Optimal control of the spatial allocation of COVID-19 vaccines: Italy as a case study

While campaigns of vaccination against SARS-CoV-2 are underway across the world, communities face the challenge of a fair and effective distribution of a limited supply of doses. Current vaccine allocation strategies are based on criteria such as age or risk. In the light of strong spatial heterogeneities in disease history and transmission, we explore spatial allocation strategies as a complement to existing approaches. Given the practical constraints and complex epidemiological dynamics, designing effective vaccination strategies at a country scale is an intricate task. We propose a novel optimal control framework to derive the best possible vaccine allocation for given disease transmission projections and constraints on vaccine supply and distribution logistics. As a proof-of-concept, we couple our framework with an existing spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We optimize the vaccine allocation on scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021. For each scenario, the optimal solution significantly outperforms alternative strategies that prioritize provinces based on incidence, population distribution, or prevalence of susceptibles. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities implies highly non-trivial prioritization strategies for effective vaccination campaigns. Our work demonstrates the potential of optimal control for complex and heterogeneous epidemiological landscapes at country, and possibly global, scales.     

Risk perception,risk management and safety assessment: What can governments do to increase public confidence in their vaccine system?

For decades vaccine program managers and governments have devoted many resources to addressing public vaccine concerns, vaccine risk perception, risk management and safety assessment. Despite ever growing evidence that vaccines are safe and effective, public concerns continue. Education and evidence based scientific messages have not ended concerns. How can governments and programs more effectively address the public’s vaccine concerns and increase confidence in the vaccine safety system? Vaccination hesitation has been attributed to concerns about vaccine safety, perceptions of high vaccine risks and low disease risk and consequences. Even when the public believes vaccines are important for protection many still have concerns about vaccine safety. This overview explores how heuristics affect public perception of vaccines and vaccine safety, how the public finds and uses vaccine information, and then proposes strategies for changes in the approach to vaccine safety communications. Facts and evidence confirming the safety of vaccines are not enough. Vaccine beliefs and behaviours must be shaped. This will require a shift in the what, when, how and why of vaccine risk and benefit communication content and practice. A change to a behavioural change strategy such as the WHO COMBI program that has been applied to disease eradication efforts is suggested.     

A game dynamic model for delayer strategies in vaccinating behaviour for pediatric infectious diseases

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.     

Basis for vaccine recommendations

Once a new vaccine has been granted its licensing, a public health expertise is needed in order to support the decision regarding its possible inclusion within the national immunisation schedule. This analysis, based on an assessment of the benefits/risks balance and costs/effectiveness ratio, is a multidisciplinary exercise. Largely based on epidemiological and immunological expertises, it also requires bio-mathematical and economical inputs, if the long term consequences of the vaccination are to be taken into account. Indeed, the main drivers of the decision are the burden of the disease, the characteristics of the vaccine in term of effectiveness and safety, the cost of the vaccination, the feasibility of the adjunction of the vaccine in the schedule, the social demand for this vaccination and the positive or negative indirect effects of a large vaccination on the epidemiology of the disease, in addition to the direct protective effect for vaccinated individuals. New vaccines are generally characterised by a more limited epidemiological impact than older vaccines, in a context of growing requirements from our society regarding drugs, and especially vaccines, safety. Both the real and perceived benefits/risks balances for the more recent vaccines appear questionable. The possibility of detrimental epidemiological consequences of either insufficient vaccination coverage or serotype (or serogroup) replacement is another factor that makes the decision regarding vaccination strategies increasingly complex.     

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.     

Vaccine demand driven by vaccine side effects: Dynamic implications for SIR diseases

For infections for which the perceived risk of serious disease is steadily low, the perceived risk of suffering some vaccine side effects might become the driving force of the vaccine demand. We investigate the dynamics of SIR infections in homogeneously mixing populations where the vaccine uptake is a decreasing function of the current (or past) incidence, or prevalence, of vaccine side effects. We define an appropriate model where vaccine side-effects are modelled as functions of the age since vaccination.It happens that the vaccine uptake follows its own dynamics independent of epidemiological variables. We show the conditions under which the vaccine uptake lands on a globally stable equilibrium, or steadily oscillates, and the implications of such behaviour for the dynamics of epidemiological variables. We finally report some unexpected scenarios caused by trends in vaccine side effects.     

