Additive Time Series Model Research Articles

Neural additive time-series models: Explainable deep learning for multivariate time-series prediction

Deep neural networks are one of the most important methods in machine learning. The advantages of neural networks are their excellent prediction performance and versatility using deep architecture and generalized input–output forms. However, as neural networks are black-box models, they lack explanatory power for their predictions. In this study, we propose a new neural network architecture that includes the interpretability of predictions for multivariate time-series (MTS) data by employing a generalized additive method. In addition, we examine parameter sharing networks to decrease the model’s complexity, along with hard-shared networks. We conducted experiments to demonstrate that the interpretable neural architecture can quantify the contributions of each input value to the prediction of each MTS by every time step and variable. Experimental results involving a toy example and four real-world datasets demonstrate that the performance of the proposed method in predicting MTS data is comparable to that of state-of-the-art neural networks, while providing reasonable importance for each input value.

Оценка объемов ВВП России

In this article, an econometric analysis of the volume of the gross domestic product of the Russian Federation is carried out. Based on quarterly data for 2018 – the 1st half of 2022, an additive time series model was built using dummy variables, and according to the resulting model, the volume of gross domestic product for the 2nd half of 2022 was predicted.

ПРОГНОЗИРОВАНИЕ ДОХОДОВ ФЕДЕРАЛЬНОГО БЮДЖЕТА РФ ОТ ЭКСПОРТА НЕФТИ

The article presents a methodology for forecasting the revenues of the federal budget of the Russian Federation from oil exports. Based on quarterly data for the period 2018-2021. an additive time series model was built. The adequacy of the obtained model was assessed.

A MATHEMATICAL MODEL FOR PROGNOSIS OF THE COVID-19 INCIDENCE IN UKRAINE USING GOOGLE TRENDS RESOURCES IN REAL-TIME AND FOR THE FUTURE PERIOD

Digital epidemiology resources are actively used for the timely response of the health care system to the emergence and spread of diseases. Analytical methods applicable to time series of data are used for detailed analysis of seasonal fluctuations of infectious diseases. Together with the Google Trends (GT) tool, such methods allow modeling the dynamics of diseases in real-time and for future periods. Given that the COVID-19 pandemic is still at an early stage of development, new methods of epidemiological surveillance of the disease will be able to ensure a timely response of the health care system to it. The aim of this research is to study the use of GT resources to build a mathematical model for the prognosis of the COVID-19 incidence in Ukraine in real time and for future periods. Materials and methods. In the course of the study, we used the GT tool to search Google queries “ковід, ковид, COVID-19” (KKC). Data on morbidity in Ukraine were obtained using the web resource: https://index.minfin.com.ua/ua/reference/coronavirus/ukraine/. Excel, Eviews, and StatPlus software packages were used to analyze time series, construct periodograms, correlograms, and mathematical models. The mathematical model of morbidity dynamics was built based on statistical exponential smoothing. Results. As Cyrillic equivalents of the term COVID-19, Ukrainians use the queries “кові(и)д”. Correlograms of KKC requests and actual incidence show seasonal fluctuations of the same frequency, and singular spectral analysis revealed statistically significant peaks. Based on statistical exponential smoothing, a prognostic model for the incidence of COVID-19 for 2022-2024 was built, which is reliable according to the criteria of accuracy and the results of the Dickey-Fuller test. Conclusions. The GT tool is a reliable source of data for studying the dynamics of the spread of COVID-19. Together with the use of additive time series models, it allows for a real-time reliable prognosis of the development of the disease. The presented approach to modeling the dynamics of the spread of COVID-19 can be used to track outbreaks of the disease and respond promptly to them both on a national and local scale.

Combatting the imbalance of sex ratio at birth: medium-term impact of India's National Programme of Beti Bachao Beti Padhao in the Haryana State of India.

