Approximating optimal controls for networks when there are combinations of population-level and targeted measures available: chlamydia infection as a case-study

Costs, Health Benefits, and Cost-Effectiveness of Chlamydia Screening and Partner Notification in the United States, 2000-2019: A Mathematical Modeling Analysis

BACKGROUND

Chlamydia remains a significant public health problem that contributes to adverse reproductive health outcomes. In the United States, sexually active women 24 years and younger are recommended to receive annual screening for chlamydia. In this study, we evaluated the impact of estimated current levels of screening and partner notification (PN), and the impact of screening based on guidelines on chlamydia associated sequelae, quality adjusted life years (QALYs) lost and costs.

METHODS

We conducted a cost-effectiveness analysis of chlamydia screening, using a published calibrated pair formation transmission model that estimated trends in chlamydia screening coverage in the United States from 2000 to 2015 consistent with epidemiological data. We used probability trees to translate chlamydial infection outcomes into estimated numbers of chlamydia-associated sequelae, QALYs lost, and health care services costs (in 2020 US dollars). We evaluated the costs and population health benefits of screening and PN in the United States for 2000 to 2015, as compared with no screening and no PN. We also estimated the additional benefits that could be achieved by increasing screening coverage to the levels indicated by the policy recommendations for 2016 to 2019, compared with screening coverage achieved by 2015.

RESULTS

Screening and PN from 2000 to 2015 were estimated to have averted 1.3 million (95% uncertainty interval [UI] 490,000-2.3 million) cases of pelvic inflammatory disease, 430,000 (95% UI, 160,000-760,000) cases of chronic pelvic pain, 300,000 (95% UI, 104,000-570,000) cases of tubal factor infertility, and 140,000 (95% UI, 47,000-260,000) cases of ectopic pregnancy in women. We estimated that chlamydia screening and PN cost $9700 per QALY gained compared with no screening and no PN. We estimated the full realization of chlamydia screening guidelines for 2016 to 2019 to cost $30,000 per QALY gained, compared with a scenario in which chlamydia screening coverage was maintained at 2015 levels.

DISCUSSION

Chlamydia screening and PN as implemented in the United States from 2000 through 2015 has substantially improved population health and provided good value for money when considering associated health care services costs. Further population health gains are attainable by increasing screening further, at reasonable cost per QALY gained.

Optimal strategies to protect a sub-population at risk due to an established epidemic

Epidemics can particularly threaten certain sub-populations. For example, for severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the elderly are often preferentially protected. For diseases of plants and animals, certain sub-populations can drive mitigation because they are intrinsically more valuable for ecological, economic, socio-cultural or political reasons. Here, we use optimal control theory to identify strategies to optimally protect a ‘high-value’ sub-population when there is a limited budget and epidemiological uncertainty. We use protection of the Redwood National Park in California in the face of the large ongoing state-wide epidemic of sudden oak death (caused by Phytophthora ramorum) as a case study. We concentrate on whether control should be focused entirely within the National Park itself, or whether treatment of the growing epidemic in the surrounding ‘buffer region’ can instead be more profitable. We find that, depending on rates of infection and the size of the ongoing epidemic, focusing control on the high-value region is often optimal. However, priority should sometimes switch from the buffer region to the high-value region only as the local outbreak grows. We characterize how the timing of any switch depends on epidemiological and logistic parameters, and test robustness to systematic misspecification of these factors due to imperfect prior knowledge.

Contact tracing - Old models and new challenges

Contact tracing is an effective method to control emerging infectious diseases. Since the 1980's, modellers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations, and to assess the effects of contact tracing on the spread of an infectious disease. Despite the progress made in the area, there remain important open questions. In addition, technological developments, especially in the field of molecular biology (genetic sequencing of pathogens) and modern communication (digital contact tracing), have posed new challenges for the modelling community. In the present paper, we discuss modelling approaches for contact tracing and identify some of the current challenges for the field.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Applying optimal control theory to complex epidemiological models to inform real-world disease management

Mathematical models provide a rational basis to inform how, where and when to control disease. Assuming an accurate spatially explicit simulation model can be fitted to spread data, it is straightforward to use it to test the performance of a range of management strategies. However, the typical complexity of simulation models and the vast set of possible controls mean that only a small subset of all possible strategies can ever be tested. An alternative approach-optimal control theory-allows the best control to be identified unambiguously. However, the complexity of the underpinning mathematics means that disease models used to identify this optimum must be very simple. We highlight two frameworks for bridging the gap between detailed epidemic simulations and optimal control theory: open-loop and model predictive control. Both these frameworks approximate a simulation model with a simpler model more amenable to mathematical analysis. Using an illustrative example model, we show the benefits of using feedback control, in which the approximation and control are updated as the epidemic progresses. Our work illustrates a new methodology to allow the insights of optimal control theory to inform practical disease management strategies, with the potential for application to diseases of humans, animals and plants. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'. This theme issue is linked with the earlier issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'.

