study data, we fitted a "representative" seroprevalence profile for African and Indian settings. We also used a catalytic model to estimate the age-dependent force of infection for individual African and Indian studies where seroprevalence was surveyed. We used these data to quantify the effects of population density on the basic reproductive number R0. Results The peak attack rate usually occurred at age 1 year in Africa, and 1 to 2 years in India, which is earlier than in developed countries before mass vaccination. Approximately 60% of children were seropositive for measles antibody by age 2 in Africa and India, according to the representative seroprevalence profiles. A statistically significant decline in the force of infection with age was found in 4 of 6 Indian seroprevalence studies, but not in 2 African studies. This implies that the classic threshold result describing the critical proportion immune (pc) required to eradicate an infectious disease, pc = 1-1/R0, may overestimate the required proportion immune to eradicate measles in some developing country populations. A possible, though not statistically significant, positive relation between population density and R0 for various Indian and African populations was also found. These populations also showed a similar pattern of waning of maternal antibodies. Attack rates in rural Indian populations show little dependence on vaccine coverage or population density compared to urban Indian populations. Estimated R0 values varied widely across populations which has further implications for measles elimination. Conclusions It is possible to develop a broadly informative dynamic model of measles transmission in low-income country settings based on existing literature, though it may be difficult to develop a model that is closely tailored to any given country. Greater efforts to collect data specific to low-income countries would aid in control efforts by allowing highly population-specific models to be developed.

This work contributes informed estimates to the current debate about the pandemic (H1N1) 2009 mass immunization program's economic merits. We performed a cost-utility analysis of the (H1N1) 2009 mass immunization program in Ontario, Canada's most populous province. The analysis is based on a simulation model of a pandemic (H1N1) 2009 outbreak, surveillance data, and administrative data. We consider no immunization versus mass immunization reaching 30% of the population. Immunization program costs are expected to be $118 million in Ontario. Our analysis indicates this program will reduce influenza cases by 50%, preventing 35 deaths, and cutting treatment costs in half. A pandemic (H1N1) 2009 immunization program is likely to be highly cost-effective.

We have investigated the static and dynamic properties of long YBa2Cu3O(7-delta) 0-pi Josephson junctions and compared them with those of conventional 0 junctions. Scanning SQUID microscope imaging has revealed the presence of a semifluxon at the phase discontinuity point in 0-pi Josephson junctions. Zero field steps have been detected in the current-voltage characteristics of all junctions. Comparison with simulation allows us to attribute these steps to fluxons traveling in the junction for conventional 0 junctions and to fluxon-semifluxon interactions in the case of 0-pi Josephson junctions.

Background Despite the fact that approximately 70% of Canadian women undergo cervical cancer screening at least once every 3 years, approximately 1,300 women were diagnosed with cervical cancer and approximately 380 died from it in 2008. This study estimates the effectiveness and cost-effectiveness of vaccinating 12-year old Canadian females with an AS04-adjuvanted cervical cancer vaccine. The indirect effect of vaccination, via herd immunity, is also estimated. Methods A 12-health-state 1-year-cycle Markov model was developed to estimate lifetime HPV related events for a cohort of 12-year old females. Annual transition probabilities between health-states were derived from published literature and Canadian population statistics. The model was calibrated using Canadian cancer statistics. From a healthcare perspective, the cost-effectiveness of introducing a vaccine with efficacy against HPV-16/18 and evidence of cross-protection against other oncogenic HPV types was evaluated in a population undergoing current screening practices. The base-case analysis included 70% screening coverage, 75% vaccination coverage, $135/dose for vaccine, and 3% discount rate on future costs and health effects. Conservative herd immunity effects were taken into account by estimated HPV incidence using a mathematical model parameterized by reported age-stratified sexual mixing data. Sensitivity analyses were performed to address parameter uncertainties. Results Vaccinating 12-year old females (n = 100,000) was estimated to prevent between 390-633 undiscounted cervical cancer cases (reduction of 47%-77%) and 168-275 undiscounted deaths (48%-78%) over their lifetime, depending on whether or not herd immunity and cross-protection against other oncogenic HPV types were included. Vaccination was estimated to cost $18,672-$31,687 per QALY-gained, the lower range representing inclusion of cross-protective efficacy and herd immunity. The cost per QALY-gained was most sensitive to duration of vaccine protection, discount rate, and the correlation between probability of screening and probability of vaccination. Conclusion In the context of current screening patterns, vaccination of 12-year old Canadian females with an ASO4-ajuvanted cervical cancer vaccine is estimated to significantly reduce cervical cancer and mortality, and is a cost-effective option. However, the economic attractiveness of vaccination is impacted by the vaccine's duration of protection and the discount rate used in the analysis.