The Government of India initiated the Beti Bachao Beti Padhao (B3P) programme in 2015 as a flagship initiative to reduce gender imbalance in sex ratio at birth (SRB) and to ensure social protection of girls. The present study was conducted to evaluate the medium-term impact of B3P implementation in Haryana state, from 2015 to 2019, on SRB. Monthly data on SRB were collected for the entire state of Haryana through a civil registration system. Segmented time series regression analysis was used to estimate the variations in SRB after the B3P programme with the help of Winter's additive interrupted time series model. The SRB in Haryana increased from 876 girls per 1000 boys in 2015 to 923 in 2019. The results of the model demonstrated that before the inception of intervention (pre-slope), there was a significant monthly change in SRB of 0.217 (95% confidence interval: 0.144-0.290). Following the B3P programme, SRB was found to increase by 0.835 per month, which implied that an increase of 0.618 (confidence interval: 0.338, 0.898) every month in SRB can be attributed to the B3P programme. This indicated that SRB for the state of Haryana increased at the rate of 7.42 units per year as a result of the B3P programme. B3P has led to a significant improvement in SRB in Haryana state. The continuity of efforts in the same direction with a sustained focus on behaviour change will further help achieve the goal of gender parity in births and child survival.

Effect of Different Pollution Parameters and Chemical Components of PM2.5 on Health of Residents of Xinxiang City, China.

The present study was planned to explore the pollution characteristics, health risks, and influence of atmospheric fine particulate matter (PM2.5) and its components on blood routine parameters in a typical industrial city (Xinxiang City) in China. In this study, 102 effective samples 28 (April–May), 19 (July–August), 27 (September–October), 28 (December–January) of PM2.5 were collected during different seasons from 2017 to 2018. The water-soluble ions and metal elements in PM2.5 were analyzed via ion chromatography and inductively coupled plasma–mass spectrometry. The blood routine physical examination parameters under different polluted weather conditions from January to December 2017 and 2018, the corresponding PM2.5 concentration, temperature, and relative humidity during the same period were collected from Second People’s Hospital of Xinxiang during 2017–2018. Risk assessment was carried out using the generalized additive time series model (GAM). It was used to analyze the influence of PM2.5 concentration and its components on blood routine indicators of the physical examination population. The “mgcv” package in R.3.5.3 statistical software was used for modeling and analysis and used to perform nonparametric smoothing on meteorological indicators such as temperature and humidity. When Akaike’s information criterion (AIC) value is the smallest, the goodness of fit of the model is the highest. Additionally, the US EPA exposure model was used to evaluate the health risks caused by different heavy metals in PM2.5 to the human body through the respiratory pathway, including carcinogenic risk and non-carcinogenic risk. The result showed that the air particulate matter and its chemical components in Xinxiang City were higher in winter as compared to other seasons with an overall trend of winter > spring > autumn > summer. The content of nitrate (NO3−) and sulfate (SO42−) ions in the atmosphere were higher in winter, which, together with ammonium, constitute the main components of water-soluble ions in PM2.5 in Xinxiang City. Source analysis reported that mobile pollution sources (coal combustion emissions, automobile exhaust emissions, and industrial emissions) in Xinxiang City during the winter season contributed more to atmospheric pollution as compared to fixed sources. The results of the risk assessment showed that the non-carcinogenic health risk of heavy metals in fine particulate matter is acceptable to the human body, while among the carcinogenic elements, the order of lifetime carcinogenic risk is arsenic (As) > chromium(Cr) > cadmium (Cd) > cobalt(Co) > nickel (Ni). During periods of haze pollution, the exposure concentration of PM2.5 has a certain lag effect on blood routine parameters. On the day when haze pollution occurs, when the daily average concentration of PM2.5 rises by 10 μg·m−3, hemoglobin (HGB) and platelet count (PLT) increase, respectively, by 9.923% (95% CI, 8.741–11.264) and 0.068% (95% CI, 0.067–0.069). GAM model analysis predicted the maximum effect of PM2.5 exposure concentration on red blood cell count (RBC) and PLT was reached when the hysteresis accumulates for 1d (Lag0). The maximum effect of exposure concentration ofPM2.5 on MONO is reached when the lag accumulation is 3d (Lag2). When the hysteresis accumulates for 6d (Lag5), the exposure concentration of PM2.5 has the greatest effect on HGB. The maximum cumulative effect of PM2.5 on neutrophil count (NEUT) and lymphocyte (LMY) was strongest when the lag was 2d (Lag1). During periods of moderate to severe pollution, the concentration of water-soluble ions and heavy metal elements in PM2.5 increases significantly and has a significant correlation with some blood routine indicators.

