Assessing the cost-effectiveness of HPV vaccination strategies for adolescent girls and boys in the UK.

BACKGROUND: Human papillomavirus (HPV) is the most widespread sexually transmitted infection worldwide. It causes several health consequences, in particular accounting for the majority of cervical cancer cases in women. In the United Kingdom, a vaccination campaign targeting 12-year-old girls started in 2008; this campaign has been successful, with high uptake and reduced HPV prevalence observed in vaccinated cohorts. Recently, attention has focused on vaccinating both sexes, due to HPV-related diseases in males (particularly for high-risk men who have sex with men) and an equity argument over equalising levels of protection. METHODS: We constructed an epidemiological model for HPV transmission in the UK, accounting for nine of the most common HPV strains. We complemented this with an economic model to determine the likely health outcomes (healthcare costs and quality-adjusted life years) for individuals from the epidemiological model. We then tested vaccination with the three HPV vaccines currently available, vaccinating either girls alone or both sexes. For each strategy we calculated the threshold price per vaccine dose, i.e. the maximum amount paid for the added health benefits of vaccination to be worth the cost of each vaccine dose. We calculated results at 3.5% discounting, and also 1.5%, to consider the long-term health effects of HPV infection. RESULTS: At 3.5% discounting, continuing to vaccinate girls remains highly cost-effective compared to halting vaccination, with threshold dose prices of £56-£108. Vaccination of girls and boys is less cost-effective (£25-£53). Compared to vaccinating girls only, adding boys to the programme is not cost-effective, with negative threshold prices (-£6 to -£3) due to the costs of administration. All threshold prices increase when using 1.5% discounting, and adding boys becomes cost-effective (£36-£47). These results are contingent on the UK's high vaccine uptake; for lower uptake rates, adding boys (at the same uptake rate) becomes more cost effective. CONCLUSIONS: Vaccinating girls is extremely cost-effective compared with no vaccination, vaccinating both sexes is less so. Adding boys to an already successful girls-only programme has a low cost-effectiveness, as males have high protection through herd immunity. If future health effects are weighted more heavily, threshold prices increase and vaccination becomes cost-effective.

The impact of Covid-19 vaccination in Aotearoa New Zealand: A modelling study.

Aotearoa New Zealand implemented a Covid-19 elimination strategy in 2020 and 2021, which enabled a large majority of the population to be vaccinated before being exposed to the virus. This strategy delivered one of the lowest pandemic mortality rates in the world. However, quantitative estimates of the population-level health benefits of vaccination are lacking. Here, we use a validated mathematical model of Covid-19 in New Zealand to investigate counterfactual scenarios with differing levels of vaccine coverage in different age and ethnicity groups. The model builds on earlier research by adding age- and time-dependent case ascertainment, the effect of antiviral medications, improved hospitalisation rate estimates, and the impact of relaxing control measures. The model was used for scenario analysis and policy advice for the New Zealand Government in 2022 and 2023. We compare the number of Covid-19 hospitalisations, deaths, and years of life lost in each counterfactual scenario to a baseline scenario that is fitted to epidemiological data between January 2022 and June 2023. Our results estimate that vaccines saved 6650 (95% credible interval [4424, 10180]) lives, and prevented 74500 [51000, 115400] years of life lost and 45100 [34400, 55600] hospitalisations during this 18-month period. Making the same comparison before the benefit of antiviral medications is accounted for, the estimated number of lives saved by vaccines increases to 7604 [5080, 11942]. Due to inequities in the vaccine rollout, vaccination rates among Maori were lower than in people of European ethnicity. Our results show that, if vaccination rates had been equitable, an estimated 11%-26% of the 292 Maori Covid-19 deaths that were recorded in this time period could have been prevented. We conclude that Covid-19 vaccination greatly reduced health burden in New Zealand and that equity needs to be a key focus of future vaccination programmes.

Modelling the impact of the Omicron BA.5 subvariant in New Zealand.

