Stochastic modeling of empirical time series of childhood infectious diseases data before and after mass vaccination

Analysis of the Spread of COVID-19 in the USA with a Spatio-Temporal Multivariate Time Series Model

With the rapid spread of the pandemic due to the coronavirus disease 2019 (COVID-19), the virus has already led to considerable mortality and morbidity worldwide, as well as having a severe impact on economic development. In this article, we analyze the state-level correlation between COVID-19 risk and weather/climate factors in the USA. For this purpose, we consider a spatio-temporal multivariate time series model under a hierarchical framework, which is especially suitable for envisioning the virus transmission tendency across a geographic area over time. Briefly, our model decomposes the COVID-19 risk into: (i) an autoregressive component that describes the within-state COVID-19 risk effect; (ii) a spatiotemporal component that describes the across-state COVID-19 risk effect; (iii) an exogenous component that includes other factors (e.g., weather/climate) that could envision future epidemic development risk; and (iv) an endemic component that captures the function of time and other predictors mainly for individual states. Our results indicate that maximum temperature, minimum temperature, humidity, the percentage of cloud coverage, and the columnar density of total atmospheric ozone have a strong association with the COVID-19 pandemic in many states. In particular, the maximum temperature, minimum temperature, and the columnar density of total atmospheric ozone demonstrate statistically significant associations with the tendency of COVID-19 spreading in almost all states. Furthermore, our results from transmission tendency analysis suggest that the community-level transmission has been relatively mitigated in the USA, and the daily confirmed cases within a state are predominated by the earlier daily confirmed cases within that state compared to other factors, which implies that states such as Texas, California, and Florida with a large number of confirmed cases still need strategies like stay-at-home orders to prevent another outbreak.

Longitudinal profiling of the vaccination coverage in Brazil reveals a recent change in the patterns hallmarked by differential reduction across regions

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There has been a recent reduction in vaccination coverage across the Brazilian regions.

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The most relevant reduction in vaccination coverage has occurred in childhood immunization.

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Increased web searches for anti-vaccine material has been associated with the reduction in immunization coverage.

Objective

Vaccination coverage is decreasing worldwide, favoring the potential reemergence of vaccine-preventable diseases. In this study, we performed a longitudinal characterization of vaccination coverage in Brazil and compared the profiles between the distinct regions in the country to test whether there has been a substantial change over the last 5 years.

Methods

De-identified publicly available data were retrieved from the repository of the Brazilian Ministry of Health, comprising detailed information on vaccination coverage in all age groups between 1994 and 2019. The vaccination coverage for the whole country and for each Brazilian region, by year, was examined, and a time-series pattern analysis was performed.

Results

A significant decrease in overall vaccination coverage across the country regions was observed between 2017 and 2019, especially in childhood immunization. A reduction in BCG, hepatitis B, influenza, and rotavirus vaccine coverage was observed. Conversely, vaccines against measles, mumps, rubella, varicella, and meningococcus showed an increase in coverage. Region-specific changes in vaccination patterns within the study period were observed.

Conclusions

A substantial reduction in vaccination coverage was detected in Brazil, a country already highly susceptible to the emergence of epidemic infectious diseases. Continuing evaluation of the immunization program actions may help to improve vaccination coverage and prevent new epidemics.

Real time detection of farm-level swine mycobacteriosis outbreak using time series modeling of the number of condemned intestines in abattoirs

Mycobacteriosis in swine is a common zoonosis found in abattoirs during meat inspections, and the veterinary authority is expected to inform the producer for corrective actions when an outbreak is detected. The expected value of the number of condemned carcasses due to mycobacteriosis therefore would be a useful threshold to detect an outbreak, and the present study aims to develop such an expected value through time series modeling. The model was developed using eight years of inspection data (2003 to 2010) obtained at 2 abattoirs of the Higashi-Mokoto Meat Inspection Center, Japan. The resulting model was validated by comparing the predicted time-dependent values for the subsequent 2 years with the actual data for 2 years between 2011 and 2012. For the modeling, at first, periodicities were checked using Fast Fourier Transformation, and the ensemble average profiles for weekly periodicities were calculated. An Auto-Regressive Integrated Moving Average (ARIMA) model was fitted to the residual of the ensemble average on the basis of minimum Akaike's information criterion (AIC). The sum of the ARIMA model and the weekly ensemble average was regarded as the time-dependent expected value. During 2011 and 2012, the number of whole or partial condemned carcasses exceeded the 95% confidence interval of the predicted values 20 times. All of these events were associated with the slaughtering of pigs from three producers with the highest rate of condemnation due to mycobacteriosis.

Modelling the long-term dynamics of pre-vaccination pertussis

The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modelling of several data records can be found in the previous literature, the key determinants of the observed temporal patterns have not yet been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease- and vaccine-induced immunity have been debated in the previous literature on pertussis. Here, we study the effect of disease-acquired immunity on the long-term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection, based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long-term dynamics of the models. For epidemiological parameters consistent with published data, the power spectra show quantitative and even qualitative differences, which can be used to test their assumptions by comparison with ensembles of several-decades-long pre-vaccination data records. We illustrate this strategy on two publicly available historical datasets.