Beyond Rational Decision-Making: Modelling the Influence of Cognitive Biases on the Dynamics of Vaccination Coverage

Background

Theoretical studies predict that it is not possible to eradicate a disease under voluntary vaccination because of the emergence of non-vaccinating “free-riders” when vaccination coverage increases. A central tenet of this approach is that human behaviour follows an economic model of rational choice. Yet, empirical studies reveal that vaccination decisions do not necessarily maximize individual self-interest. Here we investigate the dynamics of vaccination coverage using an approach that dispenses with payoff maximization and assumes that risk perception results from the interaction between epidemiology and cognitive biases.

Methods

We consider a behaviour-incidence model in which individuals perceive actual epidemiological risks as a function of their opinion of vaccination. As a result of confirmation bias, sceptical individuals (negative opinion) overestimate infection cost while pro-vaccines individuals (positive opinion) overestimate vaccination cost. We considered a feedback between individuals and their environment as individuals could change their opinion, and thus the way they perceive risks, as a function of both the epidemiology and the most common opinion in the population.

Results

For all parameter values investigated, the infection is never eradicated under voluntary vaccination. For moderately contagious diseases, oscillations in vaccination coverage emerge because individuals process epidemiological information differently depending on their opinion. Conformism does not generate oscillations but slows down the cultural response to epidemiological change.

Conclusion

Failure to eradicate vaccine preventable disease emerges from the model because of cognitive biases that maintain heterogeneity in how people perceive risks. Thus, assumptions of economic rationality and payoff maximization are not mandatory for predicting commonly observed dynamics of vaccination coverage. This model shows that alternative notions of rationality, such as that of ecological rationality whereby individuals use simple cognitive heuristics, offer promising new avenues for modelling vaccination behaviour.     

Monitoring vaccine safety during an influenza pandemic

In the event that a vaccine is available during an influenza pandemic, vaccine safety monitoring will occur as part of comprehensive public health surveillance of the vaccination campaign. Though inactivated influenza vaccines have been widely used in the United States and much is known about their safety profile, attention will need to be paid to both common self-limited adverse reactions and rarer, more serious events that may or may not be causally related to vaccination. The primary surveillance systems used to generate and test hypotheses about vaccine safety concerns are the Vaccine Adverse Event Reporting System (VAERS) and the Vaccine Safety Datalink (VSD), respectively. Examples of recent use of these systems to investigate influenza vaccine safety and enhancements planned for use during a pandemic are presented. Ethical issues that will need to be addressed as part of an overall vaccine safety response include risk communication and injury compensation. Advance planning and the use of available technologic solutions are needed to respond to the scientific and logistic challenges involved in safely implementing mass vaccination during a pandemic.     

Human Papillomavirus Infection: Knowledge, Attitudes, and Behaviors among Lesbian, Gay Men, and Bisexual in Italy

Background

This cross-sectional study assess knowledge, attitudes, and behavior towards the human papillomavirus (HPV) and the vaccination among a random sample of 1000 lesbian, gay men, and bisexual women and men.

Methods

A face-to-face interview sought information about: socio-demographic characteristics, knowledge about HPV infection, perception of risk towards HPV infection and/or cervical, anal, and oropharyngeal cancers, perception of the benefits of a vaccination to prevent cervical, anal, and oropharyngeal cancers, sexual behaviors, health-promoting behaviors, and willingness to receive the HPV vaccine.

Results

Only 60.6% had heard about the HPV infection and this knowledge was significantly higher in female, in those being a member of a homosexual association, in those having had the first sexual experience at a younger age, in those having received information about the HPV infection from physicians, and in those having no need of information about HPV infection. A higher perceived risk of contracting HPV infection has been observed in those younger, lesbian and gay men, who have heard of HPV infection and knew the risk factors and its related diseases, who have received information about HPV infection from physicians, and who need information about HPV infection. Only 1.7% have undergone HPV immunization and 73.3% professed intent to obtain it in the future. The significant predictors of the willingness to receive this vaccine were belief that the vaccination is useful, perception to be at higher risk of contracting HPV infection, and perception to be at higher risk of developing cervical, anal, and oropharyngeal cancers.

