Process modelling of NHS cardiovascular waiting lists in response to the COVID-19 pandemic.

OBJECTIVE: To model the referral, diagnostic and treatment pathway for cardiovascular disease (CVD) in the English National Health Service (NHS) to provide commissioners and managers with a methodology to optimise patient flow and reduce waiting lists. STUDY DESIGN: A systems dynamics approach modelling the CVD healthcare system in England. The model is designed to capture current and predict future states of waiting lists. SETTING: Routinely collected, publicly available data streams of primary and secondary care, sourced from NHS Digital, NHS England, the Office of National Statistics and StatsWales. DATA COLLECTION AND EXTRACTION METHODS: The data used to train and validate the model were routinely collected and publicly available data. It was extracted and implemented in the model using the PySD package in python. RESULTS: NHS cardiovascular waiting lists in England have increased by over 40% compared with pre- COVID-19 levels. The rise in waiting lists was primarily due to restrictions in referrals from primary care, creating a bottleneck postpandemic. Predictive models show increasing point capacities within the system may paradoxically worsen downstream flow. While there is no simple rate-limiting step, the intervention that would most improve patient flow would be to increase consultant outpatient appointments. CONCLUSIONS: The increase in NHS CVD waiting lists in England can be captured using a systems dynamics approach, as can the future state of waiting lists in the presence of further shocks/interventions. It is important for those planning services to use such a systems-oriented approach because the feed-forward and feedback nature of patient flow through referral, diagnostics and treatment leads to counterintuitive effects of interventions designed to reduce waiting lists.

Getting the most out of maths: How to coordinate mathematical modelling research to support a pandemic, lessons learnt from three initiatives that were part of the COVID-19 response in the UK.

In March 2020 mathematics became a key part of the scientific advice to the UK government on the pandemic response to COVID-19. Mathematical and statistical modelling provided critical information on the spread of the virus and the potential impact of different interventions. The unprecedented scale of the challenge led the epidemiological modelling community in the UK to be pushed to its limits. At the same time, mathematical modellers across the country were keen to use their knowledge and skills to support the COVID-19 modelling effort. However, this sudden great interest in epidemiological modelling needed to be coordinated to provide much-needed support, and to limit the burden on epidemiological modellers already very stretched for time. In this paper we describe three initiatives set up in the UK in spring 2020 to coordinate the mathematical sciences research community in supporting mathematical modelling of COVID-19. Each initiative had different primary aims and worked to maximise synergies between the various projects. We reflect on the lessons learnt, highlighting the key roles of pre-existing research collaborations and focal centres of coordination in contributing to the success of these initiatives. We conclude with recommendations about important ways in which the scientific research community could be better prepared for future pandemics. This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

Comparison of Outcomes of In-Centre Haemodialysis Patients between the 1st and 2nd COVID-19 Outbreak in England, Wales, and Northern Ireland: A UK Renal Registry Analysis.

INTRODUCTION: This retrospective cohort study compares in-centre haemodialysis (ICHD) patients' outcomes between the 1st and 2nd waves of the COVID-19 pandemic in England, Wales, and Northern Ireland. METHODS: All people aged ≥18 years receiving ICHD at 31 December 2019, who were still alive and not in receipt of a kidney transplant at 1 March and who had a positive polymerase chain reaction test for SARS-CoV-2 between 1 March 2020 and 31 January 2021, were included. The COVID-19 infections were split into two "waves": wave 1 from March to August 2020 and wave 2 from September 2020 to January 2021. Cumulative incidence of COVID-19, multivariable Cox models for risk of positivity, median, and 95% credible interval of reproduction number in dialysis units were calculated separately for wave 1 and wave 2. Survival and hazard ratios for mortality were described with age- and sex-adjusted Kaplan-Meier plots and multivariable Cox proportional models. RESULTS: 4,408 ICHD patients had COVID-19 during the study period. Unadjusted survival at 28 days was similar in both waves (wave 1 75.6% [95% confidence interval [CI]: 73.7-77.5], wave 2 76.3% [95% CI 74.3-78.2]), but death occurred more rapidly after detected infection in wave 1. Long vintage treatment and not being on the transplant waiting list were associated with higher mortality in both waves. CONCLUSIONS: Risk of death of patients on ICHD treatment with COVID-19 remained unchanged between the first and second outbreaks. This highlights that this vulnerable patient group needs to be prioritized for interventions to prevent severe COVID-19, including vaccination, and the implementation of measures to reduce the risk of transmission alone is not sufficient.

Reducing dengue fever cases at the lowest budget: a constrained optimization approach applied to Thailand.

