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Department of Infectious Disease Epidemiology, Imperial College Faculty of Medicine
Centre for Sexual Health and HIV Research, Royal Free and University College Medical School, London, United Kingdom
Prompt treatment of infectious diseases plays an important role in infection control. In the face of the increasing incidence of sexually transmitted infection, the ability of genitourinary medicine services to provide appropriate and timely care is reduced. To explore the relationship between capacity and demand for care, we developed and analyzed a mathematical model of gonorrhea transmission, incorporating patient flow through treatment services and heterogeneity in sexual risk behavior. Two equilibrium levels of infection incidence"high" and "low"exist for the same parameter values, and which of them occurs depends on starting conditions. At the high-incidence equilibrium, there is a "vicious circle" in which inadequate treatment capacity leads to many untreated infections, generating further high incidence and high demand and thus maintaining the inadequacy of services. A substantial increase in capacity is needed to interrupt this process and enter a "virtuous circle," in which adequate service provision keeps demand low, offering cost savings as well as improvements in health.
As with other curable infectious diseases, such as tuberculosis, a key component of bacterial sexually transmitted infection (STI) control is timely and appropriate treatment of infected individuals through easily and rapidly accessible treatment services, which reduces the duration of infection and, thus, the likelihood of onward transmission and of sequelae in the infected individual [1]. (Other components include primary prevention through education and condom promotion, as well as screening and active case finding.) Treatment-seeking behavior of patients and, crucially, their response to delays in receiving care will have a major impact on the spread of infection. We constructed a mathematical model of the patterns of STI service provision in Britain; although our model structure is not directly applicable to other systems, the general principles highlighted are widely applicable.
Currently in Britain, there is a resurgence of bacterial STIs, with the number of annual diagnoses of chlamydia and gonorrhea having doubled between 1997 and 2002, to 82,206 and 24,958 diagnoses, respectively [2]. The supply of genitourinary medicine (GUM) services has not kept up with this increased demand, which has led to treatment services becoming overstretched. Most GUM clinics no longer offer walk-in access, and typical waiting times for GUM services have increasedoften to weeks for an initial consultation [36]which inevitably means that some patients will be unable to obtain GUM-clinic care. Symptomatic patients are frequently unable to obtain timely care [4]. Many patients will seek care from their general practitioner (GP), where the current standard of care is variable: some GPs prescribe inappropriate treatment, many do not test for STIs, and many simply refer patients to GUM clinics [7, 8]. Other patients will not receive care at all: some patients do not go to their GP because of the stigma or are not registered with one [9]. Consequently, the proportion of cases treated appropriately has declined, and those who are treated are waiting longer, on average, to receive care. Both factors increase the average duration of infection, causing an increase in prevalence with a consequent increase in incidence, further stretching the health-care system.
Here, we explore the theoretical impact of GUM service capacity on the incidence of gonorrhea and the demand for treatment. Many diseases place demands on GUM clinics, but we consider just one infection, to understand clearly how the dynamics of patient treatment-seeking behavior and GUM-clinic capacity interact to affect the epidemiology of this infection. In particular, we consider the interaction between waiting times and patient treatment-seeking behavior. The novel features of our mathematical model are (1) the GUM-clinic appointment process, (2) the effect of GUM-clinic waiting time on the proportion of patients who choose to consult their GP instead of using the GUM clinic, and (3) patients who are "lost" to treatment because they do not persevere in seeking care at the GUM clinic. We identify the dynamic behavior of the system and the likely important parameters that should be measured in empirical studies of GUM service performance. We also address the prospects for reducing STI incidence through increased service capacity.
METHODS
Overview.
