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The authors have declared that no competing interests exist.

Conceived and designed the experiments: EELR MARP XG. Performed the experiments: EELR. Analyzed the data: EELR XG. Contributed reagents/materials/analysis tools: MEOA JIAJ. Wrote the paper: EELR MARP MAPR MAA XG.

In Latin America, there are 13 geographically isolated endemic foci distributed among Mexico, Guatemala, Colombia, Venezuela, Brazil and Ecuador. The communities of the three endemic foci found within Mexico have been receiving ivermectin treatment since 1989. In this study, we predicted the trend of occurrence of cases in Mexico by applying time series analysis to monthly onchocerciasis data reported by the Mexican Secretariat of Health between 1988 and 2011 using the software R.

A total of 15,584 cases were reported in Mexico from 1988 to 2011. The data of onchocerciasis cases are mainly from the main endemic foci of Chiapas and Oaxaca. The last case in Oaxaca was reported in 1998, but new cases were reported in the Chiapas foci up to 2011. Time series analysis performed for the foci in Mexico showed a decreasing trend of the disease over time. The best-fitted models with the smallest Akaike Information Criterion (AIC) were Auto-Regressive Integrated Moving Average (ARIMA) models, which were used to predict the tendency of onchocerciasis cases for two years ahead. According to the ARIMA models predictions, the cases in very low number (below 1) are expected for the disease between 2012 and 2013 in Chiapas, the last endemic region in Mexico.

The endemic regions of Mexico evolved from high onchocerciasis-endemic states to the interruption of transmission due to the strategies followed by the MSH, based on treatment with ivermectin. The extremely low level of expected cases as predicted by ARIMA models for the next two years suggest that the onchocerciasis is being eliminated in Mexico. To our knowledge, it is the first study utilizing time series for predicting case dynamics of onchocerciasis, which could be used as a benchmark during monitoring and post-treatment surveillance.

Mexico is one of the countries where human onchocerciasis (river blindness) can be found in Latin America. In 1989, the onchocerciasis program in Mexico started the treatment with ivermectin only for symptomatic individuals and then mass distribution of ivermectin was initiated for all eligible residents from 1994, either annually, twice or four times a year in endemic foci, coordinated by Mexican Secretariat of Health (MSH). In our study, we used a statistical method to analyse the cases of the disease reported by MSH from 1988 to 2011. The analysis showed that the cases of the disease have marginally decreased since 1999. The results also predicted an extremely low number (absence) of cases between 2012 and 2013 in the Chiapas region, the last endemic area, suggesting that disease is on a trend towards elimination in Mexico. Meanwhile, it could provide a benchmark for surveillance after mass treatment has been halted in 2012.

Human onchocerciasis is caused by the filarial worm

The discovery of onchocerciasis in America was in 1915 by Rodolfo Robles in Guatemala; hence it was first named as Robles's disease. In Mexico, the first cases of onchocerciasis were documented in 1923 in Chiapas, originated as a consequence of active seasonal migration of coffee workers from the endemic areas between Guatemala and Mexico. The regions in Chiapas and Oaxaca of Mexico are associated with the presence of abundant vector populations

The onchocerciasis control program in Mexico was first established in 1930 and has worked continuously up to date. During 1930–1946, a sporadic larval vector control campaign using Creolin was carried out to eliminate vector populations from breeding sites together with nodulectomy (removal of nodules) campaigns

The time series analysis has been applied in the field of epidemiological research on infectious diseases for the prediction of epidemiological spread tendency, which provided valuable information for making decisions in the control of such diseases

The univariate Auto-Regressive Integrated Moving Average (ARIMA) models are a kind of time series analysis for forecasting a time series data

Herein, the cases of onchocerciasis reported by the Mexican Secretariat of Health (MSH) during the past two decades were analyzed using time series analysis. We adopted the ARIMA approach for describing the case dynamics of onchocerciasis in the endemic foci and predicted the tendency of occurrence of onchocerciasis cases in the immediate future.