Conclusions

Information and interventions are strongly needed in order to overcome the lack of knowledge about HPV infection and its vaccination. Inclusion of boys in the national vaccination program and initiate a catch-up program for men who have sex with men up to 26 years may reduce their burden of HPV-related disease.     

Evolving public perceptions and stability in vaccine uptake

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 influence of social norms on the dynamics of vaccinating behaviour for paediatric infectious diseases

Mathematical models that couple disease dynamics and vaccinating behaviour often assume that the incentive to vaccinate disappears if disease prevalence is zero. Hence, they predict that vaccine refusal should be the rule, and elimination should be difficult or impossible. In reality, countries with non-mandatory vaccination policies have usually been able to maintain elimination or very low incidence of paediatric infectious diseases for long periods of time. Here, we show that including injunctive social norms can reconcile such behaviour-incidence models to observations. Adding social norms to a coupled behaviour-incidence model enables the model to better explain pertussis vaccine uptake and disease dynamics in the UK from 1967 to 2010, in both the vaccine-scare years and the years of high vaccine coverage. The model also illustrates how a vaccine scare can perpetuate suboptimal vaccine coverage long after perceived risk has returned to baseline, pre-vaccine-scare levels. However, at other model parameter values, social norms can perpetuate depressed vaccine coverage during a vaccine scare well beyond the time when the population''s baseline vaccine risk perception returns to pre-scare levels. Social norms can strongly suppress vaccine uptake despite frequent outbreaks, as observed in some small communities. Significant portions of the parameter space also exhibit bistability, meaning long-term outcomes depend on the initial conditions. Depending on the context, social norms can either support or hinder immunization goals.     

Predicting the impact of a nonsterilizing vaccine against human immunodeficiency virus

Studies of human immunodeficiency virus (HIV) vaccines in animal models suggest that it is difficult to induce complete protection from infection (sterilizing immunity) but that it is possible to reduce the viral load and to slow or prevent disease progression following infection. We have developed an age-structured epidemiological model of the effects of a disease-modifying HIV vaccine that incorporates the intrahost dynamics of infection, a transmission rate and host mortality that depend on the viral load, the possible evolution and transmission of vaccine escape mutant viruses, a finite duration of vaccine protection, and possible changes in sexual behavior. Using this model, we investigated the long-term outcome of a disease-modifying vaccine and utilized uncertainty analysis to quantify the effects of our lack of precise knowledge of various parameters. Our results suggest that the extent of viral load reduction in vaccinated infected individuals (compared to unvaccinated individuals) is the key predictor of vaccine efficacy. Reductions in viral load of about 1 log(10) copies ml(-1) would be sufficient to significantly reduce HIV-associated mortality in the first 20 years after the introduction of vaccination. Changes in sexual risk behavior also had a strong impact on the epidemic outcome. The impact of vaccination is dependent on the population in which it is used, with disease-modifying vaccines predicted to have the most impact in areas of low prevalence and rapid epidemic growth. Surprisingly, the extent to which vaccination alters disease progression, the rate of generation of escape mutants, and the transmission of escape mutants are predicted to have only a weak impact on the epidemic outcome over the first 25 years after the introduction of a vaccine.     

Multiple attractors in the response to a vaccination program

Though it is well known that multiple attractors may co-exist in the SEIR (susceptible/exposed/infective/recovered) epidemic model with vital dynamics and seasonally forced oscillations in transmission, the epidemiological significance of multiple attractors has been a subject of debate. I show that the co-existence of attractors is relevant in using the model to study the dynamics of the introduction of a vaccination program into a stable epidemic cycle. Responses to the program may include more than one attractor. The exact timing of the introduction of the program relative to the original epidemic cycle is critical in determining which attractor appears in the response. Analysis of this simple model suggests that the role of multiple attractors in the response to vaccination should be examined in more realistic epidemiological models.     

