Using autoregressive integrated moving average (ARIMA) models to predict and monitor the number of beds occupied during a SARS outbreak in a tertiary hospital in Singapore

Towards reliable forecasting of healthcare capacity needs: A scoping review and evidence mapping

BACKGROUND

The COVID-19 pandemic has highlighted the critical importance of robust healthcare capacity planning and preparedness for emerging crises. However, healthcare systems must also adapt to more gradual temporal changes in disease prevalence and demographic composition over time. To support proactive healthcare planning, statistical capacity forecasting models can provide valuable information to healthcare planners. This systematic literature review and evidence mapping aims to identify and describe studies that have used statistical forecasting models to estimate healthcare capacity needs within hospital settings.

METHOD

Studies were identified in the databases MEDLINE and Embase and screened for relevance before items were defined and extracted within the following categories: forecast methodology, measure of capacity, forecast horizon, healthcare setting, target diagnosis, validation methods, and implementation.

RESULTS

84 studies were selected, all focusing on various capacity outcomes, including number of hospital beds/ patients, staffing, and length of stay. The selected studies employed different analytical models grouped in six items; discrete event simulation (N = 13, 15 %), generalized linear models (N = 21, 25 %), rate multiplication (N = 15, 18 %), compartmental models (N = 14, 17 %), time series analysis (N = 22, 26 %), and machine learning not otherwise categorizable (N = 12, 14 %). The review further provides insights into disease areas with infectious diseases (N = 24, 29 %) and cancer (N = 12, 14 %) being predominant, though several studies forecasted healthcare capacity needs in general (N = 24, 29 %). Only about half of the models were validated using either temporal validation (N = 39, 46 %), cross-validation (N = 2, 2 %) or/and geographical validation (N = 4, 5 %).

CONCLUSION

The forecasting models' applicability can serve as a resource for healthcare stakeholders involved in designing future healthcare capacity estimation. The lack of routine performance validation of the used algorithms is concerning. There is very little information on implementation and follow-up validation of capacity planning models.

Impact of the COVID-19 pandemic on hospital episodes for falls and fractures associated with new-onset disability and frailty in England: a national cohort study

BACKGROUND

Older people with frailty are at risk of harm from immobility or isolation, yet data about how COVID-19 lockdowns affected them are limited. Falls and fractures are easily measurable adverse outcomes correlated with frailty. We investigated whether English hospital admission rates for falls and fractures varied from the expected trajectory during the COVID-19 pandemic, and how these varied by frailty status.

METHODS

NHS England Hospital Episode Statistics Admitted Patient Care data were analysed for observed versus predicted outcome rates for 24 January 2020 to 31 December 2021. An auto-regressive integrated moving average time-series model was trained using falls and fracture incidence data from 2013 to 2018 and validated using data from 2019. Models included national and age-, sex- and region-stratified forecasts. Outcome measures were hospital admissions for falls, fractures, and falls and fractures combined. Frailty was defined using the Hospital Frailty Risk Score.

RESULTS

144,148,915 pre-pandemic hospital admissions were compared with 42,267,318 admissions after pandemic onset. For the whole population, falls and fracture rates were below predicted for the first period of national lockdown, followed by a rapid return to rates close to predicted. Thereafter, rates followed expected trends. For people living with frailty, however, falls and fractures increased above expected rates during periods of national lockdown and remained elevated throughout the study period. Effects of frailty were independent of age.

CONCLUSIONS

People living with frailty experienced increased fall and fracture rates above expected during and following periods of national lockdown. These remained persistently elevated throughout the study period.

Real-time forecasting of COVID-19 spread according to protective behavior and vaccination: autoregressive integrated moving average models

BACKGROUND

Mathematical and statistical models are used to predict trends in epidemic spread and determine the effectiveness of control measures. Automatic regressive integrated moving average (ARIMA) models are used for time-series forecasting, but only few models of the 2019 coronavirus disease (COVID-19) pandemic have incorporated protective behaviors or vaccination, known to be effective for pandemic control.

METHODS

To improve the accuracy of prediction, we applied newly developed ARIMA models with predictors (mask wearing, avoiding going out, and vaccination) to forecast weekly COVID-19 case growth rates in Canada, France, Italy, and Israel between January 2021 and March 2022. The open-source data was sourced from the YouGov survey and Our World in Data. Prediction performance was evaluated using the root mean square error (RMSE) and the corrected Akaike information criterion (AICc).