A mathematical model of gonorrhea, based on that of Hethcote and Yorke [10], was further developed to describe the spread of infection and treatment-seeking behavior of British heterosexual individuals 1645 years of age. Eighty-five percent of GUM-clinicdiagnosed gonorrhea infections occur in heterosexuals [11], and those 1645 years of age experience 95% of those infections and have the best behavioral data available [12]. The model population comprises 100,000 heterosexual individuals, with equal numbers of each sex. There is no mortality, and the rate of entry into the population (E) at age 16 years is set to maintain a constant population size and age structure. Individuals leave the population on their 46th birthday. The population is stratified, by age (into six 5-year age classes), sex, and "activity" class, into subgroups with characteristic rates of heterosexual partner change. In the model, an individual's sexual behavior is determined by sex, age, and activity class. Estimates of rates of sex-partner change (table 1) were obtained by analysis of unpublished data from the British National Survey of Sexual Attitudes and Lifestyles in 2000 ("Natsal 2000") [12], by fitting a Weibull function to the frequency distribution of the reported number of new partners during the past year, stratified by sex and age class, and then discretizing the fitted continuous distribution into activity classes. For simplicity, we used 5-year age categories and, thus, assumed that individuals who are 45 years of age (who were not surveyed in Natsal 2000) have the same sexual behavior as those who are 4144 years of age. Mixing coefficients (1 and 2, which describe patterns of partner choice with respect to age and sexual behavior; see the Appendix) and transmission probabilities (0 and 1) were taken from a previous study [13]. The model comprises a set of partial differential equations (see the Appendix), which were solved numerically by use of the programming language C++. Here, we describe the "flow" of individuals through the health-care system.
Behavior of infected individuals and their flow through the health-care system.
The model (figure 1) provides a simplified description of the process of seeking and receiving care, which captures the essential details by dividing the population into compartments according to infection status and health-careseeking status. Those compartments are stratified by sex (k), age (a), activity class (l)and, in the case of the GUM-clinic compartment (see below), waiting time (w)and have a time dimension (t). Parameter estimates are summarized in table 2. In the model, after infection, individuals leave the susceptible compartment, Skl(a,t); those who do not seek care enter the untreated compartment, Ukl(a,t); and those who do seek care enter the reporting delay compartment, Rkl(a,t). Disease signs are associated with gonorrhea in 50% of women (p0 = 0.5) and 90% of men (p1 = 0.9) [10], and, in the British context, we assume that the majority (90%) of those with disease signs will recognize them as symptoms and seek care (s = 0.9). Untreated individuals eventually recover from infection through natural immune processes, returning to the susceptible compartment. Estimates of the mean infectious period in untreated individuals (1/) are typically in the range of 26 months [14, 15]; we use the geometric midpoint of the rangethat is, 3.5 months (21 weeks). Those in the reporting delay compartment seek care after a mean period (1/r) of 4 days [9], with proportion g(t) choosing a GP (Gkl(a,t)) and the remainder, 1 - g(t), choosing a GUM clinic (Ckl(a,t,w)). (The proportion g(t) is a function of the mean GUM-clinic waiting time and is described further below.) Most individuals seeking care (65%) abstain from sexual activity ( = 0.65) [16, 17]. When individuals seek care at a GUM clinic, they are given the earliest available appointment, which is represented in the model by adding them to the back of a queue in the "awaiting the GUM-clinic consultation" compartment, which is stratified by waiting time, as described above. As described by the "quitting" function, Q(w) (Appendix), those who seek GUM-clinic care abandon their attempts (and enter the untreated compartment), if not treated, at a rate of 4.95% per day of waiting (q = 0.0495), set so that one-half will persevere for 2 weeks, and one-third will persevere for the maximum period (wmax) of 3 weeks [5], after which time they, too, abandon their attempts.
We assume that the proportion of those seeking care who initially consult a GP, g(t), has a minimum value (gmin) of 0.53 when the mean waiting time for those treated at GUM clinics (mean(t)) is negligible and that g(t) increases linearly with increasingly mean(t). We assume that g(t) has a maximum value (gmax) of 0.9, because 10% of GUM-clinic attendees are not registered with a GP, and some individuals who are registered would prefer not to see their GP [9]. In the model, g(t) reaches gmax when mean(t) is 2 weeks (our estimate of ). (See the Appendix for details of the estimation of gmin, gmax, and .) Both g(t) and mean(t) are dynamic (intrinsic) variables of the model, not extrinsically specified parameters; mean waiting time varies according to how well the GUM clinic is coping with demand and how long patients persevere in their attempts to obtain care. It is GUM-clinic capacity () that is extrinsically specified (see below). In contrast to GUM-clinic waiting time, we assume that the mean waiting time for GP consultation (1/g) is 2.5 days [9] and does not vary with demand for STI treatment, since it represents a very small proportion of a typical GP's case load, so even a large proportionate change in demand for STI treatment will have a very small effect on the GP's total case load and associated waiting times. We assume that all those who seek a GP consultation obtain one.
