Chris T. Bauch

Statistical physics of vaccination

Historically, infectious diseases caused considerable damage to human societies, and they continue to do so today. To help reduce their impact, mathematical models of disease transmission have been studied to help understand disease dynamics and inform prevention strategies. Vaccination - one of the most important preventive measures of modern times - is of great interest both theoretically and empirically. And in contrast to traditional approaches, recent research increasingly explores the pivotal implications of individual behavior and heterogeneous contact patterns in populations. Our report reviews the developmental arc of theoretical epidemiology with emphasis on vaccination, as it led from classical models assuming homogeneously mixing (mean-field) populations and ignoring human behavior, to recent models that account for behavioral feedback and/or population spatial/social structure. Many of the methods used originated in statistical physics, such as lattice and network models, and their associated analytical frameworks. Similarly, the feedback loop between vaccinating behavior and disease propagation forms a coupled nonlinear system with analogs in physics. We also review the new paradigm of digital epidemiology, wherein sources of digital data such as online social media are mined for high-resolution information on epidemiologically relevant individual behavior. Armed with the tools and concepts of statistical physics, and further assisted by new sources of digital data, models that capture nonlinear interactions between behavior and disease dynamics offer a novel way of modeling real-world phenomena, and can help improve health outcomes. We conclude the review by discussing open problems in the field and promising directions for future research.

Group interest versus self-interest in smallpox vaccination policy

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.

Comparing influenza vaccine efficacy against mismatched and matched strains: a systematic review and meta-analysis

BackgroundInfluenza vaccines are most effective when the antigens in the vaccine match those of circulating strains. However, antigens contained in the vaccines do not always match circulating strains. In the present work we aimed to examine the vaccine efficacy (VE) afforded by influenza vaccines when they are not well matched to circulating strains.MethodsWe identified randomized clinical trials (RCTs) through MEDLINE, EMBASE, the Cochrane Library, and references of included RCTs. RCTs reporting laboratory-confirmed influenza among healthy participants vaccinated with antigens of matching and non-matching influenza strains were included. Two independent reviewers screened citations/full-text articles, abstracted data, and appraised risk of bias. Conflicts were resolved by discussion. A random effects meta-analysis was conducted. VE was calculated using the following formula: (1 - relative risk × 100%).ResultsWe included 34 RCTs, providing data on 47 influenza seasons and 94,821 participants. The live-attenuated influenza vaccine (LAIV) showed significant protection against mismatched (six RCTs, VE 54%, 95% confidence interval (CI) 28% to 71%) and matched (seven RCTs, VE 83%, 95% CI 75% to 88%) influenza strains among children aged 6 to 36 months. Differences were observed between the point estimates for mismatched influenza A (five RCTs, VE 75%, 95% CI 41% to 90%) and mismatched influenza B (five RCTs, VE 42%, 95% CI 22% to 56%) estimates among children aged 6 to 36 months. The trivalent inactivated vaccine (TIV) also afforded significant protection against mismatched (nine RCTs, VE 52%, 95% CI 37% to 63%) and matched (eight RCTs, VE 65%, 95% CI 54% to 73%) influenza strains among adults. Numerical differences were observed between the point estimates for mismatched influenza A (five RCTs, VE 64%, 95% CI 23% to 82%) and mismatched influenza B (eight RCTs, VE 52%, 95% CI 19% to 72%) estimates among adults. Statistical heterogeneity was low (I2 <50%) across all meta-analyses, except for the LAIV meta-analyses among children (I2 = 79%).ConclusionsThe TIV and LAIV vaccines can provide cross protection against non-matching circulating strains. The point estimates for VE were different for matching versus non-matching strains, with overlapping CIs.

Imitation dynamics predict vaccinating behaviour

There exists an interplay between vaccine coverage, disease prevalence and the vaccinating behaviour of individuals. Moreover, because of herd immunity, there is also a strategic interaction between individuals when they are deciding whether or not to vaccinate, because the probability that an individual becomes infected depends upon how many other individuals are vaccinated. To understand this potentially complex interplay, a game dynamic model is developed in which individuals adopt strategies according to an imitation dynamic (a learning process), and base vaccination decisions on disease prevalence and perceived risks of vaccines and disease. The model predicts that oscillations in vaccine uptake are more likely in populations where individuals imitate others more readily or where vaccinating behaviour is more sensitive to changes in disease prevalence. Oscillations are also more likely when the perceived risk of vaccines is high. The model reproduces salient features of the time evolution of vaccine uptake and disease prevalence during the whole-cell pertussis vaccine scare in England and Wales during the 1970s. This suggests that using game theoretical models to predict, and even manage, the population dynamics of vaccinating behaviour may be feasible.

Coupled disease-behavior dynamics on complex networks: A review.