Procedure for Estimation of Additive Time Series Model

Procedure for Estimation of Additive Time Series Model

Использование статистических методов для анализа и прогноза udp-flood атак

Web resources are an integral part of the life of a modern person, who are now more and more often subjected to hacker attacks. The most popular types of attacks are the SQL-injections and cross-site scripting, but DDoS attacks continue to be in the top 10 of network attacks and lead to serious crashes and failures of web resources. The most common type of DDoS attack is UDP flood attack, based on the infinite sending of UDP packets to ports of various UDP services. The scientific novelty of the work lies in the fact that to increase the level of security of web resources a medium-term forecast of cyber attacks of the UDP-flood type, using the methods of correlation analysis, based on the additive time series model, is proposed taking into account seasonal factors and time duration, which will ensure the necessary level of web security -resources. The type of UDP-flood attacks was chosen as the object of study. Using the methods of correlation analysis and modeling, we calculated the seasonal index of UDP flood attacks, and the autocorrelation of the time series of this type of attack. Using the method of simple exponential smoothing, a forecast of UDP-flood attacks is constructed. The paper proposes a classification of DDoS attacks, describes protection methods. Based on the correlation analysis, the predicted values of the impact of UDP flood attacks on web resources are calculated, and the seasonal factor is revealed. The largest number of attacks is expected in the IV quarter of 2020. For DDoS attacks lasting up to 20 minutes, seasonality was also revealed in the 1st quarter of the calendar year, which means that in the 1st quarter of 2020 the largest number of attacks of this duration should be expected. Prospects for further research into the problem of protection against DDoS attacks are presented in the further development of the methodology for countering UDP flood attacks and information security algorithms for web resources, which will reduce the number of UDP flood attacks and increase the level of web resource security.

Effects of meteorological factors on blood donation

Background and objectivesBlood donation can be affected by various factors including time, weather, and other events (such as disasters). To better understand how meteorological factors affect blood donation, this study builds a novel predictive model for blood supply in North Taiwan to facilitate better blood supply chain and inventory management. Materials and methodsThis study uses a two-step prediction model that combines generalized additive models (GAM) and time series models to investigate the meteorological and the day-of-the-week effects on blood donation. For the period 2010–2014, blood donation data and weather information of Big Taipei area are described and analyzed. A bootstrap method was also implemented on the residuals produced by the two-step model to construct the prediction intervals. ResultsDaily average temperature and daily cumulative precipitation have non-linear effects on blood donation. By including weather information into the model, the prediction model not only can account for the fluctuation affected by the day-of-the-week effects but also the weather (e.g., temperature and rainfall) effects. The prediction intervals can be used to detect the anomaly donation patterns or to signal possible shortages when there is a forecast of an extreme weather event. ConclusionThe findings underscore the need for quantitatively modeling meteorological effects in blood supply chain management, and provide important implications for the authority of a blood center to take necessary intervention and measures to reduce shortages and excessive expirations.

Impact of seasonal influenza on polyclinic attendances for upper respiratory tract infections in Singapore.

PurposeThe burden of influenza on primary health-care services is not well established in tropical countries, where there are no clearly defined influenza seasons. We aimed to estimate the association between influenza infection activity and polyclinic attendance rates for upper respiratory tract infections (URTIs) in the Singapore population.MethodsWe used generalized additive time series models to estimate the association between the proportion of respiratory tests positive for influenza infection in Singapore reported to the World Health Organization every week, and the population rate of polyclinic attendances in Singapore for physician-diagnosed URTI, which includes influenza-like illness (ILI), for six years from 2012 through 2017. Where data were available, we controlled for other infections that can cause fever or respiratory symptoms.ResultsInfluenza, dengue fever and chickenpox (varicella) were positively associated with acute URTI polyclinic attendances. The estimated URTI polyclinic attendance rates attributable to influenza, dengue fever and chickenpox were 618.9 (95% confidence interval [CI]: 501.6–736.3), 153.3 (95% CI: 16.5–290.2) and 1751.5 (95% CI: 1246.3–2256.8) per 100 000 population per year, respectively.ConclusionInfluenza poses a considerable burden on primary health-care services in Singapore. However, a substantial number of polyclinic attendances due to febrile infections such as dengue fever and chickenpox appear to be recorded as URTI in the polyclinic database. These associations require further investigation.