Background. Cohort models are often used in cost-effectiveness analysis (CEA) of vaccination. However, because they cannot capture herd immunity effects, cohort models underestimate the reduction in incidence caused by vaccination. Dynamic models capture herd immunity effects but are often not adopted in vaccine CEA. Objective. The objective was to develop a pseudo-dynamic approximation that can be incorporated into an existing cohort model to capture herd immunity effects. Methods. The authors approximated changing force of infection due to universal vaccination for a pediatric infectious disease. The projected lifetime cases in a cohort were compared under 1) a cohort model, 2) a cohort model with pseudo-dynamic approximation, and 3) an age-structured susceptible-exposed-infectious-recovered compartmental (dynamic) model. The authors extended the methodology to sexually transmitted infections. Results. For average to high values of vaccine coverage (P > 60%) and small to average values of the basic reproduction number (R 0 < 10), which describes school-based vaccination programs for many common infections, the pseudo-dynamic approximation significantly improved projected lifetime cases and was close to projections of the full dynamic model. For large values of R0 (R0 > 15), projected lifetime cases were similar under the dynamic model and the cohort model, both with and without pseudo-dynamic approximation. The approximation captures changes in the mean age at infection in the 1st vaccinated cohort. Conclusions. This methodology allows for preliminary assessment of herd immunity effects on CEA of universal vaccination for pediatric infectious diseases. The method requires simple adjustments to an existing cohort model and less data than a full dynamic model.

Large-scale vaccination campaigns (SIAs) and improved routine immunization (RI) have greatly reduced measles incidence in low-income countries. However, the interval between SIAs required to maintain these gains over the long term is not clear. We developed a dynamic model of measles transmission to assess measles vaccination strategies in Cambodia, Ghana, India, Morocco, Nigeria, and Uganda. We projected measles cases from 2008 to 2050 under (a) holding SIAs every 2, 4, 6, or 8 years, (b) improvements in first dose routine measles vaccine (MCV1) coverage of 0%, 1%, 3% annually, and (c) introducing MCV2 once MCV1 coverage reaches 70%, 80%, 90%. If MCV1 continues improving, then India and Nigeria could hold SIAs every 4 years without significant probability of large outbreaks, and the other countries every 6-8 years. If RI remains stagnant, India and Nigeria should hold SIAs every 2 years, and the other countries every 4-6 years.

Background. Evaluating the cost-effectiveness of vaccine programs with dynamic modeling requires accurate estimates of incidence over time. Because infectious diseases are often underreported, supplementary data and statistical analyses are required to estimate true incidence. This study estimates the true incidence of hepatitis A virus (HAV) infection in Canada using a catalytic model. Methods. A catalytic model was used to reconcile HAV seroprevalence data with the corresponding true cumulative risk of infection estimated from incidence data. Results. The average annual reported incidence was 6.2 cases per 100 000 from 1980 to 1989 and 7.7/100 000 from 1990 to 1999, indicating that Canada is a low-incidence country. The seroprevalence in Canadian-born individuals (n = 7 studies) was approximately 1%−8% in ages