The impact of vaccine side effects on the natural history of immunization programmes: an imitation-game approach

When the incidence and prevalence of most common vaccine preventable childhood infectious diseases are constantly low, as is the case in many industrialized countries, the incidence of vaccine-associated side effects might become a key determinant in vaccine demand. We study an SIR transmission model with dynamic vaccine demand based on an imitation mechanism where the perceived risk of vaccination is modelled as a function of the incidence of vaccine side effects. The model shows some important differences compared to previous game dynamic models of vaccination, and allows noteworthy inferences as regards both the past and future lifetime of vaccination programmes. In particular it is suggested that a huge disproportion between the perceived risk of disease and vaccination is necessary in order to achieve high coverages. This disproportion is further increased in highly industrialised countries. Such considerations represent serious challenges for future vaccination programmes.     

Healthy Bodies,Toxic Medicines: College Students and the Rhetorics of Flu Vaccination

This article examines flu vaccination beliefs and practices produced during a survey of undergraduate students in Spring 2012 (IRB#10-732). This research uses the methods of rhetorical analysis — or the study of persuasive features and arguments used in language — to examine statements respondents made regarding flu and flu vaccine. In these responses, students generated unique categories of arguments about the perceived dangers of flu vaccination, including the assertion that vaccines cause disease (including illnesses and conditions other than flu), that vaccines are toxic medicines, and that vaccines carry unknown, population-wide risks that are inadequately acknowledged. This study provides insight into vaccination beliefs and rationales among a population at risk of flu (college students) and suggests that further study of this population may yield important keys to addressing flu vaccine concerns as expressed by college students. Rhetorical analysis also offers a useful set of methods to understanding vaccination beliefs and practices, adding to existing methods of study and analysis of vaccination practices and beliefs in medicine and public health.     

Balancing Evidence and Uncertainty when Considering Rubella Vaccine Introduction

Background

Despite a safe and effective vaccine, rubella vaccination programs with inadequate coverage can raise the average age of rubella infection; thereby increasing rubella cases among pregnant women and the resulting congenital rubella syndrome (CRS) in their newborns. The vaccination coverage necessary to reduce CRS depends on the birthrate in a country and the reproductive number, R₀, a measure of how efficiently a disease transmits. While the birthrate within a country can be known with some accuracy, R₀ varies between settings and can be difficult to measure. Here we aim to provide guidance on the safe introduction of rubella vaccine into countries in the face of substantial uncertainty in R₀.

Methods

We estimated the distribution of R₀ in African countries based on the age distribution of rubella infection using Bayesian hierarchical models. We developed an age specific model of rubella transmission to predict the level of R₀ that would result in an increase in CRS burden for specific birth rates and coverage levels. Combining these results, we summarize the safety of introducing rubella vaccine across demographic and coverage contexts.

Findings

The median R₀ of rubella in the African region is 5.2, with 90% of countries expected to have an R₀ between 4.0 and 6.7. Overall, we predict that countries maintaining routine vaccination coverage of 80% or higher are can be confident in seeing a reduction in CRS over a 30 year time horizon.

Conclusions

Under realistic assumptions about human contact, our results suggest that even in low birth rate settings high vaccine coverage must be maintained to avoid an increase in CRS. These results lend further support to the WHO recommendation that countries reach 80% coverage for measles vaccine before introducing rubella vaccination, and highlight the importance of maintaining high levels of vaccination coverage once the vaccine is introduced.     

Dynamics of Vaccination Strategies via Projected Dynamical Systems

Previous game theoretical analyses of vaccinating behaviour have underscored the strategic interaction between individuals attempting to maximise their health states, in situations where an individual's health state depends upon the vaccination decisions of others due to the presence of herd immunity. Here, we extend such analyses by applying the theories of variational inequalities (VI) and projected dynamical systems (PDS) to vaccination games. A PDS provides a dynamics that gives the conditions for existence, uniqueness and stability properties of Nash equilibria. In this paper, it is used to analyse the dynamics of vaccinating behaviour in a population consisting of distinct social groups, where each group has different perceptions of vaccine and disease risks. In particular, we study populations with two groups, where the size of one group is strictly larger than the size of the other group (a majority/minority population). We find that a population with a vaccine-inclined majority group and a vaccine-averse minority group exhibits higher average vaccine coverage than the corresponding homogeneous population, when the vaccine is perceived as being risky relative to the disease. Our model also reproduces a feature of real populations: In certain parameter regimes, it is possible to have a majority group adopting high vaccination rates and simultaneously a vaccine-averse minority group adopting low vaccination rates. Moreover, we find that minority groups will tend to exhibit more extreme changes in vaccinating behaviour for a given change in risk perception, in comparison to majority groups. These results emphasise the important role played by social heterogeneity in vaccination behaviour, while also highlighting the valuable role that can be played by PDS and VI in mathematical epidemiology.     