RESULTS

A model with mask wearing and vaccination variables performed best for the pandemic period in which the Alpha and Delta viral variants were predominant (before November 2021). A model using only past case growth rates as autoregressive predictors performed best for the Omicron period (after December 2021). The models suggested that protective behaviors and vaccination are associated with the reduction of COVID-19 case growth rates, with booster vaccine coverage playing a particularly vital role during the Omicron period. For example, each unit increase in mask wearing and avoiding going out significantly reduced the case growth rate during the Alpha/Delta period in Canada (-0.81 and -0.54, respectively; both p < 0.05). In the Omicron period, each unit increase in the number of booster doses resulted in a significant reduction of the case growth rate in Canada (-0.03), Israel (-0.12), Italy (-0.02), and France (-0.03); all p < 0.05.

CONCLUSIONS

The key findings of this study are incorporating behavior and vaccination as predictors led to accurate predictions and highlighted their significant role in controlling the pandemic. These models are easily interpretable and can be embedded in a "real-time" schedule with weekly data updates. They can support timely decision making about policies to control dynamically changing epidemics.

Automatic Forecast of Intensive Care Unit Admissions: The Experience During the COVID-19 Pandemic in Italy

The experience of the COVID-19 pandemic showed the importance of timely monitoring of admissions to the ICU admissions. The ability to promptly forecast the epidemic impact on the occupancy of beds in the ICU is a key issue for adequate management of the health care system.Despite this, most of the literature on predictive COVID-19 models in Italy has focused on predicting the number of infections, leaving trends in ordinary hospitalizations and ICU occupancies in the background.This work aims to present an ETS approach (Exponential Smoothing Time Series) time series forecasting tool for admissions to the ICU admissions based on ETS models. The results of the forecasting model are presented for the regions most affected by the epidemic, such as Veneto, Lombardy, Emilia-Romagna, and Piedmont.The mean absolute percentage errors (MAPE) between observed and predicted admissions to the ICU admissions remain lower than 11% for all considered geographical areas.In this epidemiological context, the proposed ETS forecasting model could be suitable to monitor, in a timely manner, the impact of COVID-19 disease on the health care system, not only during the early stages of the pandemic but also during the vaccination campaign, to quickly adapt possible preventive interventions.

Modelling the persistence of Covid-19 positivity rate in Italy

The current Covid-19 pandemic is severely affecting public health and global economies. In this context, accurately predicting its evolution is essential for planning and providing resources effectively. This paper aims at capturing the dynamics of the positivity rate (PPR) of the novel coronavirus using the Heterogeneous Autoregressive (HAR) model. The use of this model is motivated by two main empirical features arising from the analysis of PPR time series: the changing long-run level and the persistent autocorrelation structure. Compared to the most frequently used Autoregressive Integrated Moving Average (ARIMA) models, the HAR is able to reproduce the strong persistence of the data by using components aggregated at different interval sizes, remaining parsimonious and easy to estimate. The relative merits of the proposed approach are assessed by performing a forecasting study on the Italian dataset. As a robustness check, the analysis of the positivity rate is also conducted by considering the case of the United States. The ability of the HAR-type models to predict the PPR at different horizons is evaluated through several loss functions, comparing the results with those generated by ARIMA models. The Model Confidence Set is used to test the significance of differences in the predictive performances of the models under analysis. Our findings suggest that HAR-type models significantly outperform ARIMA specifications in terms of forecasting accuracy. We also find that the PPR could represent an important metric for monitoring the evolution of hospitalizations, as the peak of patients in intensive care units occurs within 12-16 days after the peak in the positivity rate. This can help governments in planning socio-economic and health policies in advance.