After treatment at a GUM clinic (described by the "treatment" function, T(t,w); see the Appendix), individuals return to the susceptible compartment; for simplicity, we assume that this occurs immediately, which is reasonable for cases of gonorrhea that are diagnosed on the basis of disease signs and treated with a single-dose antibiotic. Typically, GPs are reluctant to treat STIs, but we assume that when GUM-clinic waiting times are long, GPs will be more willing to do so. In the model, the proportion of patients treated by GPs, (t), increases linearly with the mean GUM-clinic waiting time, mean(t), from its minimum value (min) of 0.4 [1820], when mean(t) is negligible, to its maximum (max) of 0.8, when mean(t) is 2 weeks (our estimate of ). We assume that 60% of gonorrhea cases treated by GPs are treated effectively (eg = 0.6), which is slightly higher than the proportion of chlamydia cases treated appropriately by GPs, because gonorrhea treatment requires a simpler regimen [8, 20]. Effectively treated patients reenter the susceptible compartment; ineffectively treated ones enter the untreated compartment. Those who seek treatment in a GUM clinic after a GP consultation are then assumed to have the same perseverance as those who did not consult a GP.
To estimate the baseline GUM-clinic capacity for treatment of gonorrhea (), we divided the annual number of GUM-clinic diagnoses of gonorrhea in heterosexuals 1645 years of age in Britain in 2002 (21,236, based on [11] and data obtained by request from Health Protection Scotland [contact details available at: http://www.hps.scot.nhs.uk/]; see the Appendix) by the number of individuals in that age range (23.6 million [21]), giving an estimate of 90 cases per 100,000 persons 1645 years of age per year. Note that this estimates the "effective" capacity that is available to treat gonorrhea, which is one of many demands on GUM clinics. We examine the effect that varying has on the incidence of infection and the demand for health care.
RESULTS
Bistability: high- and low-incidence equilibria for the same parameter values.
The model has 2 equilibria (steady states) where infection is present. One equilibrium has a "high" incidence and prevalence of infection, when the GUM clinic is failing to cope with demand: GUM-clinic waiting times are long, many patients are treated by GPs instead, and relatively few patients are treated at all. There is a "vicious circle": on average, infected individuals remain infectious for some time, causing high incidence and thus maintaining high demand for treatment services. In contrast, at the other ("low") equilibrium, there is a "virtuous circle": there is a low incidence and prevalence of infection, and the GUM clinic is coping with demand for treatment: all patients seeking GUM-clinicbased care receive it in a timely manner, so most patients with STIs are treated at the GUM clinic rather than by GPs, GUM-clinic waiting times are short, and few patients are lost to treatment.
Bringing infection under control from the high-incidence equilibrium.
From a starting point at the high-incidence equilibrium, if the capacity of the GUM clinic is increased by a relatively small amount, then the number of patients treated at the GUM clinic per unit time is increased, which reduces the equilibrium prevalence and incidence of infection by a small amount; however, the GUM clinic remains at "full stretch," and waiting times are not reduced significantly (figure 2A). If clinic capacity is increased by a sufficiently large amount, however, then there is a sustained decline to a low equilibrium in which the clinic is coping with demand (figure 2B2D). The vicious circle is broken and a virtuous circle is entered: rates of transmission of infection are reduced by increasingly rapid treatment of an increasing proportion of infected individuals, thus reducing demand for treatment services and further improving the quality of care. However, some transmission continues, mainly because not all infected persons seek care. At the low-incidence equilibrium, the rate of treatment at the GUM clinic is less than at the starting high-incidence equilibrium (figure 2B2D), so, in addition to greatly improved sexual and reproductive health of the population, there are potential cost savings accruing from bringing transmission of infection under control. However, it does take some time for the demand for treatment to fall to within the clinic's capacity and, thus, for the benefit of the intervention to become apparent from routine surveillance and monitoring of waiting times.