Background Hepatitis A (HA) is a low-incidence, non-endemic disease in Canada and the United States (US). However, a large difference in HA incidence between Canada and HA-endemic countries has made travel an important contributor to hepatitis A prevalence in Canada. There is also a (smaller) incidence differential between Canada and the US. Although the US has only moderately higher HA incidence, the volume of travel by Canadians to the US is many times higher than travel volume to endemic countries. Hence, travel to the US may constitute a source of low to moderate risk for Canadian travelers. To our knowledge, travel to the US has never been included as a potential risk factor for HA infection in Canadian epidemiologic analyses. The objective of this study was to use dynamic models to investigate the possible effects on hepatitis A incidence in Canada due to (1) implementing vaccination in the US, and (2) varying the volume of travel by Canadians to the US. Methods We developed and analyzed age-structured compartmental models for the transmission and vaccination of hepatitis A, for both Canada and the US. Models were parameterized using data on seroprevalence, case reporting, and travel patterns. The potential effect of hepatitis A prevalence in the US on hepatitis A prevalence in Canada was captured through a term representing infection of Canadians due to travel in the US. Results The model suggests that approximately 22% of HA cases in Canada in the mid 1990s may have been attributable to travel to the US. A universal vaccination programme that attained 70% coverage in young children in the US in the mid 1990s could have reduced Canadian incidence by 21% within 5 years. Conclusion Since not all necessary data were available to parameterize the model, the results should be considered exploratory. However, the analysis shows that, under plausible assumptions, the US may be more important for determining HA prevalence in Canada than is currently supposed. As international travel continues to grow, making vaccination policies ever more relevant to populations beyond a country's borders, such multi-country models will most likely come into wider use as predictive aids for policy development.

Photons are fundamental excitations of the electromagnetic field and can be captured in cavities. For a given cavity with a certain size, the fundamental mode has a fixed frequency {\it f} which gives the photons a specific "color". The cavity also has a typical lifetime $\tau$, which results in a finite linewidth $\delta${\it f}. If the size of the cavity is changed fast compared to $\tau$, and so that the frequency change $\Delta${\it f} $\gg \delta${\it f}, then it is possible to change the "color" of the captured photons. Here we demonstrate superconducting microwave cavities, with tunable effective lengths. The tuning is obtained by varying a Josephson inductance at one end of the cavity. We show data on four different samples and demonstrate tuning by several hundred linewidths in a time $\Delta t \ll \tau$. Working in the few photon limit, we show that photons stored in the cavity at one frequency will leak out from the cavity with the new frequency after the detuning. The characteristics of the measured devices make them suitable for different applications such as dynamic coupling of qubits and parametric amplification., Comment: 2nd International Workshop on Solid-State Quantum Computing, June 2008, Taipei, Taiwan

Infectious childhood diseases such as measles are characterized by recurrent outbreaks. Mathematicians have long used models in an effort to better understand and predict these recurrent outbreak patterns. This paper summarizes and comments upon those efforts, providing a historical outline of childhood disease models that have been developed since the start of the twentieth century. This paper also discusses the influence of data analysis techniques, such as spectral analysis, on the understanding and modelling of childhood disease dynamics.

Hepatitis A vaccines have been available for more than a decade. Because the burden of hepatitis A virus has fallen in developed countries, the appropriate role of vaccination programmes, especially universal vaccination strategies, remains unclear. Cost-effectiveness analysis is a useful method of relating the costs of vaccination to its benefits, and may inform policy. This article systematically reviews the evidence on the cost effectiveness of hepatitis A vaccination in varying populations, and explores the effects of methodological quality and key modelling issues on the cost-effectiveness ratios.Cost-effectiveness/cost-utility studies of hepatitis A vaccine were identified via a series of literature searches (MEDLINE, EMBASE, HSTAR and SSCI). Citations and full-text articles were reviewed independently by two reviewers. Reference searching, author searches and expert consultation ensured literature saturation. Incremental cost-effectiveness ratios (ICERs) were abstracted for base-case analyses, converted to $US, year 2005 values, and categorised to reflect various levels of cost effectiveness. Quality of reporting, methodological issues and key modelling issues were assessed using frameworks published in the literature.Thirty-one cost-effectiveness studies (including 12 cost-utility analyses) were included from full-text article review (n = 58) and citation screening (n = 570). These studies evaluated universal mass vaccination (n = 14), targeted vaccination (n = 17) and vaccination of susceptibles (i.e. individuals initially screened for antibody and, if susceptible, vaccinated) [n = 13]. For universal vaccination, 50% of the ICERs were$US20 000 per QALY or life-year gained. Analyses evaluating vaccination in children, particularly in high incidence areas, produced the most attractive ICERs. For targeted vaccination, cost effectiveness was highly dependent on the risk of infection.Incidence, vaccine cost and discount rate were the most influential parameters in sensitivity analyses. Overall, analyses that evaluated the combined hepatitis A/hepatitis B vaccine, adjusted incidence for under-reporting, included societal costs and that came from studies of higher methodological quality tended to have more attractive cost-effectiveness ratios. Methodological quality varied across studies. Major methodological flaws included inappropriate model type, comparator, incidence estimate and inclusion/exclusion of costs.