The official norm NOM-032-SSA2-2002 of MSH has defined that a case of onchocerciasis should comply with at least one of with the following requirements: demonstration of microfilariae through microscopic examination of superficial skin snips, identification of adult worms by removing nodules, observation of microfilariae in the cornea and anterior chamber of the eye, positive PCR and hybridization from skin snips or nodules. The individual should also present typical clinical manifestations of the disease, and inhabit or have resided in areas of active transmission. Monthly data of onchocerciasis cases between 1988 and 2010 were obtained from the MSH web site (

Time series analysis for identifying significant predictors as well as for forecasting monthly onchocerciasis cases were carried out using the statistical analysis ARIMA model. The data in 1990 for Oaxaca and in 2001 for Chiapas was not available. The cases of onchocerciasis in Chiapas and Oaxaca from 1988 to 1993 were recorded every two months, which could result in data bias (one month with 0 cases after one month with data). Considering that the month without data does not indicate no case occurrence but the cases not reported, and then the cases of that month accumulated in the data of next month, we thus decided to adjust the data by assigning the half part of cases of a month to the previous zero-case month. Because of disease control activities (ivermectin distribution), cases of infection have been greatly reduced, giving rise to an abundance of zeros in the monthly case data. It needs to stabilize the variance of the series before seeking the best model that fits each dataset. The square root (sqrt) transformation was applied to stationarize our datasets. After stabilizing the variance, the descriptive method procedure was performed for plotting the onchocerciasis data through the autocorrelation function (ACF) and partial autocorrelation function (PACF) to identify the order of differentiation as well seasonal and non-seasonal effects. The residuals of the models fitted were inspected with the ACF and PACF plots and further verified with the Ljung-Box test. The best ARIMA model was selected for analysis according to the lowest Akaike Information Criterion (AIC). The ARIMA models were represented by the form as (p, d, q) (P, D, Q)S, where p is the order of auto-regression, d is the order of differencing (or integration), and q is the order of moving-average for non-seasonal series. P, D, Q are their seasonal counterparts, and S is the seasonal period. If the parameters p and q or P and Q are together present in the non-seasonal or seasonal series, the model was termed as mixed ARIMA model. We estimated the parameters of ARIMA models with the “arima” function implemented in the software R

The cases of onchocerciasis in Mexico from 1988 to 2011 were summarized in

The dark grey areas indicate the Oaxaca focus and the Northern and Southern Chiapas foci.

In Oaxaca, there were no reported cases since 1999. This observation gave a good example for us to test if the Time Series Analysis describes well the dynamics of infection cases and predicted the approximate time of disease elimination in Oaxaca. The plot of sqrt-transformed onchocerciasis cases for Oaxaca showed a decreased trend since 1990 (_{12} (AIC = 388.28) seasonal non-stationary model. All coefficients of ARIMA models for Oaxaca were significant (

A and C) Time series profile of the square root values of onchocerciasis cases in Oaxaca and Chiapas. Dashed blue line indicates the trend of onchocerciasis series. B and D) Autocorrelation function (ACF) of onchocerciasis cases from Oaxaca and Chiapas. The x-axis represents the number of lags. Dashed blue line indicates 95% confidence interval.

A and B) Autocorrelation function (ACF) and Partial ACF (PACF) plot of the residuals of the ARIMA (1,1,1)x(0,0,1)_{12} model fitted for Oaxaca. C and D) Autocorrelation function (ACF) and Partial ACF (PACF) plot of the residuals of the ARIMA (1,1,1)x(1,0,0)_{12} model fitted for Chiapas. The x-axis represents the number of lags. Dashed blue lines indicate 95% confidence interval.

A). Black line: The square root curve of observed onchocerciasis cases in Oaxaca for the period 1988–1998. Solid red line: ARIMA (0,1,2)x(0,0,1)_{12} model's fitted values (1988–1997) and 1-step ahead predicted values (year 1998–1999) with their 95% prediction intervals (dashed blue line). B) Black line: The square root curve of observed onchocerciasis cases in Chiapas for the period 1988–2011. Solid red line: ARIMA (1,1,1)x(1,0,1)_{12} model's fitted values (1988–2011) and 1-step ahead predicted values (year 2012–2013) with their 95% prediction intervals (dashed blue lines).

Region | ARIMA Model | Parameter | Coefficient | Stnd. Error | t statistic | P-value |

Oaxaca | (0,1,2)×(0,0,1)_{12} |
MA(1) | −0.2235 | 0.0867 | −2.57785467 | 2.48e^{−03} |

MA(2) | −0.5917 | 0.0855 | −6.92046784 | 1.11e^{−12} |
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SMA(1) | 0.286 | 0.1015 | 2.81773399 | 1.21e^{−03} |
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Chiapas | (1,1,1)×(1,0,1)_{12} |
AR(1) | 0.5862 | 0.078 | 7.515384615 | 1.37e^{−14} |

MA(1) | −0.8974 | 0.0432 | −20.7731481 | 0.00e^{+00} |
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SAR(1) | 0.8675 | 0.0841 | 10.31510107 | 0.00e^{+00} |
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SMA(1) | −0.746 | 0.1149 | −6.49260226 | 2.15e^{−11} |