New Zealand experienced a wave of the Omicron variant of SARS-CoV-2 in early 2022, which occurred against a backdrop of high two-dose vaccination rates, ongoing roll-out of boosters and paediatric doses, and negligible levels of prior infection. New Omicron subvariants have subsequently emerged with a significant growth advantage over the previously dominant BA.2. We investigated a mathematical model that included waning of vaccine-derived and infection-derived immunity, as well as the impact of the BA.5 subvariant which began spreading in New Zealand in May 2022. The model was used to provide scenarios to the New Zealand Government with differing levels of BA.5 growth advantage, helping to inform policy response and healthcare system preparedness during the winter period. In all scenarios investigated, the projected peak in new infections during the BA.5 wave was smaller than in the first Omicron wave in March 2022. However, results indicated that the peak hospital occupancy was likely to be higher than in March 2022, primarily due to a shift in the age distribution of infections to older groups. We compare model results with subsequent epidemiological data and show that the model provided a good projection of cases, hospitalizations and deaths during the BA.5 wave.

A stability analysis of the power-law steady state of marine size spectra.

This paper investigates the stability of the power-law steady state often observed in marine ecosystems. Three dynamical systems are considered, describing the abundance of organisms as a function of body mass and time: a "jump-growth" equation, a first order approximation which is the widely used McKendrick-von Foerster equation, and a second order approximation which is the McKendrick-von Foerster equation with a diffusion term. All of these yield a power-law steady state. We derive, for the first time, the eigenvalue spectrum for the linearised evolution operator, under certain constraints on the parameters. This provides new knowledge of the stability properties of the power-law steady state. It is shown analytically that the steady state of the McKendrick-von Foerster equation without the diffusion term is always unstable. Furthermore, numerical plots show that eigenvalue spectra of the McKendrick-von Foerster equation with diffusion give a good approximation to those of the jump-growth equation. The steady state is more likely to be stable with a low preferred predator:prey mass ratio, a large diet breadth and a high feeding efficiency. The effects of demographic stochasticity are also investigated and it is concluded that these are likely to be small in real systems.

From data compilation to model validation: comparing three ecosystem models of the Tasman and Golden Bays, New Zealand.

The Tasman and Golden Bays (TBGB) are a semi-enclosed embayment system in New Zealand that supports numerous commercial and recreational activities. We present three ecosystem models of the TBGB ecosystem with varying levels of complexity, aimed at contributing as tools to aid in understanding this ecosystem and its responses to anthropogenic and natural pressures. We describe the process of data compilation through to model validation and analyse the importance of knowledge gaps with respect to model dynamics and results. We compare responses in all three models to historical fishing, and analyse similarities and differences in the dynamics of the three models. We assessed the most complex of the models against initialisation uncertainty and sensitivity to oceanographic variability and found it most sensitive to the latter. We recommend that scenarios relating to ecosystem dynamics of the TBGB ecosystem include sensitivities, especially oceanographic uncertainty, and compare responses across all three models where it is possible to do so.

Developing a Framework for Public Involvement in Mathematical and Economic Modelling: Bringing New Dynamism to Vaccination Policy Recommendations.

OBJECTIVES: The Mathematical and Economic Modelling for Vaccination and Immunisation Evaluation (MEMVIE) programme aimed to explore, capture and support the potential contribution of the public to mathematical and economic modelling, in order to identify the values that underpin public involvement (PI) in modelling and co-produce a framework that identifies the nature and type of PI in modelling and supports its implementation. METHODS: We established a PI Reference Group, who worked collaboratively with the academic contributors to create a deliberative knowledge space, which valued different forms of knowledge, expertise and evidence. Together, we explored the key steps of mathematical and economic methods in 21 meetings during 2015-2020. These deliberations generated rich discussion, through which we identified potential points of public contribution and the values that underpin PI in modelling. We iteratively developed a framework to guide future practice of PI in modelling. RESULTS: We present the MEMVIE Public Involvement Framework in two forms: a short form to summarise key elements, and a long form framework to provide a detailed description of each potential type of public contribution at each stage of the modelling process. At a macro level, the public can contribute to reviewing context, reviewing relevance, assessing data and justifying model choice, troubleshooting, and interpreting and reviewing outcomes and decision making. The underpinning values that drive involvement include the public contributing to the validity of the model, potentially enhancing its relevance, utility and transparency through diverse inputs, and enhancing the credibility, consistency and continuous development through scrutiny, in addition to contextualising the model within a wider societal view. DISCUSSION AND CONCLUSION: PI in modelling is in its infancy. The MEMVIE Framework is the first attempt to identify potential points of collaborative public contribution to modelling, but it requires further evaluation and refinement that we are undertaking in a subsequent study.

A jump-growth model for predator-prey dynamics: derivation and application to marine ecosystems.