The emergence and rapid global spread of the severe acute respiratory syndrome (SARS) coronavirus in 2002-2003 prompted efforts by modelers to characterize SARS epidemiology and inform control policies. We overview and discuss models for emerging infectious diseases (EIDs), provide a critical survey of SARS modeling literature, and discuss promising future directions for research. We reconcile discrepancies between published estimates of the basic reproductive number R0 for SARS (a crucial epidemiologic parameter), discuss insights regarding SARS control measures that have emerged uniquely from a modeling approach, and argue that high priorities for future modeling of SARS and similar respiratory EIDs should include informing quarantine policy and better understanding the impact of population heterogeneity on transmission patterns.

Recent vaccine scares and sudden spikes in vaccine demand remind us that the effectiveness of mass vaccination programs is governed by the public perception of vaccination. Previous work has shown that the tendency of individuals to optimize self-interest can lead to vaccination levels that are suboptimal for a community. We use game theory to relate population-level demand for vaccines to decision-making by individuals with varied beliefs about the costs of infection and vaccination. In contrast to previous work proposing that universal vaccination is impossible in a game theoretic context, we show that optimal individual behavior can vary between universal vaccination and no vaccination, depending on the relative costs and benefits to individuals. By coupling game models and epidemic models, we demonstrate that the pursuit of self-interest often leads to stable dynamics but can lead to oscillations in vaccine uptake over time. The instability is exacerbated in populations that are more homogeneous with respect to their perceptions of vaccine and infection risks. This research illustrates the importance of applying temporal models to an inherently temporal situation, namely, the time evolution of vaccine coverage in an informed population with a voluntary vaccination policy.

The escape rate from the zero voltage state in a superconducting Josephson junction (JJ) is determined by the temperature, but it saturates at low temperature due to macroscopic quantum tunneling (MQT). Complications due to d-wave symmetry in a high temperature superconductor, like low energy quasiparticles and an unconventional current-phase relation, may influence the escape rate. We report, for the first time to our knowledge, the observation of MQT in a YBa(2)Cu(3)O(7-delta) grain boundary biepitaxial JJ. This proves that dissipation can be significantly reduced by a proper junction configuration, which is of significance for quantum coherence.

Voluntary vaccination policies for childhood diseases present parents with a subtle challenge: if a sufficient proportion of the population is already immune, either naturally or by vaccination, then even the slightest risk associated with vaccination will outweigh the risk from infection. As a result, individual self-interest might preclude complete eradication of a vaccine-preventable disease. We show that a formal game theoretical analysis of this problem leads to new insights that help to explain human decision-making with respect to vaccination. Increases in perceived vaccine risk will tend to induce larger declines in vaccine uptake for pathogens that cause more secondary infections (such as measles and pertussis). After a vaccine scare, even if perceived vaccine risk is greatly reduced, it will be relatively difficult to restore prescare vaccine coverage levels.

The invasion of new species and the spread of emergent infectious diseases in spatially structured populations has stimulated the study of explicit spatial models such as cellular automata, network models and lattice models. However, the analytic intractability of these models calls for the development of tractable mathematical approximations that can capture the dynamics of discrete, spatially-structured populations. Here we explore moment closure approximations for the invasion of an SIS epidemic on a regular lattice. We use moment closure methods to derive an expression for the basic reproductive number, R(0), in a lattice population. On lattices, R(0) should be bounded above by the number of neighbors per individual. However, we show that conventional pair approximations actually predict unbounded growth in R(0) with increasing transmission rates. To correct this problem, we propose an 'invasory' pair approximation which yields a relatively simple expression for R(0) that remains bounded above, and also predicts R(0) values from lattice model simulations more accurately than conventional pair and triple approximations. The invasory pair approximation is applicable to any spatial model, since it takes into account characteristics of invasions that are common to all spatially structured populations.