Studies in Astronomical Time-series Analysis. VII. An Enquiry Concerning Nonlinearity, the rms–Mean Flux Relation, and Lognormal Flux Distributions

Abstract A broad and widely used class of stationary, linear, additive time-series models can have statistical properties that many authors have asserted imply that the underlying process must be nonlinear, nonstationary, multiplicative, or inconsistent with shot noise. This result is demonstrated with exact and numerical evaluation of the model flux distribution function and dependence of flux standard deviation on mean flux (here and in the literature called the rms–flux relation). These models can (1) exhibit normal, lognormal, or other flux distributions; (2) show linear or slightly nonlinear rms–mean flux dependencies; and (3) match arbitrary second-order statistics of the time-series data. Accordingly, the above assertions cannot be made on the basis of statistical time-series analysis alone. Also discussed are ambiguities in the meaning of terms relevant to this study—linear, stationary, and multiplicative—and functions that can transform observed fluxes to a normal distribution as well as or better than the logarithm.

Road Traffic Accident Scenario, Pattern and Forecasting in Bangladesh

The main aim of this research work is to be aware of the road traffic accident scenario, injurious effects and pattern in Bangladesh. Moreover we are interested to forecast the magnitude of road traffic accidents for the future so that decision makers can make appropriate decision for precaution. This study also provides an assessment of road traffic accidents in Bangladesh and its impact based on data collected for the period of 1971 to 2017. In this study we have tried to pick up the main reasons of road accidents and to observe the tremendous situation. The study observed that the general trends of road traffic accident (RTA), deaths and injuries reveal that the number of RTA, deaths and injuries increased gradually with little fluctuations form 1971 to 2007 and after 2007 there is a slow decreasing trend. Although the number of RTA and deaths observed decreasing trend in recent years, the ratio of number of deaths to number of accident increased significantly. The rate of register vehicles per 10,000 people increased moderately throughout the period but a sharp increment is exhibited from 2009. Highest percentage of RTA (34%) and deaths is due to RTA (32%) in Dhaka division while the lowest percentage of RTA (4%) in Barisal and Sylhet divisions and deaths is due to RTA (3%) in Barisal division. It is noticed that the maximum number of injuries occurred between ages 21 and 30 while the maximum number of deaths occurred between ages 11 and 30. Most of the RTA and deaths due to RTA are caused by run over by vehicles and head to head collision. The severity of occurring road accident and number of deaths are higher during the festive periods because of involving higher frequency of traveling than usual. The time plot shows that the graph maintains a decreasing movement from 2012 to 2015 but increases from 2015 to 2017. In the research an additive time series model approach is applied. It included the estimation of trend, seasonal variation and random variation using triple exponential smoothing method. We performed forecasting of RTA eliminating seasonal impact for the next three consecutive years (2018-2020) with 95% confidence interval using Holt-Winters exponential technique.

Probabilistic forecasting of industrial electricity load with regime switching behavior

This paper suggests a novel inhomogeneous Markov switching approach for the probabilistic forecasting of industrial companies’ electricity loads, for which the load switches at random times between production and standby regimes. The model that we propose describes the transitions between the regimes using a hidden Markov chain with time-varying transition probabilities that depend on calendar variables. We model the demand during the production regime using an autoregressive moving-average (ARMA) process with seasonal patterns, whereas we use a much simpler model for the standby regime in order to reduce the complexity. The maximum likelihood estimation of the parameters is implemented using a differential evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness-of-fit of our model for probabilistic forecasting, it is shown that this model often outperforms classical additive time series models, as well as homogeneous Markov switching models. We also propose a simple procedure for classifying load profiles into those with and without regime-switching behaviors.

Emergency Department demand associated with seasonal influenza, 2010 through 2014, New South Wales, Australia.