This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master equation, we derive a deterministic equation for the macroscopic dynamics, which we call the deterministic jump-growth equation, and a linear Fokker-Planck equation for the stochastic fluctuations. The McKendrick-von Foerster equation, used in previous studies, is shown to be a first-order approximation, appropriate in equilibrium systems where predators are much larger than their prey. The model has a power-law steady state consistent with the approximate constancy of mass density in logarithmic intervals of body mass often observed in marine ecosystems. The behaviours of the stochastic process, the deterministic jump-growth equation, and the McKendrick-von Foerster equation are compared using numerical methods. The numerical analysis shows two classes of attractors: steady states and travelling waves.

Spatio-temporal modelling of Leishmania infantum infection among domestic dogs: a simulation study and sensitivity analysis applied to rural Brazil.

BACKGROUND: The parasite Leishmania infantum causes zoonotic visceral leishmaniasis (VL), a potentially fatal vector-borne disease of canids and humans. Zoonotic VL poses a significant risk to public health, with regions of Latin America being particularly afflicted by the disease. Leishmania infantum parasites are transmitted between hosts during blood-feeding by infected female phlebotomine sand flies. With a principal reservoir host of L. infantum being domestic dogs, limiting prevalence in this reservoir may result in a reduced risk of infection for the human population. To this end, a primary focus of research efforts has been to understand disease transmission dynamics among dogs. One way this can be achieved is through the use of mathematical models. METHODS: We have developed a stochastic, spatial, individual-based mechanistic model of L. infantum transmission in domestic dogs. The model framework was applied to a rural Brazilian village setting with parameter values informed by fieldwork and laboratory data. To ensure household and sand fly populations were realistic, we statistically fitted distributions for these entities to existing survey data. To identify the model parameters of highest importance, we performed a stochastic parameter sensitivity analysis of the prevalence of infection among dogs to the model parameters. RESULTS: We computed parametric distributions for the number of humans and animals per household and a non-parametric temporal profile for sand fly abundance. The stochastic parameter sensitivity analysis determined prevalence of L. infantum infection in dogs to be most strongly affected by the sand fly associated parameters and the proportion of immigrant dogs already infected with L. infantum parasites. CONCLUSIONS: Establishing the model parameters with the highest sensitivity of average L. infantum infection prevalence in dogs to their variation helps motivate future data collection efforts focusing on these elements. Moreover, the proposed mechanistic modelling framework provides a foundation that can be expanded to explore spatial patterns of zoonotic VL in humans and to assess spatially targeted interventions.

Capturing sexual contact patterns in modelling the spread of sexually transmitted infections: Evidence using Natsal-3.

BACKGROUND: Understanding the spread of sexually transmitted infections (STIs) in a population is of great importance to the planning and delivery of health services globally. The worldwide rise of HIV since the 1980's, and the recent increase in common STIs (including HPV and Chlamydia) in many countries, means that there is an urgent need to understand transmission dynamics in order to better predict the spread of such infections in the population. Unlike many other infections which can be captured by assumptions of random mixing, STI transmission is intimately linked to the number and pattern of sexual contacts. In fact, it is the huge variation in the number of new sexual partners that gives rise to the extremes of risk within populations which need to be captured in predictive models of STI transmission. Such models are vital in providing the necessary scientific evidence to determine whether a range of controls (from education to screening to vaccination) are cost-effective. METHOD AND RESULTS: We use probability sample survey data from Britain's third National Survey of Sexual Attitudes and Lifestyles (Natsal-3) to determine robust distributions for the rate of new partnerships that involve condomless sex and can therefore facilitate the spread of STIs. Different distributions are defined depending on four individual-level characteristics: age, sex, sexual orientation, and previous sexual experience. As individual behaviour patterns can change (e.g. by remaining in a monogamous relationship for a long period) we allow risk-percentiles to be randomly redrawn, to capture longer term behaviour as measured by Natsal-3. We demonstrate how this model formulation interacts with the transmission of infection by constructing an individual-based SIS-P (Susceptible-Infected-Susceptible-Protected) transmission model for the spread of a generic STI, and observing overall population demographics when varying the transmission probability within a partnership, recovery rate and the level of population protection (e.g. from vaccination where applicable).

The role of case proximity in transmission of visceral leishmaniasis in a highly endemic village in Bangladesh.