Background and Purpose: The comet assay offers the opportunity to measure the amount of DNA damage and the effectiveness of DNA repair in single cells. In a first part, experiments are presented comparing three different protocols of the comet assay technique with respect to the analysis of the induction of DNA damage after X-irradiation in isolated human lymphocytes and CHO cells. In a second part, the restriction enzyme AluI, an agent producing DNA double-strand breaks exclusively, was introduced into CHO cells by electroporation and the effects were analyzed using the different comet assay protocols. The experiments were carried out in order to test the assertion that comet assay techniques can measure different types of DNA damages at different pH conditions of lysis and electrophoresis. Material and Methods: Three different comet assay protocols were used for the analysis of DNA damage in lymphocytes and CHO cells. Results: The results clearly indicate that among the three protocols the modified comet assay technique used by the authors showed the highest sensitivity in the radiotherapy-relevant dose range between 0 and 2 Gy. All three protocols were capable of detecting an effect by AluI. This effect, however, was clearly different from radiation effects. Whereas after radiation exposure all cell nuclei show a dose-dependent increase in DNA content in the comet tail, most of the cell nuclei were unaffected by an AluI uptake. Nevertheless, there was an effect by AluI that could be detected in all three assay versions: between 5% and 15% of the nuclei showed clearly abnormal comet morphologies. Conclusion: Neither the strictly alkaline nor the strictly neutral comet assay is applicable in the radiation dose range of about 2 Gy. The restriction enzyme results show that other factors than just DNA strand breaks contribute to DNA migration into the tail of the comets.

The recent threat of bioterrorism has fueled debate on smallpox vaccination policy for the United States. Certain policy proposals call for voluntary mass vaccination; however, if individuals decide whether to vaccinate according to self-interest, the level of herd immunity achieved may differ from what is best for the population as a whole. We present a synthesis of game theory and epidemic modeling that formalizes this conflict between self-interest and group interest and shows that voluntary vaccination is unlikely to reach the group-optimal level. This shortfall results in a substantial increase in expected mortality after an attack.

We develop a moment closure approximation (MCA) to a network model of sexually transmitted disease (STD) spread through a steady/casual partnership network. MCA has been used previously to approximate static, regular lattices, whereas application to dynamic, irregular networks is a new endeavour, and application to sociologically-motivated network models has not been attempted. Our goals are 1). to investigate issues relating to the application of moment closure approximations to dynamic and irregular networks, and 2). to understand the impact of concurrent casual partnerships on STD transmission through a population of predominantly steady monogamous partnerships. We are able to derive a moment closure approximation for a dynamic irregular network representing sexual partnership dynamics, however, we are forced to use a triple approximation due to the large error of the standard pair approximation. This example underscores the importance of doing error analysis for moment closure approximations. We also find that a small number of casual partnerships drastically increases the prevalence and rate of spread of the epidemic. Finally, although the approximation is derived for a specific network model, we can recover approximations to a broad range of network models simply by varying model parameters which control the structure of the dynamic network. Thus our moment closure approximation is very flexible in the kinds of network models it can approximate.

There is currently little evidence to close the question of whether the type-specific HPV vaccines will cause increased prevalence of non-targeted, oncogenic types, a scenario known as ‘type replacement’. The abundance of hypotheses in the literature about how HPV types interact (facilitation, immune-mediated competition and independence) illustrates the perplexing nature of within-host HPV type interactions. In this talk, I will present analyses of within-host mathematical models that represent multiple HPV type co-infections and that are based on ecological theory. The results suggest that co-existence found at the patient level can arise even when types are interacting. I will also show how some common assumptions being made about HPV types are in conflict with current ecological theory. Finally, I will discuss some work I am currently conducting in Montpellier where we are fitting epidemiological models to multiple infection prevalence data. These kinds of collaborations between ecologists and HPV specialists will be essential to resolving why the vaccines may or may not cause type replacement for the benefit of future vaccination programs.