Abstract It is increasingly recognized that a key component of successful infection control efforts is understanding the complex, two-way interaction between disease dynamics and human behavioral and social dynamics. Human behavior such as contact precautions and social distancing clearly influence disease prevalence, but disease prevalence can in turn alter human behavior, forming a coupled, nonlinear system. Moreover, in many cases, the spatial structure of the population cannot be ignored, such that social and behavioral processes and/or transmission of infection must be represented with complex networks. Research on studying coupled disease–behavior dynamics in complex networks in particular is growing rapidly, and frequently makes use of analysis methods and concepts from statistical physics. Here, we review some of the growing literature in this area. We contrast network-based approaches to homogeneous-mixing approaches, point out how their predictions differ, and describe the rich and often surprising behavior of disease–behavior dynamics on complex networks, and compare them to processes in statistical physics. We discuss how these models can capture the dynamics that characterize many real-world scenarios, thereby suggesting ways that policy makers can better design effective prevention strategies. We also describe the growing sources of digital data that are facilitating research in this area. Finally, we suggest pitfalls which might be faced by researchers in the field, and we suggest several ways in which the field could move forward in the coming years.

Modelling mitigation strategies for pandemic (H1N1) 2009

Background: The 2009 influenza A (H1N1) pandemic has required decision-makers to act in the face of substantial uncertainties. Simulation models can be used to project the effectiveness of mitigation strategies, but the choice of the best scenario may change depending on model assumptions and uncertainties. Methods: We developed a simulation model of a pandemic (H1N1) 2009 outbreak in a structured population using demographic data from a medium-sized city in Ontario and epidemiologic influenza pandemic data. We projected the attack rate under different combinations of vaccination, school closure and antiviral drug strategies (with corresponding “trigger” conditions). To assess the impact of epidemiologic and program uncertainty, we used “combinatorial uncertainty analysis.” This permitted us to identify the general features of public health response programs that resulted in the lowest attack rates. Results: Delays in vaccination of 30 days or more reduced the effectiveness of vaccination in lowering the attack rate. However, pre-existing immunity in 15% or more of the population kept the attack rates low, even if the whole population was not vaccinated or vaccination was delayed. School closure was effective in reducing the attack rate, especially if applied early in the outbreak, but this is not necessary if vaccine is available early or if pre-existing immunity is strong. Interpretation: Early action, especially rapid vaccine deployment, is disproportionately effective in reducing the attack rate. This finding is particularly important given the early appearance of pandemic (H1N1) 2009 in many schools in September 2009.

Social Contact Networks and Disease Eradicability under Voluntary Vaccination

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell pertussis vaccine, that are consistent with this theory. On the other hand, smallpox was globally eradicated by 1980 despite voluntary vaccination policies in many jurisdictions. Previous modeling studies of the interplay between disease dynamics and individual vaccinating behavior have assumed that infection is transmitted in a homogeneously mixing population. By comparison, here we simulate transmission of a vaccine-preventable SEIR infection through a random, static contact network. Individuals choose whether to vaccinate based on infection risks from neighbors, and based on vaccine risks. When neighborhood size is small, rational vaccinating behavior results in rapid containment of the infection through voluntary ring vaccination. As neighborhood size increases (while the average force of infection is held constant), a threshold is reached beyond which the infection can break through partially vaccinated rings, percolating through the whole population and resulting in considerable epidemic final sizes and a large number vaccinated. The former outcome represents convergence between individually and socially optimal outcomes, whereas the latter represents their divergence, as observed in most models of individual vaccinating behavior that assume homogeneous mixing. Similar effects are observed in an extended model using smallpox-specific natural history and transmissibility assumptions. This work illustrates the significant qualitative differences between behavior–infection dynamics in discrete contact-structured populations versus continuous unstructured populations. This work also shows how disease eradicability in populations where voluntary vaccination is the primary control mechanism may depend partly on whether the disease is transmissible only to a few close social contacts or to a larger subset of the population.

Transients and attractors in epidemics

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Stray dog population demographics in Jodhpur, India following a population control/rabies vaccination program.

Animal Birth Control (ABC) is a program by which stray dogs are sterilized and vaccinated against rabies with the aim of controlling both dog population size and rabies. Population size and demographics of stray dogs were measured before and after implementation of an ABC program in Jodhpur, India. Dog population size declined (p<0.05) in three of five areas surveyed, showed a decreasing trend (p>0.05) in 1 area, and remained stable in 1 area between 2005 and 2007. By 2007, 61.8-86.5% of the free-roaming dog population was surgically sterilized and vaccinated for rabies in the areas surveyed. In March-May, 2007, adults comprised 80-96% of the free-roaming dog population, while subadults and puppies comprised 0-18 and 0-4%, respectively. The male:female ratio among dogs>3 months old was 1.4:1. A population demographic model predicted that at the current level of sterilization/rabies vaccination, vaccination coverage would remain above 70%, and the dog population would decrease by 69% reaching stability after 13-18 years. A surgical sterilization coverage under 40% would maintain the dog population at current levels.

The impact of media coverage on the transmission dynamics of human influenza

BackgroundThere 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.MethodsWe 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.ResultsA 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.ConclusionsThe effects of media on an outbreak are complex. Simplified understandings of disease epidemiology, propogated through media soundbites, may make the disease significantly worse.