Optimal mix of screening and contact tracing for endemic diseases

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.     

Modeling the impact of random screening and contact tracing in reducing the spread of HIV

Mathematical models can help predict the effectiveness of control measures on the spread of HIV and other sexually transmitted diseases (STDs) by reducing the uncertainty in assessing the impact of intervention strategies such as random screening and contact tracing. Even though contact tracing is one of the most effective methods used for controlling treatable STDs, it is still a controversial strategy for controlling HIV because of cost and confidentiality issues. To help estimate the effectiveness of these control measures, we formulate two models with random screening and contact tracing based on the differential infectivity (DI) model and the staged-progression (SP) model. We derive formulas for the reproductive numbers and the endemic equilibria and compare the impact that random screening and contact tracing have in slowing the epidemic in the two models. In the DI model the infected population is divided into groups according to their infectiousness, and HIV is largely spread by a small, highly infectious, group of superspreaders. In this model contact tracing is an effective approach to identifying the superspreaders and has a large effect in slowing the epidemic. In the SP model every infected individual goes through a series of infection stages and the virus is primarily spread by individuals in an initial highly infectious stage or in the late stages of the disease. In this model random screening is more effective than for the DI model, and contact tracing is less effective. Thus the effectiveness of the intervention strategy strongly depends on the underlying etiology of the disease transmission.     

Contact tracing efficiency,transmission heterogeneity,and accelerating COVID-19 epidemics

Simultaneously controlling COVID-19 epidemics and limiting economic and societal impacts presents a difficult challenge, especially with limited public health budgets. Testing, contact tracing, and isolating/quarantining is a key strategy that has been used to reduce transmission of SARS-CoV-2, the virus that causes COVID-19 and other pathogens. However, manual contact tracing is a time-consuming process and as case numbers increase a smaller fraction of cases’ contacts can be traced, leading to additional virus spread. Delays between symptom onset and being tested (and receiving results), and a low fraction of symptomatic cases being tested and traced can also reduce the impact of contact tracing on transmission. We examined the relationship between increasing cases and delays and the pathogen reproductive number R_t, and the implications for infection dynamics using deterministic and stochastic compartmental models of SARS-CoV-2. We found that R_t increased sigmoidally with the number of cases due to decreasing contact tracing efficacy. This relationship results in accelerating epidemics because R_t initially increases, rather than declines, as infections increase. Shifting contact tracers from locations with high and low case burdens relative to capacity to locations with intermediate case burdens maximizes their impact in reducing R_t (but minimizing total infections may be more complicated). Contact tracing efficacy decreased sharply with increasing delays between symptom onset and tracing and with lower fraction of symptomatic infections being tested. Finally, testing and tracing reductions in R_t can sometimes greatly delay epidemics due to the highly heterogeneous transmission dynamics of SARS-CoV-2. These results demonstrate the importance of having an expandable or mobile team of contact tracers that can be used to control surges in cases. They also highlight the synergistic value of high capacity, easy access testing and rapid turn-around of testing results, and outreach efforts to encourage symptomatic cases to be tested immediately after symptom onset.     

Disease contact tracing in random and clustered networks

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic 'moment closure' models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.     

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.     

A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0

We present a novel SEIR (susceptible-exposure-infective-recovered) model that is suitable for modeling the eradication of diseases by mass vaccination or control of diseases by case isolation combined with contact tracing, incorporating the vaccine efficacy or the control efficacy into the model. Moreover, relying on this novel SEIR model and some probabilistic arguments, we have found four formulas that are suitable for estimating the basic reproductive numbers R(0) in terms of the ratio of the mean infectious period to the mean latent period of a disease. The ranges of R(0) for most known diseases, that are calculated by our formulas, coincide very well with the values of R(0) estimated by the usual method of fitting the models to observed data.     

Testing,tracing and isolation in compartmental models

Existing compartmental mathematical modelling methods for epidemics, such as SEIR models, cannot accurately represent effects of contact tracing. This makes them inappropriate for evaluating testing and contact tracing strategies to contain an outbreak. An alternative used in practice is the application of agent- or individual-based models (ABM). However ABMs are complex, less well-understood and much more computationally expensive. This paper presents a new method for accurately including the effects of Testing, contact-Tracing and Isolation (TTI) strategies in standard compartmental models. We derive our method using a careful probabilistic argument to show how contact tracing at the individual level is reflected in aggregate on the population level. We show that the resultant SEIR-TTI model accurately approximates the behaviour of a mechanistic agent-based model at far less computational cost. The computational efficiency is such that it can be easily and cheaply used for exploratory modelling to quantify the required levels of testing and tracing, alone and with other interventions, to assist adaptive planning for managing disease outbreaks.     

