Optimal mix of screening and contact tracing for endemic diseases

High Community Transmission of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) Associated With Decreased Contact Tracing Effectiveness for Identifying Persons at Elevated Risk of Infection-Vermont

Vermont contact tracing consistently identified people at risk for coronavirus disease 2019 (COVID-19). However, the prevalence ratio (PR) of COVID-19 among contacts compared with noncontacts when viral transmission was high (PR, 13.5 [95% confidence interval {CI}, 13.2-13.9]) was significantly less than when transmission was low (PR, 49.3 [95% CI, 43.2-56.3]).

Lessons from past pandemics: a systematic review of evidence-based, cost-effective interventions to suppress COVID-19

BACKGROUND

In an unparalleled global response, during the COVID-19 pandemic, 90 countries asked 3.9 billion people to stay home. Yet other countries avoided lockdowns and focused on other strategies, like contact tracing. How effective and cost-effective are these strategies? We aimed to provide a comprehensive summary of the evidence on past pandemic controls, with a focus on cost-effectiveness.

METHODS

Following PRISMA guidelines, MEDLINE (1946 to April week 2, 2020) and EMBASE (1974 to April 17, 2020) were searched using a range of terms related to pandemic control. Articles reporting on the effectiveness or cost-effectiveness of at least one intervention were included.

RESULTS

We found 1653 papers; 62 were included. The effectiveness of hand-washing and face masks was supported by randomized trials. These measures were highly cost-effective. For other interventions, only observational and modelling studies were found. They suggested that (1) the most cost-effective interventions are swift contact tracing and case isolation, surveillance networks, protective equipment for healthcare workers, and early vaccination (when available); (2) home quarantines and stockpiling antivirals are less cost-effective; (3) social distancing measures like workplace and school closures are effective but costly, making them the least cost-effective options; (4) combinations are more cost-effective than single interventions; and (5) interventions are more cost-effective when adopted early. For 2009 H1N1 influenza, contact tracing was estimated to be 4363 times more cost-effective than school closure ($2260 vs. $9,860,000 per death prevented).

CONCLUSIONS AND CONTRIBUTIONS

For COVID-19, a cautious interpretation suggests that (1) workplace and school closures are effective but costly, especially when adopted late, and (2) scaling up as early as possible a combination of interventions that includes hand-washing, face masks, ample protective equipment for healthcare workers, and swift contact tracing and case isolation is likely to be the most cost-effective strategy.

DYNAMICS OF AN INFECTIOUS DISEASE IN THE PRESENCE OF SATURATED MEDICAL TREATMENT OF HOLLING TYPE III AND SELF-PROTECTION

A nonlinear SEIR model is formulated and analyzed. This model accounts for three important interventions — the saturated treatment on infective individuals, the screening on the exposed individuals and the information induced self-protection on susceptible individuals. Existence and stability of equilibria are discussed. A sensitivity analysis for the model parameters is performed and we identified the parameters which are more sensitive to the model system. The sensitivity analysis is further followed up with the two parameters heat plot that determines the regions for the parametric values in which the system is either stable or unstable. Further, an optimal control problem is formulated by considering screening and treatment as control variables and corresponding cost functional is constructed. Using Pontryagin’s Maximum Principle, paths of optimal controls are obtained analytically. A comparative study is conducted numerically to explore and analyze analytical results. We note that in absence of treatment, screening policy may be a cost-effective choice to keep a tab on the disease. However, comprehensive effect of both screening and treatment has a huge impact, which is highly effective and least expensive. It is also noted that treatment is effective for mild epidemic whereas screening has a significant effect on the disease burden while epidemic is severe. For a range of basic reproduction number, effect of self-protection and saturation in treatment is also explored numerically.

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.

Contact tracing performance during the Ebola epidemic in Liberia, 2014-2015

BACKGROUND

During the Ebola virus disease (EVD) epidemic in Liberia, contact tracing was implemented to rapidly detect new cases and prevent further transmission. We describe the scope and characteristics of contact tracing in Liberia and assess its performance during the 2014-2015 EVD epidemic.