IntroductionInfluenza’s impact on health and health care is underestimated by influenza diagnoses recorded in health-care databases. We aimed to estimate total and non-admitted influenza-attributable hospital Emergency Department (ED) demand in New South Wales (NSW), Australia.MethodsWe used generalized additive time series models to estimate the association between weekly counts of laboratory-confirmed influenza infections and weekly rates of total and non-admitted respiratory, infection, cardiovascular and all-cause ED visits in NSW, Australia for the period 2010 through 2014. Visit categories were based on the coded ED diagnosis or the free-text presenting problem if no diagnosis was recorded.ResultsThe estimated all-age, annual influenza-attributable respiratory, infection, cardiovascular and all-cause visit rates/100 000 population/year were, respectively, 120.6 (99.9% confidence interval [CI] 102.3 to 138.8), 79.7 (99.9% CI: 70.6 to 88.9), 14.0 (99.9% CI: 6.8 to 21.3) and 309.0 (99.9% CI: 208.0 to 410.1). Among respiratory visits, influenza-attributable rates were highest among < 5-year-olds and ≥ 85-year-olds. For infection and all-cause visits, rates were highest among children; cardiovascular rates did not vary significantly by age. Annual rates varied substantially by year and age group, and statistically significant associations were absent in several years or age groups. Of the respiratory visits, 73.4% did not require admission. The non-admitted proportion was higher for the other clinical categories. Around 1 in 100 total visits and more than 1 in 10 respiratory or infection visits were associated with influenza.DiscussionInfluenza is associated with a substantial and annually varying burden of hospital-attended illness in NSW.

Evaluation of a provincial intervention to reduce redundant hemoglobin A1c testing

BackgroundThe Canadian Diabetes Association recommends testing most individuals with diabetes mellitus using HbA1c once every 3months. In Alberta, Canada, a provincial intervention to reduce inappropriate HbA1c test orders was implemented to align with this guideline, where only one HbA1c test request every 90days for most individuals can be processed. Here, we evaluated the provincial intervention to reduce redundant HbA1c testing in Alberta. MethodsTotal counts of all HbA1c tests ordered within Edmonton and Calgary, Alberta, were collected from the respective Laboratory Information Systems each month between January 2013 and December 2016. Winters' Additive time series model was built to predict the HbA1c test volume after intervention (November 1, 2015 onwards) and compared with the observed test volume to estimate the effect of the intervention. The estimated change in test volume was then multiplied by the estimated cost to determine the economic impact. ResultsDuring the first 14months of the intervention for Alberta, there was a 3.3% reduction in the number of observed HbA1c tests compared to the predicted volume. With an estimated marginal reagent cost of $3.50 per unit, this resulted in a cost savings of $145,422 in the first 14months of the provincial intervention. ConclusionA modest reduction in HbA1c test orders was observed in the urban areas of Alberta since the implementation of this provincial initiative.

Prediction of landslide displacement with step-like behavior based on multialgorithm optimization and a support vector regression model

Landslide prediction is important for mitigating geohazards but is very challenging. In landslide evolution, displacement depends on the local geological conditions and variations in the controlling factors. Such factors have led to the “step-like” deformation of landslides in the Three Gorges Reservoir area of China. Based on displacement monitoring data and the deformation characteristics of the Baishuihe Landslide, an additive time series model was established for landslide displacement prediction. In the model, cumulative displacement was divided into three parts: trend, periodic, and random terms. These terms reflect internal factors (geological environmental, gravity, etc.), external factors (rainfall, reservoir water level, etc.), and random factors (uncertainties). After statistically analyzing the displacement data, a cubic polynomial model was proposed to predict the trend term of displacement. Then, multiple algorithms were used to determine the optimal support vector regression (SVR) model and train and predict the periodic term. The results showed that the landslide displacement values predicted based on data time series and the genetic algorithm (GA-SVR) model are better than those based on grid search (GS-SVR) and particle swarm optimization (PSO-SVR) models. Finally, the random term was accurately predicted by GA-SVR. Therefore, the coupled model based on temporal data series and GA-SVR can be used to predict landslide displacement. Additionally, the GA-SVR model has broad application potential in the prediction of landslide displacement with “step-like” behavior.

Probabilistic Forecasting of Electricity Load with Inhomogeneous Markov Switching Models

In this paper we suggest a novel inhomogeneous Markov switching approach for probabilistic forecasting of electricity load of industrial companies, for which the load switches at random times between a production and a standby regime. The model we propose describes the transitions between the regimes by a hidden Markov chain with time-varying transition probabilities depending on calendar variables. The demand during the production regime is modeled by an ARMA process with seasonal patterns, whereas we use a much simpler model for the standby regime to reduce complexity. The maximum likelihood estimation of the parameters is implemented with a Differential Evolution algorithm. Using the continuous ranked probability score (CRPS) to evaluate the goodness of fit of our model for probabilistic forecasting it is shown that this model often outperforms classical additive time series models as well as homogeneous Markov switching models. We also propose a simple procedure to classify load profiles into ones with and without regime-switching behavior.