Protective impacts of household-based tuberculosis contact tracing are robust across endemic incidence levels and community contact patterns

There is an emerging consensus that achieving global tuberculosis control targets will require more proactive case finding approaches than are currently used in high-incidence settings. Household contact tracing (HHCT), for which households of newly diagnosed cases are actively screened for additional infected individuals is a potentially efficient approach to finding new cases of tuberculosis, however randomized trials assessing the population-level effects of such interventions in settings with sustained community transmission have shown mixed results. One potential explanation for this is that household transmission is responsible for a variable proportion of population-level tuberculosis burden between settings. For example, transmission is more likely to occur in households in settings with a lower tuberculosis burden and where individuals mix preferentially in local areas, compared with settings with higher disease burden and more dispersed mixing. To better understand the relationship between endemic incidence levels, social mixing, and the impact of HHCT, we developed a spatially explicit model of coupled household and community transmission. We found that the impact of HHCT was robust across settings of varied incidence and community contact patterns. In contrast, we found that the effects of community contact tracing interventions were sensitive to community contact patterns. Our results suggest that the protective benefits of HHCT are robust and the benefits of this intervention are likely to be maintained across epidemiological settings.     

Predictors of asymptomatic gonorrhea among patients seen by private practitioners

Nineteen physicians participating in a program for detecting and treating gonorrhea and other sexually transmitted diseases (STD) in high-risk groups filled out encounter forms for the initial visits by the first 3144 patients. This information was used to describe the program users and, by means of logistic regression analysis, to identify predictors of gonorrhea in asymptomatic patients. Overall, 17.3% of the users had culture-proved gonorrhea. Of the symptomatic patients 24.5% had gonorrhea. Of the asymptomatic patients 20.4% of those with a history of contact with a known or suspected case of STD had the disease, and 5.3% of those without a history of contact had the disease. The independent predictors of gonorrhea identified were, in order of importance, a history of contact with a case of STD and being aged less than 30 years. These predictors underline the importance of contact tracing, an underused but productive method of gonorrhea control that can be used effectively in private practice.     

The Impact of Contact Tracing in Clustered Populations

The tracing of potentially infectious contacts has become an important part of the control strategy for many infectious diseases, from early cases of novel infections to endemic sexually transmitted infections. Here, we make use of mathematical models to consider the case of partner notification for sexually transmitted infection, however these models are sufficiently simple to allow more general conclusions to be drawn. We show that, when contact network structure is considered in addition to contact tracing, standard “mass action” models are generally inadequate. To consider the impact of mutual contacts (specifically clustering) we develop an improvement to existing pairwise network models, which we use to demonstrate that ceteris paribus, clustering improves the efficacy of contact tracing for a large region of parameter space. This result is sometimes reversed, however, for the case of highly effective contact tracing. We also develop stochastic simulations for comparison, using simple re-wiring methods that allow the generation of appropriate comparator networks. In this way we contribute to the general theory of network-based interventions against infectious disease.     

Audit of a tuberculosis contact tracing clinic.

OBJECTIVE--To determine the efficiency of tuberculosis contact tracing in South Glamorgan 1987-9. DESIGN--Review of records of contact tracing clinic and of data from the Mycobacterium Reference Unit. The clinic''s practice was compared with 1983 British Thoracic Society''s recommendations. SETTING--Health authority tuberculosis control programme. MAIN OUTCOME MEASURES--Proportion of contacts screened, follow up attendance rates, number of secondary cases detected, and quality of record keeping. RESULTS--101 index patients and 611 contacts were identified. 596 (97.5%) contacts were screened, of whom 139 should not have been. Of 356 contacts requiring a Heaf test, 237 were tested, seven refused the test, and 112 had chest radiography without a Heaf test. 95 contacts were unnecessarily tested. 87 contacts had chest radiography unnecessarily and seven should have had radiography but did not. 34 contacts were given follow up appointments inappropriately and seven were overlooked for follow up. Tuberculosis was diagnosed in five asymptomatic contacts, all at initial screening and all close contacts of index patients with pulmonary disease. CONCLUSION--Inadequacy of data, non-adherence to contact tracing guidelines, and failure to define the term highly infectious index case resulted in many contacts being unnecessarily screened or followed up. IMPLICATIONS--The efficiency of tracing contacts would be improved by specifying smear results and ethnic origin of the index case on the notification form, clearly classifying contacts as close or causal, and clearly defining the term highly infectious.     