The greater the increase in clinic capacity, the more rapidly incidence is brought under control and the more short term that increase in capacity can be. Consequently, within reasonable limits, it is more cost-effective to have a larger increase in capacity than a smaller one.
Importantly, the equilibrium position is the state that the system moves toward, and it can take some time to reach that state (figure 2). This means that, if control is lost, then the sooner an increase in capacity is made, the smaller it needs to be to catch up with the epidemic and regain control. The capacity increase only needs to reach the threshold for gaining control (G) of the high-incidence equilibrium (figure 3) if the system has been allowed time to return to that equilibrium. As a corollary, it also takes time to gain control of spreading of infection, so interventions may take years to have their full effect.
DISCUSSION
Our analysis of a model describing treatment of gonorrhea in Britain has exposed critical dynamic behaviors that are generally applicable to planning health care for infectious diseases for which appropriate timely treatment limits further spread and service capacity affects treatment provision. The fundamental principle is that inadequate treatment capacity results in preventable onward transmission of infection, which maintains high demand for treatment. Similar results were found for the control of hospital-acquired methicillin-resistant Staphylococcus aureus [22].
The model demonstrates the importance of timely delivery of appropriate health care in preventing the onward transmission of infection. There are 2 equilibria (steady states) where infection is present, which the system can "flip" between, depending on rates of health-care provision relative to demand. In terms of resources, it is easier to maintain control of transmission than to regain it once it has been lost, since the threshold level of provision required to move away from the high-incidence, "out-of-control" equilibrium (G) is greater than the threshold for loss of control (L). A sufficiently large increase in GUM-clinic capacity can bring infection under control by reducing waiting times and, thus, greatly increasing the proportion of infections that receive treatment. Increased capacity is required only temporarily, because gaining control of spreading of infection reduces future demand for treatment. The larger this increase in capacity, the more short term it can be (figure 2). Also, the sooner this increase occurs, the smaller it needs to be to catch up with the epidemic before it reaches the high-incidence equilibrium. Gaining control of transmission reduces the number of future infections requiring treatment and the incidence of complications such as infertility.
Currently in Britain, it appears that GUM-clinic capacity is overwhelmed and that the spreading of STIs is out of control, with both waiting times and rates of treatment of infection (which underestimate the true incidenceand by an increasing amount as waiting times increase) increasing [25]. That is, it appears that the system is moving toward the high-incidence equilibrium. Although the model considers just 1 of the infections treated by GUM clinics (i.e., gonorrhea) and considers only heterosexuals, this allows us to focus on the fundamental dynamics of treatment-seeking behavior and treatment service capacity, which are generally applicable (e.g., to other STIs and to homosexuals as well as heterosexuals). In fact, different infections may indirectly promote each other's spread, since an increase in the incidence of one infection increases the demand placed on GUM-clinic capacity, which reduces the capacity available for treatment of other infections. Conversely, gaining control of the spreading of one infection increases the capacity that is available to treat other infections.
Increasing the capacity for treatment of acute infections requires allocation of increased resources to GUM clinics, along with other measures, such as reducing the number of follow-up appointments and routine test of cure [5, 23]. A significant demand is placed on GUM-clinic capacity by individualsmany of whom may be at low risk of infection ("the worried well")seeking reassurance through diagnostic screening for infections such as chlamydia. This could be reduced by improving STI screening and treatment services offered by GPs [9] and promoting their use by patients.
