article: In many infectious diseases, a core group of individuals plays a disproportionate role in transmission. If these individuals were effectively prevented from transmitting infection, for example with a perfect vaccine, then the disease would disappear in the remainder of the community. No vaccine has yet proven effective against the ocular strains of chlamydia that cause trachoma. However, repeated treatment with oral azithromycin may be able to prevent individuals from effectively transmitting trachoma. Here we assess several methods for identifying a core group for trachoma, assuming varying degrees of knowledge about the transmission process. We determine the minimal core group from a completely specified model, fitted to results from a large Ethiopian trial. We compare this benchmark to a core group that could actually be identified from information available to trachoma programs. For example, determined from the rate of return of infection in a community after mass treatments, or from the equilibrium prevalence of infection. Sufficient groups are relatively easy for programs to identify, but will likely be larger than the theoretical minimum.
  Core groups can play a disproportionate role in transmission of an infectious disease [1–3]. If transmission were terminated in this group, the disease would by definition eventually disappear in the entire community [1]. Important key populations have been proposed for sexually transmitted infections such as gonorrhea and HIV, as well as non-sexually transmitted diseases such as trachoma [3–10]. For vaccine-preventable diseases, the group sufficient to vaccinate to achieve herd immunity constitutes a core group. No vaccine has yet been proven effective for trachoma. However, intensive drug administration could effectively remove a core group from transmission, preventing infection from being sustainable in the remainder of the community [5]. Young age and previous infection are by far the largest risk factors for transmission of ocular chlamydia, the causative organism of trachoma [11,12]. Children have a longer duration of infection and higher load than adults [13,14]. In one study, repeated targeting of children reduced infection in untreated adults, suggesting a form of herd protection [15]. In another, essentially no infection could be found in adults after three years of repeated treatment of children [16]. A modeling study suggested that treating children under 10 annually could eventually eliminate infection, limiting treatment to those under 5 years might require quarterly treatments to achieve a similar result [5]. Another important risk factor is prior infection. Those with clinical or laboratory findings of trachoma at one time point are at high risk at subsequent time points, even if cleared from infection in the interim, presumably due to special vulnerability or critical placement in the transmission network [11,17]. If all heterogeneities were identified and a mathematical transmission were completely specified, then a minimum core group could be determined analytically. However, this is rarely, if ever, feasible in practice. In this report, we hypothesize that a sufficient core group can be identified knowing very little detail about transmission. We use results from a large community-randomized trachoma trial to estimate a minimal core group for transmission. We compare several methods of estimating a sufficient core group, assuming various levels of information ranging from complete specification of the transmission dynamics to knowledge of the equilibrium prevalence alone.
  To explore the 5 different methods for determining a sufficient core group under different conditions, we modeled 3 possible scenarios:
  Given a transmission model estimated from the TANA study, the theoretical minimum core group includes 64% of the children and none of the adults for a total of 32% of the total population (Fig 1 and Table 1). Sufficient core groups using linear programming, the maximum eigenvalue, or the equilibrium prevalence included more than twice the total number of individuals. In the presence of years of mass annual treatment, a new equilibrium may be reached. Here, 21% of children and adults remain affected. A residual core group remains, in the presence of the annual treatments (Fig 2, Table 1). The sufficient core groups obtained from the rate of return of infection and from the residual equilibrium are still larger as the theoretical minimum of 15%, including 21–22% of the population. In the most severely affected areas, transmission can be sustained in either the children alone or the adults alone. Therefore, all sufficient core groups would necessarily include both children and adults. Here, the more practical methods approach the theoretical minimum (Fig 3, Table 1). In this scenario, both the primal (B) and dual (C) linear programs have identified core groups that contain both children and adults. Although the combinations are different, they contain the same number of individuals as demonstrated by the second (higher) grey iso-population line, as guaranteed by the Duality Theorem [18]. Note that transmission in adults in this scenario is likely unrealistically high, although we have included it as an illustrative example.