Evaluating Spatial Overlap and Relatedness of White-tailed Deer in a Chronic Wasting Disease Management Zone

Wildlife disease transmission, at a local scale, can occur from interactions between infected and susceptible conspecifics or from a contaminated environment. Thus, the degree of spatial overlap and rate of contact among deer is likely to impact both direct and indirect transmission of infectious diseases such chronic wasting disease (CWD) or bovine tuberculosis. We identified a strong relationship between degree of spatial overlap (volume of intersection) and genetic relatedness for female white-tailed deer in Wisconsin’s area of highest CWD prevalence. We used volume of intersection as a surrogate for contact rates between deer and concluded that related deer are more likely to have contact, which may drive disease transmission dynamics. In addition, we found that age of deer influences overlap, with fawns exhibiting the highest degree of overlap with other deer. Our results further support the finding that female social groups have higher contact among related deer which can result in transmission of infectious diseases. We suggest that control of large social groups comprised of closely related deer may be an effective strategy in slowing the transmission of infectious pathogens, and CWD in particular.     

Gonorrhea modeling: a comparison of control methods

A population dynamics model for a heterogeneous population is used to compare the effectiveness of six prevention methods for gonorrhea involving population screening and contact tracing of selected groups. The population is subdivided according to sex, sexual activity, and symptomatic or asymptomatic infection. For this model contact tracing of certain groups is more effective than general population screening.     

Pooled testing of traced contacts under superspreading dynamics

Testing is recommended for all close contacts of confirmed COVID-19 patients. However, existing pooled testing methods are oblivious to the circumstances of contagion provided by contact tracing. Here, we build upon a well-known semi-adaptive pooled testing method, Dorfman’s method with imperfect tests, and derive a simple pooled testing method based on dynamic programming that is specifically designed to use information provided by contact tracing. Experiments using a variety of reproduction numbers and dispersion levels, including those estimated in the context of the COVID-19 pandemic, show that the pools found using our method result in a significantly lower number of tests than those found using Dorfman’s method. Our method provides the greatest competitive advantage when the number of contacts of an infected individual is small, or the distribution of secondary infections is highly overdispersed. Moreover, it maintains this competitive advantage under imperfect contact tracing and significant levels of dilution.     

Epidemic management and control through risk-dependent individual contact interventions

Testing, contact tracing, and isolation (TTI) is an epidemic management and control approach that is difficult to implement at scale because it relies on manual tracing of contacts. Exposure notification apps have been developed to digitally scale up TTI by harnessing contact data obtained from mobile devices; however, exposure notification apps provide users only with limited binary information when they have been directly exposed to a known infection source. Here we demonstrate a scalable improvement to TTI and exposure notification apps that uses data assimilation (DA) on a contact network. Network DA exploits diverse sources of health data together with the proximity data from mobile devices that exposure notification apps rely upon. It provides users with continuously assessed individual risks of exposure and infection, which can form the basis for targeting individual contact interventions. Simulations of the early COVID-19 epidemic in New York City are used to establish proof-of-concept. In the simulations, network DA identifies up to a factor 2 more infections than contact tracing when both harness the same contact data and diagnostic test data. This remains true even when only a relatively small fraction of the population uses network DA. When a sufficiently large fraction of the population (≳ 75%) uses network DA and complies with individual contact interventions, targeting contact interventions with network DA reduces deaths by up to a factor 4 relative to TTI. Network DA can be implemented by expanding the computational backend of existing exposure notification apps, thus greatly enhancing their capabilities. Implemented at scale, it has the potential to precisely and effectively control future epidemics while minimizing economic disruption.     

Epidemic Contact Tracing via Communication Traces

Traditional contact tracing relies on knowledge of the interpersonal network of physical interactions, where contagious outbreaks propagate. However, due to privacy constraints and noisy data assimilation, this network is generally difficult to reconstruct accurately. Communication traces obtained by mobile phones are known to be good proxies for the physical interaction network, and they may provide a valuable tool for contact tracing. Motivated by this assumption, we propose a model for contact tracing, where an infection is spreading in the physical interpersonal network, which can never be fully recovered; and contact tracing is occurring in a communication network which acts as a proxy for the first. We apply this dual model to a dataset covering 72 students over a 9 month period, for which both the physical interactions as well as the mobile communication traces are known. Our results suggest that a wide range of contact tracing strategies may significantly reduce the final size of the epidemic, by mainly affecting its peak of incidence. However, we find that for low overlap between the face-to-face and communication interaction network, contact tracing is only efficient at the beginning of the outbreak, due to rapidly increasing costs as the epidemic evolves. Overall, contact tracing via mobile phone communication traces may be a viable option to arrest contagious outbreaks.     