The present study has highlighted several requirements for novel empirical data. Particularly important questions are how the length of the waiting time at GUM clinics affects the proportion of patients who choose to obtain care there, how long those patients persevere in seeking GUM-clinic care, where patients seek care as an alternative to GUM clinics, and what quality of care they receive from different clinical services. The model shows that, when GUM clinics are overstretchedas, at present, in Britainthe incidence of infection may be substantially greater than the recorded rate of GUM-based diagnoses, partly because more diagnoses will be made by GPs but also because many infections will go undiagnosed. At present, data on the proportion of incident infections that go untreated are lacking, so empirical studies should estimate the proportion of patients who seek, but fail to obtain, appropriate care. It is known that, for chlamydia, there is a high prevalence of untreated infection in Britain [24, 25], and, although data for gonorrhea are lacking, a US study that found chlamydia at a prevalence similar to that in the United Kingdom also found a high prevalence of untreated gonorrhea [26].
The important waiting time is the duration between the patient first seeking care and receiving that care, which may be much longer than the time between successfully obtaining an appointment for a consultation and attending that consultation. Many GUM clinics now book appointments only for a limited time ahead (e.g., 48 h) [5], so the true waiting time is not apparent from the appointment-booking system and must be obtained from patients at the consultation. Importantly, there is no simple, routine way to measure the waiting times of patients who abandon their attempts to obtain care and so do not attend a consultation.
Increases in sexual risk behavior in Britain [12] will have played a part in causing GUM-clinic services to become overstretched, by shifting the losing-control threshold (L) (as well as the gaining-control threshold, G) to higher GUM-clinic capacities, prompting the loss of control of the spreading of STIs and causing the system to move toward the high-incidence equilibrium. There may be a need for a sustained increase in the underlying capacity to meet the increased demand associated with increased risk behavior. Nevertheless, the key message of this articlethat is, that a temporary (additional) increase in capacity to bring the spreading of STI under control brings long-term benefitsstill holds. Furthermore, the stochastic introduction of infection into densely connected sexual-partnership networks can cause episodic increases in incidence [27]; without spare capacity, such episodes can trigger a shift toward the high-incidence equilibrium, causing a long-term loss of control of infection with extensive adverse consequences.
Acknowledgments
We thank the principal investigators of the British National Survey of Sexual Attitudes and Lifestyles 2000 study for providing access to the data, and Anne Johnson additionally provided helpful comments. Two anonymous referees also made useful suggestions. G.P.G. and P.J.W. thank the Wellcome Trust, and J.A.C., G.P.G., and C.H.M. thank the UK Medical Research Council, for grant support.
APPENDIX
MODEL EQUATIONS AND DETAILED DESCRIPTION
Model equations.
Model equations are given below; see Methods for definitions of symbols. Note that entry into the GUM-clinic compartment, Ckl(a,t,w)referred to hereafter as the "clinic" compartmentoccurs only at the boundary w = 0 (see the expressions for boundary conditions below). However, individuals can leave the clinic compartment after any waiting time; hence, the rates of movement from the clinic compartment to other compartments are integrals over the w dimension.
and
where the subscript i denotes age class (numbered 05), kli(t) is the force of infection (see below), min(t) is the minimum waiting time of GUM-clinic patients who are treated at time t, and other symbols are as defined in Methods and in table 2.
The total number of individuals of sex k, activity class l, in age class i, Nkli(t), is given by the expression
Boundary conditions.
Those entering the model population are all uninfectedthat is,
and
where E is the rate of entry into the population, which is equal to number of individuals of each sex in the total population (50,000) divided by duration spent in the model population (30 years)that is, 1666.667 per yearand Pl is the proportion of individuals that are in activity class l (see table 1). Entry into the clinic compartment occurs only at the boundary w = 0that is,
Force of infection.
The force of infection (i.e., the probability of infection per unit time) experienced by a susceptible individual is a function of the transmission probability per partnership (, which depends on the sex of the partner), the rate of sex partner change of the individual, the age class and activity class of the individual's chosen partners, and the prevalence of infection among those chosen partners [28].
The expression for the force of infection experienced by individuals of sex k, age class i, in activity class l who choose partners of sex k (opposite sex to k), age class j, in activity class m is
where c is the "adjusted" partner change rate resulting from the "compromise" in partner change rates (see below), and klmij is the mixing matrix (see below).
