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Conceived and designed the experiments: TML TCP RLB AWS MJB DM. Performed the experiments: KJR TML. Analyzed the data: KJR TML JDK. Contributed reagents/materials/analysis tools: KJR TML TCP JDK RLB MJB EHE MJH DM. Wrote the paper: KJR TML TCP JDK AWS DM.

The authors have declared that no competing interests exist.

Repeated mass azithromycin distributions are effective in controlling the ocular strains of chlamydia that cause trachoma. However, it is unclear when treatments can be discontinued. Investigators have proposed

A stochastic model of trachoma transmission was constructed, using the parameters with the maximum likelihood of obtaining results observed from studies in Tanzania (with 16% infection in children pre-treatment), The Gambia (9%), and Ethiopia (64%). The expected prevalence of infection at 3 years was obtained, given different thresholds for graduation and varying the characteristics of the diagnostic test.

The model projects that three annual treatments at 80% coverage would reduce the mean prevalence of infection to 0.03% in Tanzanian, 2.4% in Gambian, and 12.9% in the Ethiopian communities. If communities

Models suggest that graduating communities from a program when the infection is reduced to 5% is a reasonable strategy and could reduce the amount of antibiotic distributed in some areas by more than 2-fold.

Trachoma, the major cause of infectious blindness in the world, occurs when repeated infections of the ocular strains of

Over 40 million doses of oral azithromycin have already been distributed to control the ocular strains of chlamydia that cause trachoma

Less expensive diagnostic laboratory testing for infection may become available for trachoma programs in the near future. Estimates of the prevalence of infection using PCR-based tests can be made more cost-effective by sampling individuals within communities and by pooling several samples into one test

Data were collected in three countries at baseline, and 2 and 6 months after treatment as previously described

Previously, we constructed a simple stochastic SIS model (_{0}

For clarity, we expressed _{0} (where _{0}_{0} is defined as the mean number of secondary infectious cases caused by a single infectious case in an otherwise completely susceptible community

Parameters for this stochastic model were fitted to baseline and 6-month data for each country using maximum likelihood estimation. We initiated simulations at the average prevalence for that region, and simulated the Kolmogorov-forward equations for 40 years to allow the distribution of prevalence to approximate the pre-treatment distribution at time point zero. We also initiated the model at the observed 2-month prevalence and simulated the equations for 4 months to estimate the expected distribution of prevalence at 6-months. The total log-likelihood was the sum of the baseline and the 6 month log-likelihoods for each of the communities in the area. Note that any event that occurred between baseline and 2-months (such as treatment, or mass re-infection from travel) would not bias these results _{0}_{0}_{0}

The variance of these estimates was assessed by inverting the Hessian of the log-likelihood evaluated at the maximum likelihood estimate (although note that the 95% confidence interval could not include _{0}_{0}

Country | Mean Baseline Prevalence (95% CI) | Mean number of Children per Village (Ages 0–9) | Total Number of Communities | References |

16% (10%, 22%) | 24 | 15 | 19 | |

10% (0%, 20%) | 38 | 14 | 8 | |

64% (56%, 72%) | 50 | 16 | 6 |

Characteristics of the observed data from the three countries are shown in _{0}_{0}_{0}_{0}_{0}

Country | R_{0} (95% CI) |
Standard Deviation of R_{0} (95% CI) |
Recovery Rate, Gamma (95% CI) weeks^{−1} |
Exogenous infection rate, Nu (95% CI) weeks^{−1} |

0.89 (0.50, 1.27) | 0.001 (0.000, 0.576) | 0.037 (0.001, 0.073) | 0.002 (0.000, 0.004) | |

1.01 (0.66, 1.36) | 0.724 (0.001, 1.447) | 0.052 (0.000, 0.113) | 0.0002 (0.000, 0.001) | |

3.14 (2.51, 3.77) | 0.7315 (0.232, 1.231) | 0.0123 (0.005, 0.02) | 0.001 (0.000, 0.002) |

The WHO-recommended strategy of three annual mass treatments (before subsequent re-evaluation for further treatment) resulted in an estimated mean prevalence of 0.0% in Tanzanian, 2.4% in Gambian, and 12.9% in Ethiopian communities at three years (

Each curve represents the mean of 1000 stochastic simulations of community prevalence of ocular chlamydial infection in children with three annual mass treatments versus annual mass treatments with graduation, in Tanzania (A), the Gambia (B), and Ethiopia (C). In the graduation strategy, communities received an initial mass treatment, and two subsequent annual mass treatments until the prevalence was reduced below 5%.