Exposure variable selection in heat – health risk assessment and implications for interventions

Introduction: Exposure variable selection is an important component of heat health risk assessment that has received little explicit attention in the scientific literature. The choice between different exposure variables, such as maximum daily temperature or mean daily heat index, can influence our understanding of the causal pathways by which people succumb to adverse health events associated with thermal stress. This knowledge also affects also our ability to design, prioritize, and implement intervention strategies. Methods: We explored how the statistical association between six different health events and warm season weather varied across 54 exposure variables in the chronically hot setting of Maricopa County, Arizona, USA over the period 2000–2012. Variables were evaluated based on cross-validation scores derived from generalized additive time series models. We subsequently tested how different exposure variables performed in their hypothetical application as triggering criteria for an early warning system. Results: We found that exposure variable selection had a large impact on statistical model performance for health events for which heat was known to be a contributing factor (death, hospitalization, and emergency department visit from direct exposure to environmental heat). Exposure variable selection had a negligible impact on model performance for broader categories of health events (all-cause death, cardiovascular death, and death from consequences of heat and dehydration). Variable selection significantly changed the set of days identified for heat warnings, but no single criterion was obviously superior. Conclusions: Rigorous consideration of the exposure variable in heat-health risk assessment can likely provide important guidance for public health preparedness activities related to extreme heat. In our geographic setting, such analysis leads us to recommend that intervention measures that focus on reducing daytime exposure be prioritized.

Short Term Effects Of Meteorological Factors On Hand, Foot And Mouth Disease In A Chinese Subtropical City

Hand, Foot and Mouth Disease (HFMD), predominantly transmitted in Asia, is an infectious enteric disease commonly caused by Coxsackievirus A16 and Enterovirus 71 and primarily affecting children under 5 years old. And there is substantial evidence showing that the earth is undergoing significant temperature elevation in the last century. This study aims to quantify the impact of weather variation on Hand, Foot and Mouth disease in a large southwest city with subtropical climate in China. Generalized additive time-series models were used to model daily HFMD cases as a function of daily mean temperature, relative humidity, wind speed, total sun duration and rainfall, adjusting for time trend, seasonality, and autoregressive terms, and allowing for lagged effects up to 14 days. There was an apparent bi-annual pattern during the study period, with a major peak in May and a minor one in November. Relative humidity below 80% was found to be positively associated with HFMD with a shorter lag (0-7 days). However, there was a delayed inverse U-shape effect of mean temperature on HFMD two weeks later, with a peak of 18 degrees Celsius. More HFMD cases were reported during days with heavier rainfall since 5th day and afterwards. In addition, stronger wind (speed above 16km/h) was also observed to be a risk factor for HFMD, with lagged effects up to the maximum lag-14 days. The quantification of meteorological influence could be able to facilitate the prediction and prevention of HFMD especially for the vulnerable group-children younger than 5 years old. Global warming and other environmental change are likely to lead to an increase in severe HFMD cases in subtropical areas in the absence of further interventions.

Epidemiology of measles in Southwest Nigeria: an analysis of measles case-based surveillance data from 2007 to 2012

In Nigeria, a system of measles case-based surveillance with laboratory confirmation of suspected cases was introduced in 2005 as one of the strategies for the control of measles morbidity and mortality. In this report, we provide an epidemiological distribution of confirmed cases of measles reported from the southwest of the country between 2007 and 2012, and predict the expected number of cases for the ensuing years. A descriptive analysis of persons and place and time of confirmed measles cases (laboratory and epidemiological link) reported in the case-based surveillance data was carried out. Using an additive time series model, we predicted the expected number of cases to the year 2015, assuming that current interventional efforts were sustained. From the 10 187 suspected cases investigated during the time period, 1631 (16.0%) cases of measles were confirmed. The annual incidence rose from <1 case per million in 2007 to 23 cases per million in 2011. Cases were confirmed from all six states within the zone and most (97.4%) were in individuals aged less than 20 years. Seasonal variation existed with peaks of infection in the first and second quarters of the year. There was an increasing trend in the number of expected cases based on projections. Case-based surveillance provided an insight into understanding the epidemiology of measles infection in Southwest Nigeria. There is a need to work out alternate strategies for control of measles and to strengthen the surveillance system.