Patterns of partner choice are described by the mixing matrix, klmij, whose elements indicate the proportion of sex partners chosen from each age and activity class by opposite-sex individuals in each age and activity class. The formula for the mixing matrix is
where 1 and 2 are the mixing coefficients (see below) with respect to age and activity class, respectively; c is the partner change rate of individuals of sex k activity class m, age class j; N is the total number of individuals of sex k, activity class m, age class j; and ij and lm are identity matrices.
Patterns of mixing vary from random (proportionate) to fully assortative (like with like) with respect to age and activity class, determined by the parameters 1 and 2, respectively, where the value 1 represents random mixing and 0 represents assortative partner choice. In a closed heterosexual population, the number of partnerships chosen by women must equal the number chosen by men. Since there is a discrepancy, with more partnerships being reported by men [12], we "balance" the partnerships by use of the approach of Garnett and Anderson [28] in which, for each combination of age and activity class of index partner and chosen partner, partner change rates are adjusted so that the number of partnerships formed per unit of time is equal. In Garnett and Anderson's original formulation, the degree of "compromise" between the sexes could be adjusted, on a continuous scale, from one or other sex dominating; here, for simplicity, we assume a fixed, equal compromisethat is, the balanced number of partnerships is the geometric mean of the numbers of partnerships desired by the 2 sexes. Thus, our expression for the adjusted partner change rate is
Treatment of patients at the GUM clinic.
The GUM clinic treats patients seeking care in order of time spent waiting, with those who have waited longest being treated first. Hence, the clinic compartment has an additional dimension, that of the time spent waiting for treatment (w). At each point in time, everyone seeking GUM-clinic care who has waited longer than a certain (variable) time is treated, and no one who has waited for less than this time is treated. This minimum waiting time of patients who receive treatment at time t, min(t), is a dynamical variable that depends on GUM-clinic capacity and the demand for treatment at time t. min(t) is calculated by integrating the number of patients from the start of the "queue" (i.e., those who have been seeking GUM-clinic care the longest) toward the end, until GUM-clinic capacity () is reached, subject to the obvious constraint 0 min(t) < wmax, where wmax (a parameter) is the maximum time for which patients seek GUM-clinic care before abandoning their attempts ("quitting"). Note that patients are treated without regard to age, sex, or activity class. The expression for min(t) is
where wmax is the maximum time for which individuals wait for treatment before abandoning their attempts, and (t) is a dynamical variable that is calculated by solving the following expression for (t), subject to the obvious constraint, 0 (t) < wmax:
The per-capita rate of treatment of patients in the clinic compartment is described by the treatment function, T(t,w), which is a step function that takes the value 0 where w < min(t) and the value where w > min(t)that is,
Treatment of patients by GPs.
The proportion of patients treated (both effectively and ineffectively) by GPs, (t), ranges from a minimum value, min, when the mean GUM-clinic waiting time of those receiving treatment at time t, mean(t), is negligible, and increasing linearly with increasing mean(t) to its maximum value, max, which is attained when mean(t) = , where is the mean clinic waiting time that corresponds to max. (Note that (t) and mean(t) are variables, whereas min, max, and are parameters.) Thus,
where
and
Patients' choice of GP versus GUM clinic.
The proportion of patients seeking care who choose their GP, g(t), ranges from a minimum value, gmin, when the mean GUM-clinic waiting time of those receiving treatment at time t, mean(t), is negligible, rising linearly with increasing mean(t) to its maximum value, gmax, which is attained when mean(t) = , where is the mean GUM-clinic waiting time that corresponds to gmax. (Note that g(t) is a variable, whereas gmin, gmax, and are parameters.) Thus,
where
Patients abandoning attempts to obtain care.
Patients seeking care at the GUM clinic abandon their attempts at a per-capita rate that is a function of the length of time they have spent seeking care. For simplicity, we assume that this rate is a constant value, q, until patients have waited for time wmax, when they abandon their attempts. Thus, the "quitting" function, Q(w), is a combination of a step function (with value q where 0 < w < wmax and value 0 otherwise) and a Dirac delta function (with value where w = wmax and value 0 otherwise)that is,
Initialization.