Background There is an urgent need to understand how the provision of information influences individual risk perception and how this in turn shapes the evolution of epidemics. Individuals are influenced by information in complex and unpredictable ways. Emerging infectious diseases, such as the recent swine flu epidemic, may be particular hotspots for a media-fueled rush to vaccination; conversely, seasonal diseases may receive little media attention, despite their high mortality rate, due to their perceived lack of newness. Methods We formulate a deterministic transmission and vaccination model to investigate the effects of media coverage on the transmission dynamics of influenza. The population is subdivided into different classes according to their disease status. The compartmental model includes the effect of media coverage on reporting the number of infections as well as the number of individuals successfully vaccinated. Results A threshold parameter (the basic reproductive ratio) is analytically derived and used to discuss the local stability of the disease-free steady state. The impact of costs that can be incurred, which include vaccination, education, implementation and campaigns on media coverage, are also investigated using optimal control theory. A simplified version of the model with pulse vaccination shows that the media can trigger a vaccinating panic if the vaccine is imperfect and simplified messages result in the vaccinated mixing with the infectives without regard to disease risk. Conclusions The effects of media on an outbreak are complex. Simplified understandings of disease epidemiology, propogated through media soundbites, may make the disease significantly worse.

Poly(ADP-ribose) polymerase (PARP) is a DNA binding zinc finger protein that catalyzes the transfer of ADP-ribose residues from NAD(+) to itself and different chromatin constituents, forming branched ADP-ribose polymers. The enzymatic activity of PARP is induced upon DNA damage and the PARP protein is cleaved during apoptosis, which suggested a role of PARP in DNA repair and DNA damage-induced cell death. We have generated transgenic mice that lack PARP activity in thymocytes owing to the targeted expression of a dominant negative form of PARP. In the presence of single-strand DNA breaks, the absence of PARP activity correlated with a strongly increased rate of apoptosis compared to cells with intact PARP activity. We found that blockage of PARP activity leads to a drastic increase of p53 expression and activity after DNA damage and correlates with an accelerated onset of Bax expression. DNA repair is almost completely blocked in PARP-deficient thymocytes regardless of p53 status. We found the same increased susceptibility to apoptosis in PARP null mice, a similar inhibition of DNA repair kinetics, and the same upregulation of p53 in response to DNA damage. Thus, based on two different experimental in vivo models, we identify a direct, p53-independent, functional connection between poly(ADP-ribosyl)ation and the DNA excision repair machinery. Furthermore, we propose a p53-dependent link between PARP activity and DNA damage-induced cell death.

One of the central goals of biological dosimetry must be the assessment of individual radiosensitivity. Physical dosimetry is only able to give the information on the energy deposited in the human body. This is not sufficient in radiation protection, because the response of the body to radiation dose is much more important than dose itself. This response strongly depends on the individual radiosensitivity, which is not determinable by physical means Several biological indicator systems have been introduced meanwhile from which answers are hoped to be obtained. One of the major factors affecting individual radiosensitivity is the repair capacity of a person. The comet assay offers the possibility to monitor repair at the level of single cells. Thus, one obtains not only information on the average repair capacity but also on the range. Individual cells are irradiated in vitro and checked for DNA damage either immediately or after various times at 37 °C. The speed of damage removal and the amount of residual damage after a fixed time gives the desired information on the repair capacity. Pronounced differences among people have been found up to now, whereas samples taken from one person at different times show remarkably similar results. Since the introduction of the CB technique, micronuclei in lymphocytes are successfully used as a biological dosemeter after radiation exposure. Their analysis is much faster and easier than that one of dicentrics. The comparatively poor sensitivity in the low dose range can be overcome by isolating sensitive subpopulations of lymphocytes. In addition or alternatively, centromere identification within the micronuclei improves sensitivity of the assay. Very promising is the fact that automatic scoring of micronuclei is feasible and can be done routinely meanwhile.