BACKGROUND: Visceral leishmaniasis (VL) is characterised by a high degree of spatial clustering at all scales, and this feature remains even with successful control measures. VL is targeted for elimination as a public health problem in the Indian subcontinent by 2020, and incidence has been falling rapidly since 2011. Current control is based on early diagnosis and treatment of clinical cases, and blanket indoor residual spraying of insecticide (IRS) in endemic villages to kill the sandfly vectors. Spatially targeting active case detection and/or IRS to higher risk areas would greatly reduce costs of control, but its effectiveness as a control strategy is unknown. The effectiveness depends on two key unknowns: how quickly transmission risk decreases with distance from a VL case and how much asymptomatically infected individuals contribute to transmission. METHODOLOGY/PRINCIPAL FINDINGS: To estimate these key parameters, a spatiotemporal transmission model for VL was developed and fitted to geo-located epidemiological data on 2494 individuals from a highly endemic village in Mymensingh, Bangladesh. A Bayesian inference framework that could account for the unknown infection times of the VL cases, and missing symptom onset and recovery times, was developed to perform the parameter estimation. The parameter estimates obtained suggest that, in a highly endemic setting, VL risk decreases relatively quickly with distance from a case-halving within 90m-and that VL cases contribute significantly more to transmission than asymptomatic individuals. CONCLUSIONS/SIGNIFICANCE: These results suggest that spatially-targeted interventions may be effective for limiting transmission. However, the extent to which spatial transmission patterns and the asymptomatic contribution vary with VL endemicity and over time is uncertain. In any event, interventions would need to be performed promptly and in a large radius (≥300m) around a new case to reduce transmission risk.

The impact of current infection levels on the cost-benefit of vaccination.

When considering a new vaccine programme or modifying an existing one, economic cost-benefit analysis, underpinned by predictive epidemiological modelling, is a key component. This analysis is intimately linked to the willingness to pay for additional QALYs (quality-adjusted life-years) gained; currently in England and Wales a health programme is economically viable if the cost per QALY gained is less than £ 20,000, and models are often used to assess if a vaccine programme is likely to fall below this threshold cost. Before a programme begins, infection levels are generally high and therefore vaccination may be expected to have substantial effects and therefore will often be economically viable. However, once a programme is established, and infection rates are lower, it might be expected that a re-evaluation of the programme (using current incidence information) will show it to be less cost-effective. This is the scenario we examine here with analytical tools and simple ODE models. Surprisingly we show that in most cases the benefits from maintaining an existing vaccination programme are at least equal to those of starting the programme initially, and in the majority of scenarios the differences between the two are minimal. In practical terms, this is an extremely helpful finding, allowing us to assert that the action of immunising individuals does not de-value the vaccination programme.

Predicting the spread of the Asian hornet (Vespa velutina) following its incursion into Great Britain.

The yellow-legged or Asian hornet (Vespa velutina) is native to South-East Asia, and is a voracious predator of pollinating insects including honey bees. Since its accidental introduction into South-Western France in 2004, V. velutina has spread to much of western Europe. The presence of V. velutina in Great Britain was first confirmed in September 2016. The likely dynamics following an initial incursion are uncertain, especially the risk of continued spread, and the likely success of control measures. Here we extrapolate from the situation in France to quantify the potential invasion of V. velutina in Great Britain. We find that, without control, V. velutina could colonise the British mainland rapidly, depending upon how the Asian hornet responds to the colder climate in Britain compared to France. The announcement that a second hornet had been discovered in Somerset, increases the chance that the invasion first occurred before 2016. We therefore consider the likely site of first invasion and the probabilistic position of additional founding nests in late 2016 and early 2017. Given the potential dispersion of V. velutina, we conclude that vigilance is required over a large area to prevent the establishment of this threat to the pollinator population.

Invasion dynamics of Asian hornet, Vespa velutina (Hymenoptera: Vespidae): a case study of a commune in south-west France.

Asian hornet, Vespa velutina Lepeletier nests were discovered in 2007 in Andernos-les-Bains on the south-west coast of France, 3 years after the first reported sightings in France. The number of nests increased in the commune over the following 7 years, despite local authorities enacting a destruction policy. The nests existed in close proximity to one another leading to a high density of over 10 nests per square kilometre in urban areas. New information on the chosen habitat for nests is presented, and the differences between primary and secondary locations are evident, with primary nests mostly occupying buildings and man-made structures, while secondary nests were found on trees. Using Bayesian inference methods, we fit a basic model to the observational data, which allows us to estimate key demographic parameters. This model fit is highly informative for predicting V. velutina spread and colonisation of other at-risk regions, and suggests that local control has a limited impact on the spread of V. velutina once established within a region.