Infection is established in the model population by initially setting GUM-clinic capacity () to 0; introducing infection into the highest activity class of each age class, for both sexes; and allowing the model to run to equilibrium. Subsequently, GUM-clinic capacity is increased.
PARAMETER ESTIMATES
GP referral rates to GUM clinics.
Two surveys of rates of referral to GUM clinics by GPs for patients with different STIs found that GPs reported referring smaller proportions of patients with chlamydia (25%85%) than with gonorrhea (80%95%) [18, 19]. However, since distinguishing between the 2 etiologies is difficult for the nonspecialist, we used an intermediate estimate, and, since another study reported that GPs typically refer 70% of male patients with urethral discharge to GUM clinics [20], we assumed that, overall, GPs refer 60% of patients with gonorrhea to GUM clinics and attempt to treat the remainder (i.e., (t) = 0.4). Since these studies were conducted before the recent rapid increase in demands on GUM clinics, we assumed that this estimate of (t) is its minimumthat is, min = 0.4.
Patients' choice of GP versus GUM clinic.
To estimate the proportion of patients who initially seek care with their GP, we used data from 2 empirical measures: (1) the proportion of GUM-clinic attendees who had previously seen their GP [9] and (2) GPs' reported rates of patient referral to GUM clinics [1820]. To use these data, we constructed 2 simultaneous equations to describe patient flows through health-care services as follows:
and
where each term is the number of individuals per year who follow a particular care and treatment path. I denotes those who initially obtain care or advice from their GP. Some of them (C) subsequently seek care at a GUM clinic, as a result of being formally referred or advised to attend by their GP or on their own initiative; others (T) have their conditions diagnosed and treated (correctly or incorrectly) by their GP. Other patients (I) initially obtain care from a GUM clinic. The rate at which patients are treated in the GUM clinic is denoted T.
To use the data that we have available to estimate the quantities of interest, let g be the proportion of patients with gonorrhea who are seen by their GP and are referred to GUM clinics, and let g be the proportion of GUM-clinic attendees who first consulted their GP. Thus,
and
We are interested in the proportion of patients who initially seek care from a GP, :
Combining equations (A1), (A2), and (A3), we obtain
As described above, we assumed that, overall, GPs refer 60% of patients with gonorrhea to GUM clinics when waiting times are short (i.e., g = 0.6). At a GUM clinic where the waiting time was short (median, 1 day), the proportion of GUM-clinic attendees who had already consulted their GP was 40% [9, 29], so we estimated g = 0.4. Substituting our estimates of g and g into equation (A4), we estimated = 0.53. Since was estimated using data from a clinic at which the waiting time was only 1 day [9, 29], we assumed that this is the proportion of those seeking care who initially consult a GP when GUM-clinic waiting times are negligiblethat is, we assumed that this is the minimum proportion of those who go to their GP (i.e., = gmin).
GUM-clinic treatment capacity for gonorrhea in heterosexuals.
In England and Wales, there were 20,493 gonorrhea diagnoses in 2002 (under the assumption that the age distribution of the 94 cases of unknown age was the same as that of those whose ages were known) [11], and there were 22.2 million individuals 1645 years of age in 2001 [21], giving an estimate of 92 cases per 100,000 persons 1645 years of age per year. The latest data for Scotland are from 2001 (data obtained by request from Health Protection Scotland [http://www.hps.scot.nhs.uk/]); therefore, to obtain an estimate for Britain (England, Wales, and Scotland) in 2002, we had to estimate the number of Scottish cases for that year. In the period 19962001, Scotland accounted for 3.5% of the gonorrhea cases in heterosexuals in Britain that were recorded in GUM clinics [11], and, if we assume that this was also the case for 2002, then the number of cases in Britain was 21,236, in a population of 23.6 million individuals 1645 years of age [21], giving 90 cases per 100,000 persons 1645 years of age per year.
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