Responding to Vaccine Safety Signals during Pandemic Influenza: A Modeling Study

Background

Managing emerging vaccine safety signals during an influenza pandemic is challenging. Federal regulators must balance vaccine risks against benefits while maintaining public confidence in the public health system.

Methods

We developed a multi-criteria decision analysis model to explore regulatory decision-making in the context of emerging vaccine safety signals during a pandemic. We simulated vaccine safety surveillance system capabilities and used an age-structured compartmental model to develop potential pandemic scenarios. We used an expert-derived multi-attribute utility function to evaluate potential regulatory responses by combining four outcome measures into a single measure of interest: 1) expected vaccination benefit from averted influenza; 2) expected vaccination risk from vaccine-associated febrile seizures; 3) expected vaccination risk from vaccine-associated Guillain-Barre Syndrome; and 4) expected change in vaccine-seeking behavior in future influenza seasons.

Results

Over multiple scenarios, risk communication, with or without suspension of vaccination of high-risk persons, were the consistently preferred regulatory responses over no action or general suspension when safety signals were detected during a pandemic influenza. On average, the expert panel valued near-term vaccine-related outcomes relative to long-term projected outcomes by 3∶1. However, when decision-makers had minimal ability to influence near-term outcomes, the response was selected primarily by projected impacts on future vaccine-seeking behavior.

Conclusions

The selected regulatory response depends on how quickly a vaccine safety signal is identified relative to the peak of the pandemic and the initiation of vaccination. Our analysis suggested two areas for future investment: efforts to improve the size and timeliness of the surveillance system and behavioral research to understand changes in vaccine-seeking behavior.     

Theoretical Assessment of Public Health Impact of Imperfect Prophylactic HIV-1 Vaccines with Therapeutic Benefits

This paper presents a number of deterministic models for theoretically assessing the potential impact of an imperfect prophylactic HIV-1 vaccine that has five biological modes of action, namely “take,” “degree,” “duration,” “infectiousness,” and “progression,” and can lead to increased risky behavior. The models, which are of the form of systems of nonlinear differential equations, are constructed via a progressive refinement of a basic model to incorporate more realistic features of HIV pathogenesis and epidemiology such as staged progression, differential infectivity, and HIV transmission by AIDS patients. The models are analyzed to gain insights into the qualitative features of the associated equilibria. This allows the determination of important epidemiological thresholds such as the basic reproduction numbers and a measure for vaccine impact or efficacy. The key findings of the study include the following (i) if the vaccinated reproduction number is greater than unity, each of the models considered has a locally unstable disease-free equilibrium and a unique endemic equilibrium; (ii) owing to the vaccine-induced backward bifurcation in these models, the classical epidemiological requirement of vaccinated reproduction number being less than unity does not guarantee disease elimination in these models; (iii) an imperfect vaccine will reduce HIV prevalence and mortality if the reproduction number for a wholly vaccinated population is less than the corresponding reproduction number in the absence of vaccination; (iv) the expressions for the vaccine characteristics of the refined models take the same general structure as those of the basic model.     

The co-circulation of two infectious diseases and the impact of vaccination against one of them

An epidemiological model based on probabilistic cellular automaton is proposed to investigate the dynamics of two co-circulating infections. In the model, one of these two diseases compromises the immune response to future infections; however, there is vaccine against this immunosuppressive disease. The goal is to evaluate the impact of the vaccination coverage on the prevalence and on the cumulative deaths associated with both contagious diseases. The performed numerical simulations highlight the importance of vaccination on decreasing morbidity and mortality. The results are discussed from a public health standpoint, by taking into account outbreaks of measles and COVID-19.