Conceived and designed the experiments: MG MGB IJ DCM NCG. Performed the experiments: MG MGB DCM NCG. Analyzed the data: MG CAD NCG. Contributed reagents/materials/analysis tools: MG MJB AWS MJH NCG. Wrote the paper: MG MGB MJB AWS RLB MJH IMB CAD IJ DCM NCG. Contributed data. Contributed data: AWS. Developed and supervised laboratory testing: MJH.
The authors have declared that no competing interests exist.
Trachoma, the worldwide leading infectious cause of blindness, is due to repeated conjunctival infection with
The model is based on the concept of multiple reinfections leading to progressive conjunctival scarring, trichiasis, corneal opacity and blindness. It also includes aspects of trachoma natural history, such as an increasing rate of recovery from infection and a decreasing chlamydial load with subsequent infections that depend upon a (presumed) acquired immunity that clears infection with age more rapidly. Parameters were estimated using maximum likelihood by fitting the model to precontrol infection prevalence data from hypo, meso and hyperendemic communities from The Gambia and Tanzania. The model reproduces key features of trachoma epidemiology: 1) the ageprofile of infection prevalence, which increases to a peak at very young ages and declines at older ages; 2) a shift in this prevalence peak, toward younger ages in higher force of infection environments; 3) a raised overall profile of infection prevalence with higher force of infection; and 4) a rising profile, with age, of the prevalence of the ensuing severe sequelae (trachomatous scarring, trichiasis), as well as estimates of the number of infections that need to occur before these sequelae appear.
We present a framework that is sufficiently comprehensive to examine the outcomes of the A (antibiotic) component of the SAFE strategy on disease. The suitability of the model for representing populationlevel patterns of infection and disease sequelae is discussed in view of the individual processes leading to these patterns.
Trachoma is the worldwide leading infectious cause of blindness and is due to repeated conjunctival infection with
Trachoma is the leading infectious cause of blindness in the world; 8 million people are blind or severely visually impaired due to trachoma and 63 million have active disease
Previous mathematical models of trachoma infection at the population level have primarily looked at the effects of treatment with antibiotics, and the rebound in the prevalence of active disease that follows treatment cessation
A mathematical model of ocular infection with
The model developed here represents ocular infection with
A compartmental diagram illustrating the model described in the text. Each susceptible and infected compartment is connected to the compartment above so that the population passes up a ‘ladder’ of infection. The subscript
Since birth and death rates are important when determining prevalence levels of the more severe disease sequelae, the demography of the population is included in the model. The disease sequelae are more prevalent at older ages and, once the population has had the antibiotic component of the SAFE strategy successfully implemented, we assume that the rate at which disease prevalence levels decline depends upon mortality among older individuals. Agespecific death rates and the crude birth rate for The Gambia and Tanzania were based on WHO life table estimates for the year 2001
It is the explicit inclusion of disease sequelae, age structure, differential infectivity and immunity considerations that distinguish this model from those that have been previously reported
Several studies have postulated that the sequelae of trachoma are caused by immunopathological processes that increase in severity with increasing age
In trachomaendemic communities, bacterial infection load among individuals at young ages is higher than that at older ages
The model assumes that scarring worsens through repeat infection with
A schematic representation of the way in which the model determines the presence of disease sequelae: trachomatous scarring (TS) and trachomatous trichiasis (TT) (TS and TT—but not corneal opacity, CO—are considered to be caused exclusively by reinfection with
The model was fitted using maximum likelihood to preintervention prevalence and chlamydial load data collected in studies carried out in The Gambia and Tanzania, the details of which have been described by Burton
Location and country  Infection prevalence  Active disease prevalence  Source  Endemicity level 
Upper Saloum district, The Gambia  7%  8%  Hypoendemic (<10% active disease)  
Rombo district, Tanzania  10%  18%  Mesoendemic (10–20% active disease)  
Kongwa district, Tanzania  52%  36%  Hyperendemic (>20% active disease) 
Provenance of the data from three trachomaendemic regions that are used in this paper for model fitting. Active disease is measured as trachoma follicular (TF) and/or trachoma inflammation (TI) on the World Health Organization simplified grading scheme
The model was first fitted using maximum likelihood to the hyperendemic data set for which three distinct data types were available: ageprofiles of the prevalence of infection and the infection load from a community in Tanzania
Parameter  Parameter definition  Maximum likelihood estimate [95%CI] and units 
Mean duration of first infection  15.1 [6.5,23.3] months  
Mean duration of infection after multiple prior infections  2.8 [2.4, 3.2] months  
Rate of drop of duration of infection per prior infection  0.7 [0.1,∞] infection^{−1}  
Infection load per person at first infection  1.0×10^{5}[0.9, 1.3×10^{5}] copies 

Rate of drop of infection load per prior infection  0.05 [0.03, 0.07] infection^{−1}  
Transmission coefficient: the rate of transmission (per year) of infection between individuals  Hyperendemic: 27.7 [21.8, 35.1] year^{−1}  
Mesoendemic: 2.4 [2.0, 2.9] year^{−1}  
Hypoendemic: 1.8 [1.6, 2.1] year^{−1} 
Parameter definitions and estimates, with 95% confidence intervals, for the model obtained through maximum likelihood fitting using a function combining infection prevalence, bacterial load, and recovery rate data from a hyperendemic setting in Tanzania. The transmission parameters for the meso and hypoendemic settings were estimated by maximum likelihood by fitting to prevalence data only. The parameter symbols refer to the model definition detailed in
The curves shown in
Ageprofiles generated by the maximum likelihood parameter estimates to the hyperendemic data set of West
Ageprofiles of the prevalence of infection generated by fitting the model (solid lines) to the data (squares and 95% confidence interval error bars) from (A) Kongwa, Tanzania