BACKGROUND: With the challenges that dengue fever (DF) presents to healthcare systems and societies, public health officials must determine where best to allocate scarce resources and restricted budgets. Constrained optimization (CO) helps to address some of the acknowledged limitations of conventional health economic analyses and has typically been used to identify the optimal allocation of resources across interventions subject to a variety of constraints. METHODS: A dynamic transmission model was developed to predict the number of dengue cases in Thailand at steady state. A CO was then applied to identify the optimal combination of interventions (release of Wolbachia-infected mosquitoes and paediatric vaccination) within the constraints of a fixed budget, set no higher than cost estimates of the current vector control programme, to minimize the number of dengue cases and disability-adjusted life years (DALYs) lost. Epidemiological, cost, and effectiveness data were informed by national data and the research literature. The time horizon was 10 years. Scenario analyses examined different disease management and intervention costs, budget constraints, vaccine efficacy, and optimization time horizon. RESULTS: Under base-case budget constraints, the optimal coverage of the two interventions to minimize dengue incidence was predicted to be nearly equal (Wolbachia 50%; paediatric vaccination 49%) with corresponding coverages under lower bound (Wolbachia 54%; paediatric vaccination 10%) and upper bound (Wolbachia 67%; paediatric vaccination 100%) budget ceilings. Scenario analyses indicated that the most impactful situations related to the costs of Wolbachia and paediatric vaccination with decreases/ increases in costs of interventions demonstrating a direct correlation with coverage (increases/ decreases) of the respective control strategies under examination. CONCLUSIONS: Determining the best investment strategy for dengue control requires the identification of the optimal mix of interventions to implement in order to maximize public health outcomes, often under fixed budget constraints. A CO model was developed with the objective of minimizing dengue cases (and DALYs lost) over a 10-year time horizon, within the constraints of the estimated budgets for vector control in the absence of vaccination and Wolbachia. The model provides a tool for developing estimates of optimal coverage of combined dengue control strategies that minimize dengue burden at the lowest budget.

The economic impact and cost-effectiveness of combined vector-control and dengue vaccination strategies in Thailand: results from a dynamic transmission model.

BACKGROUND AND AIMS: Dengue fever is a major public health problem in tropical/subtropical regions. Prior economic analyses have predominantly evaluated either vaccination or vector-control programmes in isolation and do not really consider the incremental benefits and cost-effectiveness of mixed strategies and combination control. We estimated the cost-effectiveness of single and combined approaches in Thailand. METHODS: The impacts of different control interventions were analysed using a previously published mathematical model of dengue epidemiology and control incorporating seasonality, age structure, consecutive infection, cross protection, immune enhancement and combined vector-host transmission. An economic model was applied to simulation results to estimate the cost-effectiveness of 4 interventions and their various combinations (6 strategies): i) routine vaccination of 1-year olds; ii) chemical vector control strategies targeting adult and larval stages separately; iii) environmental management/ public health education and awareness [EM/ PHEA]). Payer and societal perspectives were considered. The health burden of dengue fever was assessed using disability-adjusted life-years (DALYs) lost. Costs and effects were assessed for 10 years. Costs were discounted at 3% annually and updated to 2013 United States Dollars. Incremental cost-effectiveness analysis was carried out after strategies were rank-ordered by cost, with results presented in a table of incremental analysis. Sensitivity and scenario analyses were undertaken; and the impact and cost-effectiveness of Wolbachia was evaluated in exploratory scenario analyses. RESULTS: From the payer and societal perspectives, 2 combination strategies were considered optimal, as all other control strategies were dominated. Vaccination plus adulticide plus EM/ PHEA was deemed cost-effective according to multiple cost-effectiveness criteria. From the societal perspective, incremental differences vs. adulticide and EM/ PHEA resulted in costs of $157.6 million and DALYs lost of 12,599, giving an expected ICER of $12,508 per DALY averted. Exploratory scenario analyses showed Wolbachia to be highly cost-effective ($343 per DALY averted) vs. other single control measures. CONCLUSIONS: Our model shows that individual interventions can be cost-effective, but that important epidemiological reductions and economic impacts are demonstrated when interventions are combined as part of an integrated approach to combating dengue fever. Exploratory scenario analyses demonstrated the potential epidemiological and cost-effective impact of Wolbachia when deployed at scale on a nationwide basis. Our findings were robust in the face of sensitivity analyses.

Patient choice modelling: how do patients choose their hospitals?

As an aid to predicting future hospital admissions, we compare use of the Multinomial Logit and the Utility Maximising Nested Logit models to describe how patients choose their hospitals. The models are fitted to real data from Derbyshire, United Kingdom, which lists the postcodes of more than 200,000 admissions to six different local hospitals. Both elective and emergency admissions are analysed for this mixed urban/rural area. For characteristics that may affect a patient's choice of hospital, we consider the distance of the patient from the hospital, the number of beds at the hospital and the number of car parking spaces available at the hospital, as well as several statistics publicly available on National Health Service (NHS) websites: an average waiting time, the patient survey score for ward cleanliness, the patient safety score and the inpatient survey score for overall care. The Multinomial Logit model is successfully fitted to the data. Results obtained with the Utility Maximising Nested Logit model show that nesting according to city or town may be invalid for these data; in other words, the choice of hospital does not appear to be preceded by choice of city. In all of the analysis carried out, distance appears to be one of the main influences on a patient's choice of hospital rather than statistics available on the Internet.

Impact of combined vector-control and vaccination strategies on transmission dynamics of dengue fever: a model-based analysis.