Numerical optimal control for HIV prevention with dynamic budget allocation

This article is about numerical control of HIV propagation. The contribution of the article is threefold: first, a novel model of HIV propagation is proposed; second, the methods from numerical optimal control are successfully applied to the developed model to compute optimal control profiles; finally, the computed results are applied to the real problem yielding important and practically relevant results.

Sensitivity of joint contagiousness and susceptibility-based dynamic optimal control strategies for HIV prevention

Predicting the population-level effects of an infectious disease intervention that incorporate multiple modes of intervention is complicated by the joint non-linear dynamics of both infection transmission and the intervention itself. In this paper, we consider the sensitivity of Dynamic Optimal Control Profiles (DOCPs) for the optimal joint investment in both a contagiousness and susceptibility-based control of HIV to bio-behavioral, economic, and programmatic assumptions. The DOCP is calculated using recently developed numerical algorithms that allow controls to be represented by a set of piecewise constant functions that maintain a constant yearly budget. Our transmission model assumes multiple stages of HIV infection corresponding to acute and chronic infection and both within- and between-individual behavioral heterogeneity. We parameterize a baseline scenario from a longitudinal study of sexual behavior in MSM and consider sensitivity of the DOCPs to deviations from that baseline scenario. In the baseline scenario, the primary determinant of the dominant control were programmatic factors, regardless of budget. In sensitivity analyses, the qualitative aspects of the optimal control policy were often robust to significant deviation in assumptions regarding transmission dynamics. In addition, we found several conditions in which long-term joint investment in both interventions was optimal. Our results suggest that modeling in the service of decision support for intervention design can improve population-level effects of a limited set of economic resources. We found that economic and programmatic factors were as important as the inherent transmission dynamics in determining population-level intervention effects. Given our finding that the DOCPs were robust to alternative biological and behavioral assumptions it may be possible to identify DOCPs even when the data are not sufficient to identify a transmission model.

Impact and cost-effectiveness of chlamydia testing in Scotland: a mathematical modelling study

Background

Chlamydia is the most common sexually transmitted bacterial infection in Scotland, and is associated with potentially serious reproductive outcomes, including pelvic inflammatory disease (PID) and tubal factor infertility (TFI) in women. Chlamydia testing in Scotland is currently targeted towards symptomatic individuals, individuals at high risk of existing undetected infection, and young people. The cost-effectiveness of testing and treatment to prevent PID and TFI in Scotland is uncertain.

Methods

A compartmental deterministic dynamic model of chlamydia infection in 15–24 year olds in Scotland was developed. The model was used to estimate the impact of a change in testing strategy from baseline (16.8% overall testing coverage; 0.4 partners notified and tested/treated per treated positive index) on PID and TFI cases. Cost-effectiveness calculations informed by best-available estimates of the quality-adjusted life years (QALYs) lost due to PID and TFI were also performed.

Results

Increasing overall testing coverage by 50% from baseline to 25.2% is estimated to result in 21% fewer cases in young women each year (PID: 703 fewer; TFI: 88 fewer). A 50% decrease to 8.4% would result in 20% more PID (669 additional) and TFI (84 additional) cases occurring annually. The cost per QALY gained of current testing activities compared to no testing is £40,034, which is above the £20,000-£30,000 cost-effectiveness threshold. However, calculations are hampered by lack of reliable data. Any increase in partner notification from baseline would be cost-effective (incremental cost per QALY gained for a partner notification efficacy of 1 compared to baseline: £5,119), and would increase the cost-effectiveness of current testing strategy compared to no testing, with threshold cost-effectiveness reached at a partner notification efficacy of 1.5. However, there is uncertainty in the extent to which partner notification is currently done, and hence the amount by which it could potentially be increased.

Conclusions

Current chlamydia testing strategy in Scotland is not cost-effective under the conservative model assumptions applied. However, with better data enabling some of these assumptions to be relaxed, current coverage could be cost-effective. Meanwhile, increasing partner notification efficacy on its own would be a cost-effective way of preventing PID and TFI from current strategy.

Electronic supplementary material

The online version of this article (doi:10.1186/1742-4682-12-2) contains supplementary material, which is available to authorized users.