In the last decade the 'comet assay' or 'single cell gel electrophoresis assay' has been established as a sensitive method for the detection of DNA damage and the measurement of its recovery. The results published in the literature have often been obtained with different methods for comet structure measurement. In most cases these data are not comparable with each other. Even when using similar systems for the analysis, it is difficult to obtain matching data. This presentation will describe some technical aspects of our measurement equipment and evaluation software. It focuses on necessary experimental conditions to minimize errors in obtaining such data. The software developed here allows the rapid analysis of the microscopic samples (2 s per image). The image analysis was designed with respect to the morphological shapes of comet cells, which were investigated with a confocal laser microscope. The system is built with standard components which are commercially available. As a measure of the amount of DNA damage the ratio of fluorescence intensity was used inside the comet tail and the fluorescence intensity of the comet head. Other parameters such as DNA content, comet area, head radius, tail length and tail moment are also determined. The reproducibility of the system has been evaluated in several experiments over a period of 5 years.

We compared the amount of radiation-induced DNA damage and the extent of DNA repair in human melanoma cells (MeWo) using the 'comet assay' after neutron, boron neutron capture and X-irradiation. Using a colony-forming assay it was shown earlier that lethal effects in tumour cells treated with fast neutrons may be increased by the neutron capture reaction 10B(n, alpha)7Li. The effectiveness of boron neutron capture in killing tumour cells depends on the number of 10B atoms delivered to the tumour, the subcellular distribution of 10B and the thermal neutron fluence at the side of the tumour. Using the 'comet assay' the DNA damage of fast neutrons (mean energy 5.8 MeV) was shown to be significantly greater than for the same absorbed dose of X-rays. The presence of 600 ppm 10B (boric acid H5 10BO3) in the cell medium during irradiation with d(14) + Be neutrons in a phantom enhances the DNA damage by 20% compared with neutron irradiation alone. After DNA damage induction by neutrons and neutron capture of boron, the DNA repair capacity of the MeWo cells is significantly reduced in comparison with X-irradiation resulting in proportionally more residual DNA damage after 180 min of repair time.

It is well known that under specific conditions caffeine is able to enhance radiation risk of mammalian cells by a factor of approximately 1.5-2. Various mechanisms are discussed in the literature as possible explanations for this interaction. Inhibition of DNA repair plays a crucial role in the discussion, although direct evidence for this assumption is difficult to obtain. We used the "comet assay' in order to analyse the significance of repair inhibition by caffeine in the two-cell stage of mammalian gestation. Our data show that at the concentration necessary for increasing radiation risk (2 mM), caffeine effectively inhibits the restitution of radiation-damaged DNA.

In this work we present an agent-based model for the spread of tuberculosis where the individuals can be infected with either drug-susceptible or drug-resistant strains and can also receive a treatment. The dynamics of the model and the role of each one of the parameters are explained. The whole set of parameters is explored to check their importance in the numerical simulation results. The model captures the beneficial impact of the adequate treatment on the prevalence of tuberculosis. Nevertheless, depending on the treatment parameters range, it also captures the emergence of drug resistance. Drug resistance emergence is particularly likely to occur for parameter values corresponding to less efficacious treatment, as usually found in developing countries.

In this work we propose an alternative model of the spread of tuberculosis (TB) and the emergence of drug resistance due to the treatment with antibiotics. We implement the simulations by an agent-based model computational approach where the spatial structure is taken into account. The spread of tuberculosis occurs according to probabilities defined by the interactions among individuals. The model was validated by reproducing results already known from the literature in which different treatment regimes yield the emergence of drug resistance. The different patterns of TB spread can be visualized at any time of the system evolution. The implementation details as well as some results of this alternative approach are discussed.

An overview of the United States Space Shuttle Orbiter APU, which provides power to the Orbiter vehicle hydraulic system, is presented. Three complete APU systems, each with its own separate fuel system, supply power to three dedicated hydraulic systems. These in turn provide power to all Orbiter vehicle critical flight functions including launch, orbit, reentry, and landing. The basic APU logic diagram is presented. The APU includes a hydrazine-powered turbine that drives a hydraulic pump and various accessories through a high-speed gearbox. The APU also features a sophisticated thermal management system designed to ensure safe and reliable operation in the various launch, orbit, reentry, and landing environments.