Dengue fever is a vector-borne disease prevalent in tropical and subtropical regions. It is an important public health problem with a considerable and often under-valued disease burden in terms of frequency, cost and quality-of-life. Recent literature reviews have documented the development of mathematical models of dengue fever both to identify important characteristics for future model development as well as to assess the impact of dengue control interventions. Such reviews highlight the importance of short-term cross-protection; antibody-dependent enhancement; and seasonality (in terms of both favourable and unfavourable conditions for mosquitoes). The compartmental model extends work by Bartley (2002) and combines the following factors: seasonality, age-structure, consecutive infection by all four serotypes, cross-protection and immune enhancement, as well as combined vector-host transmission. The model is used to represent dengue transmission dynamics using parameters appropriate for Thailand and to assess the potential impact of combined vector-control and vaccination strategies including routine and catch-up vaccination strategies on disease dynamics. When seasonality and temporary cross-protection between serotypes are included, the model is able to approximate the observed incidence of dengue fever in Thailand. We find vaccination to be the most effective single intervention, albeit with imperfect efficacy (30.2 %) and limited duration of protection. However, in combination, control interventions and vaccination exhibit a marked impact on dengue fever transmission. This study shows that an imperfect vaccine can be a useful weapon in reducing disease spread within the community, although it will be most effective when promoted as one of several strategies for combating dengue fever transmission.

A worldwide investigation of tuberculosis epidemics.

We analyse the tuberculosis (TB) epidemics of 211 countries with a view to proposing more efficient and targeted TB control strategies. Countries are classified by how their TB case notification rates have evolved over time and the age distribution of those suffering from active TB disease in 2008. Further analysis of key statistics associated with each of the countries shows the impact of different indicators. As expected, HIV is a key driver of TB epidemics and affects their age-distribution and their scale. The level of development of a country and its wealth also vary with the shape and scale of a country's TB epidemic. Immigration has an influence on the shape of TB epidemics, which is particularly pronounced in highly developed countries with low levels of TB disease in the native population. We conclude by proposing how the TB control programme in each country analysed should prioritise its efforts.

Cost, affordability and cost-effectiveness of strategies to control tuberculosis in countries with high HIV prevalence.

BACKGROUND: The HIV epidemic has caused a dramatic increase in tuberculosis (TB) in East and southern Africa. Several strategies have the potential to reduce the burden of TB in high HIV prevalence settings, and cost and cost-effectiveness analyses can help to prioritize them when budget constraints exist. However, published cost and cost-effectiveness studies are limited. METHODS: Our objective was to compare the cost, affordability and cost-effectiveness of seven strategies for reducing the burden of TB in countries with high HIV prevalence. A compartmental difference equation model of TB and HIV and recent cost data were used to assess the costs (year 2003 USD prices) and effects (TB cases averted, deaths averted, DALYs gained) of these strategies in Kenya during the period 2004-2023. RESULTS: The three lowest cost and most cost-effective strategies were improving TB cure rates, improving TB case detection rates, and improving both together. The incremental cost of combined improvements to case detection and cure was below USD 15 million per year (7.5% of year 2000 government health expenditure); the mean cost per DALY gained of these three strategies ranged from USD 18 to USD 34. Antiretroviral therapy (ART) had the highest incremental costs, which by 2007 could be as large as total government health expenditures in year 2000. ART could also gain more DALYs than the other strategies, at a cost per DALY gained of around USD 260 to USD 530. Both the costs and effects of treatment for latent tuberculosis infection (TLTI) for HIV+ individuals were low; the cost per DALY gained ranged from about USD 85 to USD 370. Averting one HIV infection for less than USD 250 would be as cost-effective as improving TB case detection and cure rates to WHO target levels. CONCLUSION: To reduce the burden of TB in high HIV prevalence settings, the immediate goal should be to increase TB case detection rates and, to the extent possible, improve TB cure rates, preferably in combination. Realising the full potential of ART will require substantial new funding and strengthening of health system capacity so that increased funding can be used effectively.

Tuberculosis epidemics driven by HIV: is prevention better than cure?

OBJECTIVE: To compare the benefits of tuberculosis (TB) treatment with TB and HIV prevention for the control of TB in regions with high HIV prevalence. DESIGN AND METHODS: A compartmental difference equation model of TB and HIV has been developed and fitted to time series and other published data using Bayesian methods. The model is used to compare the effectiveness of TB chemotherapy with three strategies for prevention: highly active antiretroviral therapy (HAART), the treatment of latent TB infection (TLTI) and the reduction of HIV transmission. RESULTS: Even where the prevalence of HIV infection is high, finding and curing active TB is the most effective way to minimize the number of TB cases and deaths over the next 10 years. HAART can be as effective, but only with very high levels of coverage and compliance. TLTI is comparatively ineffective over all time scales. Reducing HIV incidence is relatively ineffective in preventing TB and TB deaths over 10 years but is much more effective over 20 years. CONCLUSIONS: In countries where the spread of HIV has led to a substantial increase in the incidence of TB, TB control programmes should maintain a strong emphasis on the treatment of active TB. To ensure effective control of TB in the longer term, methods of TB prevention should be carried out in addition to, but not as a substitute for, treating active cases.