METHODOLOGY/PRINCIPAL FINDINGS

We performed a retrospective descriptive analysis of data collection forms for contact tracing conducted in six counties during June 2014-July 2015. EVD case counts from situation reports in the same counties were used to assess contact tracing coverage and sensitivity. Contacts who presented with symptoms and/or died, and monitoring was stopped, were classified as "potential cases". Positive predictive value (PPV) was defined as the proportion of traced contacts who were identified as potential cases. Bivariate and multivariate logistic regression models were used to identify characteristics among potential cases. We analyzed 25,830 contact tracing records for contacts who had monitoring initiated or were last exposed between June 4, 2014 and July 13, 2015. Contact tracing was initiated for 26.7% of total EVD cases and detected 3.6% of all new cases during this period. Eighty-eight percent of contacts completed monitoring, and 334 contacts were identified as potential cases (PPV = 1.4%). Potential cases were more likely to be detected early in the outbreak; hail from rural areas; report multiple exposures and symptoms; have household contact or direct bodily or fluid contact; and report nausea, fever, or weakness compared to contacts who completed monitoring.

CONCLUSIONS/SIGNIFICANCE

Contact tracing was a critical intervention in Liberia and represented one of the largest contact tracing efforts during an epidemic in history. While there were notable improvements in implementation over time, these data suggest there were limitations to its performance-particularly in urban districts and during peak transmission. Recommendations for improving performance include integrated surveillance, decentralized management of multidisciplinary teams, comprehensive protocols, and community-led strategies.

Identifying cost-effective dynamic policies to control epidemics

We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population's net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. Copyright © 2016 John Wiley & Sons, Ltd.

Toward cost-effective staffing mixes for Veterans Affairs substance use disorder treatment programs

Background

In fiscal year (FY) 2008, 133,658 patients were provided services within substance use disorders treatment programs (SUDTPs) in the U.S. Department of Veterans Affairs (VA) health care system. To improve the effectiveness and cost-effectiveness of SUDTPs, we analyze the impacts of staffing mix on the benefits and costs of specialty SUD services. This study demonstrates how cost-effective staffing mixes for each type of VA SUDTPs can be defined empirically.

Methods

We used a stepwise method to derive prediction functions for benefits and costs based on patients’ treatment outcomes at VA SUDTPs nationally from 2001 to 2003, and used them to formulate optimization problems to determine recommended staffing mixes that maximize net benefits per patient for four types of SUDTPs by using the solver function with the Generalized Reduced Gradient algorithm in Microsoft Excel 2010 while conforming to limits of current practice. We conducted sensitivity analyses by varying the baseline severity of addiction problems between lower (2.5 %) and higher (97.5 %) values derived from bootstrapping.

Results and conclusions

Compared to the actual staffing mixes in FY01-FY03, the recommended staffing mixes would lower treatment costs while improving patients’ outcomes, and improved net benefits are estimated from $1472 to $17,743 per patient.

Optimizing an HIV testing program using a system dynamics model of the continuum of care

Realizing the full individual and population-wide benefits of antiretroviral therapy for human immunodeficiency virus (HIV) infection requires an efficient mechanism of HIV-related health service delivery. We developed a system dynamics model of the continuum of HIV care in Vancouver, Canada, which reflects key activities and decisions in the delivery of antiretroviral therapy, including HIV testing, linkage to care, and long-term retention in care and treatment. To measure the influence of operational interventions on population health outcomes, we incorporated an HIV transmission component into the model. We determined optimal resource allocations among targeted and routine testing programs to minimize new HIV infections over five years in Vancouver. Simulation scenarios assumed various constraints informed by the local health policy. The project was conducted in close collaboration with the local health care providers, Vancouver Coastal Health Authority and Providence Health Care.

Systems engineering methods for enhancing the value stream in public health preparedness: the role of Markov models, simulation, and optimization

OBJECTIVES

Large-scale incidents such as the 2009 H1N1 outbreak, the 2011 European Escherichia coli outbreak, and Hurricane Sandy demonstrate the need for continuous improvement in emergency preparation, alert, and response systems globally. As questions relating to emergency preparedness and response continue to rise to the forefront, the field of industrial and systems engineering (ISE) emerges, as it provides sophisticated techniques that have the ability to model the system, simulate, and optimize complex systems, even under uncertainty.