Each curve represents the proportion of 1000 simulated communities which still harbor infection, in Tanzania (A), the Gambia (B), and Ethiopia (C). Note that in Tanzanian and Gambian simulations, some communities had no identifiable infection pre-treatment, which is consistent with the observed data).

With a strategy of graduating communities from further mass antibiotics when the observed prevalence of infection falls below 5%, the estimated mean prevalence at 3 years was 0.3% in Tanzania, 3.9% in The Gambia, and 14.4% in Ethiopia (_{0}_{0}

Here we in turn varied the threshold for graduation (A), sensitivity of the diagnostic test (B), specificity of the diagnostic test (C), R_{0} (D), recovery rate γ (E), and exogenous rate ν (F). The mean prevalence at 3 years for 1000 simulations is displayed as the parameter is varied, for each of the three countries. Parameters which were not varied were assumed to be as in

The proportion of communities which still harbor infection at 36 months is displayed as the parameter is varied, for each of the three countries. Parameters varied are threshold for graduation (A), sensitivity of the diagnostic test (B), specificity of the diagnostic test (C), R_{0} (D), recovery rate γ (E), and exogenous rate ν (F). Parameters which were not varied were assumed to be as in

The percentage of individuals treated at each annual visit with mass treatment versus a graduation strategy. Note that we assume an 80% coverage for mass antibiotic treatments.

The percentage of treatments saved with a graduation strategy is displayed as the threshold for graduation (A), sensitivity of diagnostic test (B), or specificity of diagnostic test (C) is varied. Parameters which were not varied were assumed to be as in

The WHO's recommendation of a minimum of three annual antibiotic distributions with at least 80% coverage should work well in most areas. In the models representing Gambian and Tanzanian communities, infection was eliminated in more than 95% of communities during the first three years of a WHO-recommended treatment program, consistent with later observed results in the Tanzanian communities

In hyper-endemic areas like the studied in Ethiopia, we expect 3 years of treatment to eliminate infection in 40% of communities. This is consistent with a recent community-randomized clinical trial in a nearby area of Ethiopia

A strategy that graduates communities when the observed prevalence of infection in children falls below 5% appears to be reasonable. The models presented here predict that treatment could be discontinued in the vast majority of communities similar to those studied in Tanzania and The Gambia. Graduating communities had only a minimal effect on the mean prevalence of infection found in the area at the end of a 3-year trachoma program. This is because trachoma transmission is low in many of the Tanzanian and Gambian communities, and because the graduation strategy favors re-treating the communities which have higher transmission. We predict that antibiotic use could be reduced 2 to 3-fold by introducing such measures, and even more if the graduation threshold were applied before the first treatment—here, we treated all communities at least once.

The goal of trachoma programs is to efficiently use resources to eliminate trachoma as a public health concern. The cost of providing treatment for a community in Africa, estimated at $0.25–1.00 per individual, includes the costs of antibiotics, as well as wages for health workers and administrators

Mathematical models of trachoma control can be useful in determining optimal distribution strategies, and predicting what is expected from specific programs. Stochastic models have an advantage over deterministic models in this setting, because they include the effect of chance seen with the low levels of infection in communities near elimination. Models must also include variation between regions, since strategies that have proven effective in hypo-endemic areas may not translate to hyper-endemic areas. Models should also include variation between communities in the same region. To incorporate this community variation into a realistic model, we included a community-level random effect in transmission (specifically, variation in the underlying _{0}

There is a long history of the use of mathematical models of the transmission of infectious diseases. These are often used to make theoretical points, which do not require precise parameter estimates. Even when parameters are fitted to data, they are rarely fitted to data from more than one community. Community trials in trachoma control have provided longitudinal prevalence data in 14–16 communities in each of three sub-Saharan African countries. There are still many limitations of this simple model which can be explored in the future. We have included only transmission in children, the age group known to harbor most of the infection, but adults could be included with available data. We have assumed that individuals do not gain or lose immunity over the 3 year program, and that there is no antibiotic resistance; the importance of these factors has been debated

Repeated mass oral azithromycin distribution will be effective in reducing the prevalence of ocular chlamydia. But distribution costs are high, and side effects and the potential for resistance are important issues. Graduating communities when diagnostic testing reveals a prevalence of ocular chlamydia of 5% or less appears to be an appropriate strategy in most areas. More frequent treatment and different stopping rules may be required for more hyper-endemic areas similar to the region of Ethiopia studied here.