The predicted result that matches the observations in Oaxaca focus allows us to apply the same methodology to the Chiapas foci. _{12} (AIC = 960.77). All the coefficients of the ARIMA model for Chiapas were significant (

The key aspect in the control of onchocerciasis disease in Latin America is the treatment with the drug ivermectin available to all the people at risk

In 2003, the biannual treatment strategy was modified in the majority of the formerly hyperendemic communities of Southern Chiapas focus by increasing treatment frequency to four times a year in order to accelerate the interruption of parasite transmission

The above description shows that the elimination of onchocerciasis in humans is an arduous task. The evaluation of the current state and the prediction of future situations are germane for evaluating epidemiological patterns. Several mathematical models have been developed to simulate the onchocerciasis future in specific endemic zones

In the present study, sqrt transformation was chosen for stationarizing the series. Actually, Anscombe transform

One phenomenon needs to be mentioned. The predicted plot in both Oaxaca and Chiapas showed that all the data in the coming years are less than 1 case but with 95% prediction interval beyond 1 case. A prediction interval is always wider than a confidence interval because it is not only related to the value of the population mean, but also the data scatter. When it approaches the elimination of disease, the number of cases show as 0, 1, or >1, not as continuous data less than 1 but approaching to 0. It means that as much closer to elimination, the distribution data become much more discretized. In this situation, it could be difficult to expect the prediction of annual cases less than 1 with the 95% prediction intervals within one case, even though the zero cases were treated as 0.1. On the other hand, our test for the focus in Oaxaca demonstrated our prediction is acceptable despite of the 95% prediction intervals beyond 1 case. This phenomenon mentioned here could be common for times series analysis as approaching to elimination of diseases. Our analysis thus provided a good reference for such prediction of similar diseases.

We realize that the present model is adopted for predicting the cases under the same situation in the recent future. Since 2012, the mass treatments with ivermectin have been halted. Does it mean our prediction does not work? If ivermectin is the principal reason leading to reduction of cases and the transmission has been really interrupted, it is very possible that the tendency of case occurrence could keep reduction until to zero case. In other words, the mass treatments with ivermectin still keep the influence (the consequence of the treatment) and our prediction model has the condition to work. Otherwise, the mass treatments with ivermectin could need to be re-continued. To this sense, the application of this prediction model could be used as a benchmark during monitoring and surveillance after mass treatment has been withdrawn.

We are aware of the possible limitations of the present study. The data used in the current study rely on total clinical cases of onchocerciasis reported by the surveillance system of MSH, which may underestimate the true number of cases as earlier posited by various researchers

In conclusion, onchocerciasis in Mexico was a serious public health problem in the past. ARIMA models predicted an extremely low (zero) expected cases of onchocerciasis for the next two years, implying that onchocerciasis is being eliminated. These results showed that time series analysis could be a practical method for predicting onchocerciasis case tendencies and could be used as a benchmark for monitoring and surveillance on the post ivermectin-mass-treatment duration. To our knowledge, it is the first study utilizing time series analysis for predicting the case dynamics of onchocerciasis.

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_{12} model's fitted values (1988–1997) and 1-step ahead predicted values (year 1998–1999) with their 95% prediction intervals (dashed blue line). B) Black line: The Anscombe transform curve of observed onchocerciasis cases in Chiapas for the period 1988–2011. Solid red line: ARIMA (1,1,1)x(1,0,1)_{12} model's fitted values (1988–2011) and 1-step ahead predicted values (year 2012–2013) with their 95% prediction intervals (dashed blue lines).

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_{12} model's fitted values (1988–1997) and 1-step ahead predicted values (year 1998–1999) with their 95% prediction intervals (dashed blue line). B) Black line: The natural _{12} model's fitted values (1988–2011) and 1-step ahead predicted values (year 2012–2013) with their 95% prediction intervals (dashed blue lines).

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We are grateful to the Ministry of Health (the Mexican Onchocerciasis Elimination Program) who provided the open access onchocerciasis data through its web site. We are much obliged to OEPA whose enthusiastic coordination with the national program made these data feasible. The authors thank all people in endemic areas and brigades of the onchocerciasis program in the states of Oaxaca and Chiapas that have indeed contributed to the completion of databases. The Direction of Vector Borne Diseases of CENAPRECE (Dr. Armando Elizondo Quiroga as coordinator of the onchocerciasis program), Ministry of Health Mexico and the Health Services of the State of Oaxaca (Dr. Miguel Alberto Vásquez Rodríguez) and Chiapas (Dr. Francisco Gibert Prado Velasco) also supported this study as part of their tenure.