METHODS

We applied three ISE techniques--Markov modeling, operations research (OR) or optimization, and computer simulation--to public health emergency preparedness.

RESULTS

We present three models developed through a four-year partnership with stakeholders from state and local public health for effectively, efficiently, and appropriately responding to potential public health threats: (1) an OR model for optimal alerting in response to a public health event, (2) simulation models developed to respond to communicable disease events from the perspective of public health, and (3) simulation models for implementing pandemic influenza vaccination clinics representative of clinics in operation for the 2009-2010 H1N1 vaccinations in North Carolina.

CONCLUSIONS

The methods employed by the ISE discipline offer powerful new insights to understand and improve public health emergency preparedness and response systems. The models can be used by public health practitioners not only to inform their planning decisions but also to provide a quantitative argument to support public health decision making and investment.

Conflicts of interest during contact investigations: a game-theoretic analysis

The goal of contact tracing is to reduce the likelihood of transmission, particularly to individuals who are at greatest risk for developing complications of infection, as well as identifying individuals who are in need of medical treatment of other interventions. In this paper, we develop a simple mathematical model of contact investigations among a small group of individuals and apply game theory to explore conflicts of interest that may arise in the context of perceived costs of disclosure. Using analytic Kolmogorov equations, we determine whether or not it is possible for individual incentives to drive noncooperation, even though cooperation would yield a better group outcome. We found that if all individuals have a cost of disclosure, then the optimal individual decision is to simply not disclose each other. With further analysis of (1) completely offsetting the costs of disclosure and (2) partially offsetting the costs of disclosure, we found that all individuals disclose all contacts, resulting in a smaller basic reproductive number and an alignment of individual and group optimality. More data are needed to understand decision making during outbreak investigations and what the real and perceived costs are.

Optimal screening strategies for healthcare associated infections in a multi-institutional setting

Health institutions may choose to screen newly admitted patients for the presence of disease in order to reduce disease prevalence within the institution. Screening is costly, and institutions must judiciously choose which patients they wish to screen based on the dynamics of disease transmission. Since potentially infected patients move between different health institutions, the screening and treatment decisions of one institution will affect the optimal decisions of others; an institution might choose to “free-ride” off the screening and treatment decisions of neighboring institutions. We develop a theoretical model of the strategic decision problem facing a health care institution choosing to screen newly admitted patients. The model incorporates an SIS compartmental model of disease transmission into a game theoretic model of strategic decision-making. Using this setup, we are able to analyze how optimal screening is influenced by disease parameters, such as the efficacy of treatment, the disease recovery rate and the movement of patients. We find that the optimal screening level is lower for diseases that have more effective treatments. Our model also allows us to analyze how the optimal screening level varies with the number of decision makers involved in the screening process. We show that when institutions are more autonomous in selecting whom to screen, they will choose to screen at a lower rate than when screening decisions are more centralized. Results also suggest that centralized screening decisions have a greater impact on disease prevalence when the availability or efficacy of treatment is low. Our model provides insight into the factors one should consider when choosing whether to set a mandated screening policy. We find that screening mandates set at a centralized level (i.e. state or national) will have a greater impact on the control of infectious disease.

Healthcare associated infections are a major cause of morbidity and mortality. Screening patients on admission to the hospital may reduce prevalence by identifying infected individuals; infected individuals can then be treated or isolated to prevent further spread. Because screening is costly, institutions must weigh the benefits of reduced prevalence against the costs of screening. However, patients move between institutions carrying disease with them; consequently, when choosing who to screen, institutions must also consider the rates at which neighboring institutions screen patients as well. We develop a theoretical model that describes this strategic decision process. Using this model we are able to analyze the screening decision problem along three dimensions: (1) how disease specific parameters, such as the effectiveness of treatment, influence the optimal screening level, (2) how the degree of centralization in screening policy (e.g. local, state or federal) influences the optimal screening level, and (3) how these two sets of factors combine to influence the optimal screening level. Our model highlights factors to consider when choosing to implement screening policy, and results are of use to policy makers wishing to reduce the prevalence of infectious disease.

