Optimal mix of screening and contact tracing for endemic diseases

Abstract

Two common means of controlling infectious diseases are screening and contact tracing. Which should be used, and when? We consider the problem of determining the cheapest mix of screening and contact tracing necessary to achieve a desired endemic prevalence of a disease or to identify a specified number of cases. We perform a partial equilibrium analysis of small-scale interventions, assuming that prevalence is unaffected by the intervention; we develop a full equilibrium analysis where we compare the long-term cost of various combinations of screening and contact tracing needed to achieve a given equilibrium prevalence; and we solve the problem of minimizing the total costs of identifying and treating disease cases plus the cost of untreated disease cases. Our analysis provides several insights. First, contact tracing is only cost effective when prevalence is below a threshold value. This threshold depends on the relative cost per case found by screening versus contact tracing. Second, for a given contact tracing policy, the screening rate needed to achieve a given prevalence or identify a specified number of cases is a decreasing function of disease prevalence. As prevalence increases above the threshold (and contact tracing is discontinued), the screening rate jumps discontinuously to a higher level. Third, these qualitative results hold when we consider unchanged or changed prevalence, and short-term or long-term costs.

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

“…The smaller the number of untreated infections, p ( s ), and the greater the screening cost, c s , the larger the role of contact tracing in identifying people for treatment. This is analogous to a result of Armbruster and Brandeau (2007b) who considered the optimal mix of screening and contact tracing to reduce the prevalence of a curable endemic disease (assuming that contact tracing has fixed efficacy (i.e., that κ is constant)): they found that contact tracing was part of the cost-minimizing solution only when the prevalence of the disease was below a given threshold.…”

“…Their models bear some similarity to our model except that our model is complicated by the presence of additional states, the lack of a cure, and contact tracing as a second control in addition to screening. Armbruster and Brandeau (2007b) used an optimal control approach to find the best combination of screening and contact tracing to control an infectious disease. They examined a curable endemic disease (instead of a chronic one as we do here) and assumed that contact tracing has a fixed efficacy, if it is performed at all.…”

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

“…We assume that the benefit of averting each additional infection is the same as the benefit of averting any other infection, so the marginal benefit equals the average benefit. The concept of marginal benefit (and thus benefit) is equivalent to the cost-effectiveness threshold (in terms of dollars per life year or quality-adjusted life year of survival gained) used implicitly or explicitly in many cost-effectiveness analyses of HIV prevention programs [5, 6, 23-27]: it is the level of benefit the prevention program must have in order to be considered cost effective.…”

International Society for Disease Surveillance Conference 2011: Building the Future of Public Health Surveillance

“…(3) Given these costs, a single DU chooses the screening level that minimizes its net present value of discounted future costs. We solve for the symmetric, pure-strategy Nash equilibrium.…”