The infection prevalence data come to a peak at young ages (roughly 5 years) in the hypo and mesoendemic areas examined here, with model fits mirroring such peaks. Furthermore, the data also show some evidence for a peak shift
The threshold numbers of infections necessary for individuals to show signs of each of the sequelae were calculated for the hyperendemic setting. These thresholds were estimated by maximum likelihood using the published data of Munoz
Prevalence curves for trachomatous scarring (solid line) and trachomatous trichiasis (dotted line) are shown along with the data from
The model presented in this paper reproduces many important aspects of trachoma epidemiology, namely: 1) the pattern of the prevalence of infection with age, which peaks at very young ages and then declines; 2) a peak shift towards younger ages in this prevalence in higher transmission settings; 3) a rise of the prevalence level with higher transmission; and 4) a rise with age of the prevalence of the severe disease sequelae. The model also allows estimates to be made of the threshold number of infections necessary for the appearance of the severe disease sequelae. Infection and disease profiles were obtained assuming longterm stability of prevalence levels in the model, and therefore represent the equilibrium, preintervention state in each of the endemicity settings. However, a limitation of the data used to estimate model parameters is that in some areas (
Following the fitting of the model to the datasets from the three endemic settings, the prevalence curves generated show a close correspondence with the trend in the observed profiles of infection prevalence with age. While good visual fits to the data are encouraging, a full analysis of the uncertainty in the parameter estimates is essential to judge how welldetermined the model fits are. In the younger ages, the prevalence peak is caused by the long duration of infection, high chlamydial loads and intense transmission that result from patterns of assortative mixing by age. Subsequently, the prevalence of infection drops at older ages, as a consequence of the ageassociated increase in the recovery rate from infection and the drop in infectivity with age: an individual who experiences an increasing number of infections recovers faster from each infection, with accompanying reductions in chlamydial load and infectivity. (In the model, the number of infections previously experienced tracks closely the age of an individual.) There is also a peak shift of the maximum infection prevalence towards younger ages (slightly greater than 5 years of age in the hypoendemic; slightly under 5 years in the mesoendemic, and very low (under 1 year) in the hyperendemic areas). For infectious diseases in general, this effect is usually due to acquired immunity and it occurs when individuals experiencing higher forces of infection either develop adaptive protective immunity earlier or clear their infection more rapidly at younger ages than they would in environments with lower force of infection. The observation of this phenomenon here lends further support to the importance of acquired immunity in trachoma
The recovery rate from infection rises very rapidly with the number of prior infections and the 95% confidence interval of the rate of this rise includes extremely large values at the upper end. This rapidity suggests that the immune response to the first few infections is qualitatively different to that of the bulk of subsequent infections and therefore the maturation of trachoma immunity occurs after only few infections, a finding that may also be associated with limited variation in the pathogen population. Indeed, the possibility of extremely large values for the rate at which the duration of infection changes with the number of infections (unbounded upper confidence limit of the rate
Infection bacterial loads are explicitly included in the model; the chlamydial loads for those who have experienced few infections are typically higher than for those who have experienced many. The reason behind this difference is thought to be the development of acquired immunity through repeated exposure to the bacteria that, although it does not protect from incoming infection, may reduce its intensity.
A model structure in which pathogen load is explicitly accounted for has been used extensively to model helminth infections, by assuming that acquired immunity to infection may be developed with cumulative infection experience and therefore with age, leading to peaked ageprofiles of infection intensity and prevalence
The prevalence levels of the disease sequelae were modeled under the assumption that individuals who had experienced greater than or equal to a specific threshold number of infections would begin to show signs of the ocular sequelae. Threshold infection numbers were therefore estimated corresponding to each of TS and TT; these calculations were performed for the hyperendemic setting, because it would only be in communities where there has been no intervention (at true endemic equilibrium) that the transmission and repeat infection rates will give rise to current disease sequelae prevalence levels. The threshold infection numbers for TS and TT estimated in this paper are dependent upon the data we have used for the duration of infection and infection load; a higher duration, for example, would decrease these estimates and so these values are contingent upon future longitudinal studies. In those communities (the hypo and mesoendemic areas in this paper) where there has been either some intervention or possibly a secular trend that has reduced transmission, the prevalence of those suffering from sequelae will, for some time, remain much higher than the current transmission level would suggest. Another explanation for differences here is the possibility that only a given fraction of the population progresses to each of the disease sequelae and this fraction may vary between populations due to factors such as the genetic predisposition to scarring of particular individuals in each population
Although our working hypothesis is that repeat chlamydial infection is the main route to the severe disease sequelae, it may not be the only one. Some studies show that, once established, scarring complications may continue to progress, perhaps driven by factors other than
In summary, the balance between ocular exposure to
Mathematical model outline and details on the likelihood.
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At the International Trachoma Initiative, Jacob Kumaresan and Felicity Turner provided invaluable encouragement and support.