Modelling of infectious diseases for providing signal of epidemics: a measles case study in Bangladesh

The detection of unusual patterns in the occurrence of diseases is an important challenge to health workers interested in early identification of epidemics. The objective of this study was to provide an early signal of infectious disease epidemics by analyzing the disease dynamics. A two-stage monitoring system was applied, which consists of univariate Box-Jenkins model or autoregressive integrated moving average model and subsequent tracking signals from several statistical process-control charts. The analyses were illustrated on January 2000-August 2009 national measles data reported monthly to the Expanded Programme on Immunization (EPI) in Bangladesh. The results of this empirical study revealed that the most adequate model for the occurrences of measles in Bangladesh was the seasonal autoregressive integrated moving average (3, 1, 0) (0, 1, 1)12 model, and the statistical process-control charts detected no measles epidemics during September 2007-August 2009. The two-stage monitoring system performed well to capture the measles dynamics in Bangladesh without detection of an epidemic because of high measles-vaccination coverage.

Time series analysis of dengue incidence in Guadeloupe, French West Indies: forecasting models using climate variables as predictors

Background

During the last decades, dengue viruses have spread throughout the Americas region, with an increase in the number of severe forms of dengue. The surveillance system in Guadeloupe (French West Indies) is currently operational for the detection of early outbreaks of dengue. The goal of the study was to improve this surveillance system by assessing a modelling tool to predict the occurrence of dengue epidemics few months ahead and thus to help an efficient dengue control.

Methods

The Box-Jenkins approach allowed us to fit a Seasonal Autoregressive Integrated Moving Average (SARIMA) model of dengue incidence from 2000 to 2006 using clinical suspected cases. Then, this model was used for calculating dengue incidence for the year 2007 compared with observed data, using three different approaches: 1 year-ahead, 3 months-ahead and 1 month-ahead. Finally, we assessed the impact of meteorological variables (rainfall, temperature and relative humidity) on the prediction of dengue incidence and outbreaks, incorporating them in the model fitting the best.

Results

The 3 months-ahead approach was the most appropriate for an effective and operational public health response, and the most accurate (Root Mean Square Error, RMSE = 0.85). Relative humidity at lag-7 weeks, minimum temperature at lag-5 weeks and average temperature at lag-11 weeks were variables the most positively correlated to dengue incidence in Guadeloupe, meanwhile rainfall was not. The predictive power of SARIMA models was enhanced by the inclusion of climatic variables as external regressors to forecast the year 2007. Temperature significantly affected the model for better dengue incidence forecasting (p-value = 0.03 for minimum temperature lag-5, p-value = 0.02 for average temperature lag-11) but not humidity. Minimum temperature at lag-5 weeks was the best climatic variable for predicting dengue outbreaks (RMSE = 0.72).

Conclusion

Temperature improves dengue outbreaks forecasts better than humidity and rainfall. SARIMA models using climatic data as independent variables could be easily incorporated into an early (3 months-ahead) and reliably monitoring system of dengue outbreaks. This approach which is practicable for a surveillance system has public health implications in helping the prediction of dengue epidemic and therefore the timely appropriate and efficient implementation of prevention activities.

A SEASONAL AUTO-REGRESSIVE MODEL BASED SUPPORT VECTOR REGRESSION PREDICTION METHOD FOR H5N1 AVIAN INFLUENZA ANIMAL EVENTS

The time series prediction of avian influenza epidemics is a complex issue, because avian influenza has latent seasonality which is difficult to identify. Although researchers have applied a neural network (NN) model and the Box-Jenkins model for the seasonal epidemic series research area, the results are limited. In this study, we develop a new prediction seasonal auto-regressive-based support vector regression (SAR-SVR) model which combines the seasonal auto-regressive (SAR) model with a support vector regression (SVR) model to address this prediction problem to overcome existing limitations. Fast Fourier transformation is also merged into this method to identify the latent seasonality inside the time series. The experiments demonstrate that the developed SAR-SVR method out-performs SVR, Box-Jenkins models and two layer feed forward NN model-both in accuracy and stability in the avian influenza epidemic disease time series prediction.

Stochastic fluctuations in epidemics on networks

The effects of demographic stochasticity on the long-term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour of recurrent epidemics and the former the superimposed noise of observed incidence patterns. Recently, a stochastic theory based on a mechanism of resonance with internal noise has shifted the role of stochasticity closer to the centre stage, by showing that the major dynamic patterns found in the incidence data can be explained as resonant fluctuations, whose behaviour is largely independent of the amplitude of seasonal forcing, and by contrast very sensitive to the basic epidemiological parameters. Here we elaborate on that approach, by adding an ingredient which is missing in standard epidemic models, the 'mixing network' through which infection may propagate. We find that spatial correlations have a major effect on the enhancement of the amplitude and the coherence of the resonant stochastic fluctuations, providing the ordered patterns of recurrent epidemics, whose period may differ significantly from that of the small oscillations around the deterministic equilibrium. We also show that the inclusion of a more realistic, time-correlated recovery profile instead of exponentially distributed infectious periods may, even in the random-mixing limit, contribute to the same effect.