Efficient use of sentinel sites: detection of invasive honeybee pests and diseases in the UK.

Sentinel sites, where problems can be identified early or investigated in detail, form an important part of planning for exotic disease outbreaks in humans, livestock and plants. Key questions are: how many sentinels are required, where should they be positioned and how effective are they at rapidly identifying new invasions? The sentinel apiary system for invasive honeybee pests and diseases illustrates the costs and benefits of such approaches. Here, we address these issues with two mathematical modelling approaches. The first approach is generic and uses probabilistic arguments to calculate the average number of affected sites when an outbreak is first detected, providing rapid and general insights that we have applied to a range of infectious diseases. The second approach uses a computationally intensive, stochastic, spatial model to simulate multiple outbreaks and to determine appropriate sentinel locations for UK apiaries. Both models quantify the anticipated increase in success of sentinel sites as their number increases and as non-sentinel sites become worse at detection; however, unexpectedly sentinels perform relatively better for faster growing outbreaks. Additionally, the spatial model allows us to quantify the substantial role that carefully positioned sentinels can play in the rapid detection of exotic invasions.

Indirect effects of childhood pneumococcal conjugate vaccination on invasive pneumococcal disease: a systematic review and meta-analysis.

BACKGROUND: The full extent to which childhood pneumococcal conjugate vaccines (PCV) can indirectly reduce illness in unvaccinated populations is not known. We aimed to estimate the magnitude and timing of indirect effects of PCVs on invasive pneumococcal disease. METHODS: In this systematic review and meta-analysis, we searched bibliographic databases for non-randomised quasi-experimental or observational studies reporting invasive pneumococcal disease changes following PCV introduction in unvaccinated populations (studies published Sept 1, 2010, to Jan 6, 2016), updating the previous systematic review of the same topic (studies published Jan 1, 1994, to Sept 30, 2010). Two reviewers extracted summary data by consensus. We used a Bayesian mixed-effects model to account for between-study heterogeneity to estimate temporal indirect effects by pooling of invasive pneumococcal disease changes by serotype and serogroup. FINDINGS: Data were extracted from 70 studies included in the previous review and 172 additional studies, covering 27 high-income and seven middle-income countries. The predicted mean times to attaining a 90% reduction in invasive pneumococcal disease were 8·9 years (95% credible interval [CrI] 7·8-10·3) for grouped serotypes contained in the seven-valent PCV (PCV7), and 9·5 years (6·1-16·6) for the grouped six additional serotypes contained in the 13-valent PCV (PCV13) but not in PCV7. Disease due to grouped serotypes contained in the 23-valent pneumococcal polysaccharide vaccine (PPV23) decreased at similar rates per year in adults aged 19-64 years (relative risk [RR] 0·85, 95% CrI 0·75-0·95) and 65 years and older (0·87, 0·84-0·90). However, we noted no changes in either group in invasive pneumococcal disease caused by the additional 11 serotypes covered by PPV23 but not PCV13. INTERPRETATION: Population childhood PCV programmes will lead, on average, to substantial protection across the whole population within a decade. This large indirect protection should be considered when assessing vaccination of older age groups. FUNDING: Policy Research Programme of the Department of Health, England.

Modelling the spread of American foulbrood in honeybees.

We investigate the spread of American foulbrood (AFB), a disease caused by the bacterium Paenibacillus larvae, that affects bees and can be extremely damaging to beehives. Our dataset comes from an inspection period carried out during an AFB epidemic of honeybee colonies on the island of Jersey during the summer of 2010. The data include the number of hives of honeybees, location and owner of honeybee apiaries across the island. We use a spatial SIR model with an underlying owner network to simulate the epidemic and characterize the epidemic using a Markov chain Monte Carlo (MCMC) scheme to determine model parameters and infection times (including undetected 'occult' infections). Likely methods of infection spread can be inferred from the analysis, with both distance- and owner-based transmissions being found to contribute to the spread of AFB. The results of the MCMC are corroborated by simulating the epidemic using a stochastic SIR model, resulting in aggregate levels of infection that are comparable to the data. We use this stochastic SIR model to simulate the impact of different control strategies on controlling the epidemic. It is found that earlier inspections result in smaller epidemics and a higher likelihood of AFB extinction.