  A group of individuals who play a disproportionate role in the transmission of an infectious disease has been described by a number of terms, including key population, hyper-spreaders, and core group [10,23]. A stricter definition of a core group would be those individuals whose removal from transmission would be sufficient to prevent infectious trachoma from sustaining itself in the entire community [1,24]. Here, we have assumed that the process can be described by a mathematical transmission model in which individuals can be divided into a number of compartments, each one of which is homogeneous. From such a model, a sufficient core group can be estimated in a number of ways. As a relatively simple case, we divide a trachoma-endemic population into children and adults, and fit a simple model to data from a community-randomized trial in Ethiopia [15]. The fitted model allows a sufficient core group to be estimated using a number of methods. The smallest group whose removal from transmission results in the remainder of the population producing on average less than one case per infectious case. Under certain circumstances, the dual of this linear programming problem also may be a sufficient core group. If the dominant eigenvalue of a next generation matrix of the transmission model and the average duration of infectious cases in each of the groups are defined, then a sufficient core group can easily be determined. If the entire model is specified, then the absolute minimum sized core group can be found. Even when the precise details of the transmission model are not understood, a sufficient core group can still be estimated from epidemiological data. If we limit analysis to diseases that do not confer lifelong immunity and where current infection is a risk factor for future reinfection, then removal of those currently infected from future transmission would control the disease, leading to eventual elimination. For example, if infection is reduced by repeated mass antibiotic distributions given to the entire community, then it should return at a rate dependent on the maximum eigenvalue of the next generation matrix. If the average duration of infection is known, then the dominant eigenvalue of this matrix can be estimated. If all but the proportion equal to the reciprical of this eigenvalue were removed from each compartment, then infection would eventually disappear. A more practical method for determining a sufficient core group requires knowledge of who was infected prior to treatment. If we assume that current infection is a risk factor for future reinfection. This allows determination of a core group in two settings: at the beginning of a program when transmission may have reached an equilibrium, and after years of annual MDA with a new equilibrium. In the former, the goal would be to find the group of people whose effective removal from transmission would lead to eventual elimination in everyone. Community-randomized trials have found that if a core group of children are effectively removed from transmission by quarterly antibiotic treatments, infection decreases in the remainder of the community [15]. If mass antibiotics are repeated, elimination can be achieved even though not everyone was actually treated. In the setting where years of annual mass treatment have not eliminated infection, then the goal might be to find a residual core group whose removal from transmission would result in elimination if future annual mass treatment were also continued. In several areas, more than 5 years of mass azithromycin distributions have left a small amount of persistent infection [25,26]. This group could represent a residual core group. The equilibrium approach to finding a sufficient core group is dependent on a number of assumptions. For the equilibrium to form a core group, currently infected cases must be at least as likely to participate in future transmission as uninfected cases. This would not be true for an infection where acquired immunity outweighs other risk factors. Note that removing those infected at equilibrium from transmission would be expected to work regardless of whether we understand the heterogeneity in the community. Underestimates of prevalence would lead to models underestimating the size of the core group. We modeled 3 scenarios of different endemicity, reflecting different transmission. Future study could explore scenarios with an even broader spectrum of heterogeneity. While method 1 assumed an SIS model structure, that is not necessary for the other methods. However, we have assumed that current infection is a risk factor for future infection, or at least does not offer protection. If this assumption were violated, more analysis would be necessary. Sufficient core groups can be estimated from information available to trachoma control programs. The use of WHO simplified grades rather than infection data would result in a larger, more conservative estimate of the core group. In moderately affected areas, information taken from baseline surveys could be used to reduce the proportion of the population treated. In the few severely affected areas where residual core group indicates that annual MDA is inadequate, enhanced targeting of a core group might be necessary for elimination. Enhanced intervention targeted to core groups would require additional resources, but may be the final key for successful trachoma control. Resources can be directed towards core groups at the beginning of a program, or towards a residual core groups resistant to elimination in the presence of standard annual mass azithromycin distribution [21]. Precise transmission models are not absolutely necessary to estimate sufficient core groups. These models are hypothesis generating. While strategies based on core groups have been tested in community-randomized trials, the efficacy of a strategy based on residual core groups will need to be tested in current and future trials (U10 EY023939 and UG1 EY028088) [15,16,27].
summary: Public health programs can in theory target treatment to a core group of individuals responsible for a disproportionate amount of transmission. The smallest group of individuals who need to be vaccinated to eventually eliminate an infectious disease is easy to find in theory, but not in practice. While no vaccine has proven effective for trachoma, intensive periodic treatment may be able to effectively prevent individuals from transmitting infection. Here we use a variety of methods to find a core group for trachoma transmission, including methods that use information available to trachoma programs. We show that the rate that infection returns into a community after mass treatment, or the pre-treatment prevalence of an infectious disease should work, but will include more individuals than the theoretical minimum core group.
keywords: antimicrobials
  medicine and health sciences
  drugs
  tropical diseases
  microbiology
  geographical locations
  vaccines
  bacterial diseases
  mathematics
  antibiotics
  eye diseases
  sexually transmitted diseases
  algebra
  neglected tropical diseases
  linear programming
  pharmacology
  infectious disease control
  ethiopia
  africa
  research and analysis methods
  infectious diseases
  chlamydia infection
  mathematical functions
  mathematical and statistical techniques
  people and places
  linear algebra
  ophthalmology
  microbial control
  biology and life sciences
  physical sciences
  trachoma
  eigenvalues
title: Identifying a sufficient core group for trachoma transmission