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

Using a modified one-dimensional model for the spread of an SIS disease on a network, we show that the behaviour of complex network simulations can be replicated with a simpler model. This model is then used to design optimal controls for use on the network, which would otherwise be unfeasible to obtain, resulting in information about how best to combine a population-level random intervention with one that is more targeted. This technique is used to minimise intervention costs over a short time interval with a target prevalence, and also to minimise prevalence with a specified budget. When applied to chlamydia, we find results consistent with previous work; that is maximising targeted control (contact tracing) is important to using resources effectively, while high-intensity bursts of population control (screening) are more effective than maintaining a high level of coverage.

Exploring short-term responses to changes in the control strategy for Chlamydia trachomatis

Chlamydia has a significant impact on public health provision in the developed world. Using pair approximation equations we investigate the efficacy of control programmes for chlamydia on short time scales that are relevant to policy makers. We use output from the model to estimate critical measures, namely, prevalence, incidence, and positivity in those screened and their partners. We combine these measures with a costing tool to estimate the economic impact of different public health strategies. Increasing screening coverage significantly increases the annual programme costs whereas an increase in tracing efficiency initially increases annual costs but over time reduces costs below baseline, with tracing accounting for around 10% of intervention costs. We found that partner positivity is insensitive to changes in prevalence due to screening, remaining at around 33%. Whether increases occur in screening or tracing levels, the cost per treated infection increases from the baseline because of reduced prevalence.

Cost-effective control of chronic viral diseases: finding the optimal level of screening and contact tracing

Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.

Optimal investment in HIV prevention programs: more is not always better

This paper develops a mathematical/economic framework to address the following question: Given a particular population, a specific HIV prevention program, and a fixed amount of funds that could be invested in the program, how much money should be invested? We consider the impact of investment in a prevention program on the HIV sufficient contact rate (defined via production functions that describe the change in the sufficient contact rate as a function of expenditure on a prevention program), and the impact of changes in the sufficient contact rate on the spread of HIV (via an epidemic model). In general, the cost per HIV infection averted is not constant as the level of investment changes, so the fact that some investment in a program is cost effective does not mean that more investment in the program is cost effective. Our framework provides a formal means for determining how the cost per infection averted changes with the level of expenditure. We can use this information as follows: When the program has decreasing marginal cost per infection averted (which occurs, for example, with a growing epidemic and a prevention program with increasing returns to scale), it is optimal either to spend nothing on the program or to spend the entire budget. When the program has increasing marginal cost per infection averted (which occurs, for example, with a shrinking epidemic and a prevention program with decreasing returns to scale), it may be optimal to spend some but not all of the budget. The amount that should be spent depends on both the rate of disease spread and the production function for the prevention program. We illustrate our ideas with two examples: that of a needle exchange program, and that of a methadone maintenance program.

Contact tracing to control infectious disease: when enough is enough

Contact tracing (also known as partner notification) is a primary means of controlling infectious diseases such as tuberculosis (TB), human immunodeficiency virus (HIV), and sexually transmitted diseases (STDs). However, little work has been done to determine the optimal level of investment in contact tracing. In this paper, we present a methodology for evaluating the appropriate level of investment in contact tracing. We develop and apply a simulation model of contact tracing and the spread of an infectious disease among a network of individuals in order to evaluate the cost and effectiveness of different levels of contact tracing. We show that contact tracing is likely to have diminishing returns to scale in investment: incremental investments in contact tracing yield diminishing reductions in disease prevalence. In conjunction with a cost-effectiveness threshold, we then determine the optimal amount that should be invested in contact tracing. We first assume that the only incremental disease control is contact tracing. We then extend the analysis to consider the optimal allocation of a budget between contact tracing and screening for exogenous infection, and between contact tracing and screening for endogenous infection. We discuss how a simulation model of this type, appropriately tailored, could be used as a policy tool for determining the appropriate level of investment in contact tracing for a specific disease in a specific population. We present an example application to contact tracing for chlamydia control.