Two-Step Source Tracing Strategy of Yersinia pestis and Its Historical Epidemiology in a Specific Region

Source tracing of pathogens is critical for the control and prevention of infectious diseases. Genome sequencing by high throughput technologies is currently feasible and popular, leading to the burst of deciphered bacterial genome sequences. Utilizing the flooding genomic data for source tracing of pathogens in outbreaks is promising, and challenging as well. Here, we employed Yersinia pestis genomes from a plague outbreak at Xinghai county of China in 2009 as an example, to develop a simple two-step strategy for rapid source tracing of the outbreak. The first step was to define the phylogenetic position of the outbreak strains in a whole species tree, and the next step was to provide a detailed relationship across the outbreak strains and their suspected relatives. Through this strategy, we observed that the Xinghai plague outbreak was caused by Y. pestis that circulated in the local plague focus, where the majority of historical plague epidemics in the Qinghai-Tibet Plateau may originate from. The analytical strategy developed here will be of great help in fighting against the outbreaks of emerging infectious diseases, by pinpointing the source of pathogens rapidly with genomic epidemiological data and microbial forensics information.     

Leprosy New Case Detection Trends and the Future Effect of Preventive Interventions in Pará State,Brazil: A Modelling Study

BackgroundLeprosy remains a public health problem in Brazil. Although the overall number of new cases is declining, there are still areas with a high disease burden, such as Pará State in the north of the country. We aim to predict future trends in new case detection rate (NCDR) and explore the potential impact of contact tracing and chemoprophylaxis on NCDR in Pará State.MethodsWe used SIMCOLEP, an existing individual-based model for the transmission and control of M. leprae, in a population structured by households. The model was quantified to simulate the population and observed NCDR of leprosy in Pará State for the period 1990 to 2014. The baseline scenario was the current control program, consisting of multidrug therapy, passive case detection, and active case detection from 2003 onwards. Future projections of the NCDR were made until 2050 given the continuation of the current control program (i.e. baseline). We further investigated the potential impact of two scenarios for future control of leprosy: 1) discontinuation of contact tracing; and 2) continuation of current control in combination with chemoprophylaxis. Both scenarios started in 2015 and were projected until 2050.ResultsThe modelled NCDR in Pará State after 2014 shows a continuous downward trend, reaching the official elimination target of 10 cases per 100,000 population by 2030. The cessation of systematic contact tracing would not result in a higher NCDR in the long run. Systematic contact tracing in combination with chemoprophylaxis for contacts would reduce the NCDR by 40% and bring attainment of the elimination target two years forward to 2028.ConclusionThe NCDR of leprosy continues to decrease in Pará State. Elimination of leprosy as a public health problem could possibly be achieved around 2030, if the current control program is maintained. Providing chemoprophylaxis would decrease the NCDR further and would bring elimination forward by two years.     

Outbreak of tuberculosis after minimal exposure to infection.

The identification of a case of respiratory tuberculosis in a swimming-baths attendant whose sputum was smear positive was followed by intensive contact tracing of children aged 8-11 years who had visited the baths. An outbreak was discovered that otherwise might not have been detected. Out of 3764 children, 108 (2.9%) had evidence of infection: there were 16 cases of tuberculosis, of which 11 were symptomless but showed lesions on chest radiography, and a further 92 with tine test grade 3 or 4 without clinical or radiological signs. The contact of these children with the index case was apparently minimal. Early detection, isolation, and treatment of infectious cases of respiratory tuberculosis and vigorous contact tracing should be given more priority in tuberculosis control.     

Occupational risk of tuberculosis transmission in a low incidence area

Background

To investigate the occupational risk of tuberculosis (TB) infection in a low-incidence setting, data from a prospective study of patients with culture-confirmed TB conducted in Hamburg, Germany, from 1997 to 2002 were evaluated.

Methods

M. tuberculosis isolates were genotyped by IS6110 RFLP analysis. Results of contact tracing and additional patient interviews were used for further epidemiological analyses.

Results

Out of 848 cases included in the cluster analysis, 286 (33.7%) were classified into 76 clusters comprising 2 to 39 patients. In total, two patients in the non-cluster and eight patients in the cluster group were health-care workers. Logistic regression analysis confirmed work in the health-care sector as the strongest predictor for clustering (OR 17.9). However, only two of the eight transmission links among the eight clusters involving health-care workers had been detected previously. Overall, conventional contact tracing performed before genotyping had identified only 26 (25.2%) of the 103 contact persons with the disease among the clustered cases whose transmission links were epidemiologically verified.

Conclusion

Recent transmission was found to be strongly associated with health-care work in a setting with low incidence of TB. Conventional contact tracing alone was shown to be insufficient to discover recent transmission chains. The data presented also indicate the need for establishing improved TB control strategies in health-care settings.