Exploring the impact of air pollution on COVID-19 admitted cases

In urban areas, air pollution is one of the most serious global environmental issues. Using time-series approaches, this study looked into the validity of the relationship between air pollution and COVID-19 hospitalization. This time series research was carried out in the state of Kuwait; stationarity test, cointegration test, Granger causality and stability test, and test on multivariate time-series using the Vector Error Correction Model (VECM) technique. The findings reveal that the concentration rate of air pollutants ($$\hbox {O}_3$$ O 3 , $$\hbox {SO}_2$$ SO 2 , $$\hbox {NO}_2$$ NO 2 , $$\hbox {CO}$$ CO , and $$\hbox {PM}_{10}$$ PM 10 ) has an effect on COVID-19 admitted cases via Granger-cause. The Granger causation test shows that the concentration rate of air pollutants ($$\hbox {O}_3$$ O 3 , $$\hbox {PM}_{10}$$ PM 10 , $$\hbox {NO}_2$$ NO 2 , temperature and wind speed) influences and predicts the COVID-19 admitted cases. The findings suggest that sulfur dioxide ($$\hbox {SO}_2$$ SO 2 ), $$\hbox {NO}_2$$ NO 2 , temperature, and wind speed induce an increase in COVID-19 admitted cases in the short term according to VECM analysis. The evidence of a positive long-run association between COVID-19 admitted cases and environmental air pollution might be shown in the cointegration test and the VECM. There is an affirmation that the usage of air pollutants ($$\hbox {O}_3$$ O 3 , $$\hbox {SO}_2$$ SO 2 , $$\hbox {NO}_2$$ NO 2 , $$\hbox {CO}$$ CO , and $$\hbox {PM}_{10}$$ PM 10 ) has a significant impact on COVID-19-admitted cases’ prediction and its explained about 24% of increasing COVID-19 admitted cases in Kuwait.

Data analytics and knowledge management approach for COVID-19 prediction and control

The Coronavirus Disease (COVID-19) caused by SARS-CoV-2, continues to be a global threat. The major global concern among scientists and researchers is to develop innovative digital solutions for prediction and control of infection and to discover drugs for its cure. In this paper we developed a strategic technical solution for surveillance and control of COVID-19 in Delhi-National Capital Region (NCR). This work aims to elucidate the Delhi COVID-19 Data Management Framework, the backend mechanism of integrated Command and Control Center (iCCC) with plugged-in modules for various administrative, medical and field operations. Based on the time-series data extracted from iCCC repository, the forecasting of COVID-19 spread has been carried out for Delhi using the Auto-Regressive Integrated Moving Average (ARIMA) model as it can effectively predict the logistics requirements, active cases, positive patients, and death rate. The intelligence generated through this research has paved the way for the Government of National Capital Territory Delhi to strategize COVID-19 related policies formulation and implementation on real time basis. The outcome of this innovative work has led to the drastic reduction in COVID-19 positive cases and deaths in Delhi-NCR.

A comparative study for predictive monitoring of COVID-19 pandemic

COVID-19 pandemic caused by novel coronavirus (SARS-CoV-2) crippled the world economy and engendered irreparable damages to the lives and health of millions. To control the spread of the disease, it is important to make appropriate policy decisions at the right time. This can be facilitated by a robust mathematical model that can forecast the prevalence and incidence of COVID-19 with greater accuracy. This study presents an optimized ARIMA model to forecast COVID-19 cases. The proposed method first obtains a trend of the COVID-19 data using a low-pass Gaussian filter and then predicts/forecasts data using the ARIMA model. We benchmarked the optimized ARIMA model for 7-days and 14-days forecasting against five forecasting strategies used recently on the COVID-19 data. These include the auto-regressive integrated moving average (ARIMA) model, susceptible-infected-removed (SIR) model, composite Gaussian growth model, composite Logistic growth model, and dictionary learning-based model. We have considered the daily infected cases, cumulative death cases, and cumulative recovered cases of the COVID-19 data of the ten most affected countries in the world, including India, USA, UK, Russia, Brazil, Germany, France, Italy, Turkey, and Colombia. The proposed algorithm outperforms the existing models on the data of most of the countries considered in this study.

Can we accurately forecast non-elective bed occupancy and admissions in the NHS? A time-series MSARIMA analysis of longitudinal data from an NHS Trust

OBJECTIVES

The main objective of the study was to develop more accurate and precise short-term forecasting models for admissions and bed occupancy for an NHS Trust located in Bristol, England. Subforecasts for the medical and surgical specialties, and for different lengths of stay were realised DESIGN: Autoregressive integrated moving average models were specified on a training dataset of daily count data, then tested on a 6-week forecast horizon. Explanatory variables were included in the models: day of the week, holiday days, lagged temperature and precipitation.

SETTING

A secondary care hospital in an NHS Trust in South West England.

PARTICIPANTS

Hospital admissions between September 2016 and March 2020, comprising 1291 days.

PRIMARY AND SECONDARY OUTCOME MEASURES

The accuracy of the forecasts was assessed through standard measures, as well as compared with the actual data using accuracy thresholds of 10% and 20% of the mean number of admissions or occupied beds.

RESULTS

The overall Autoregressive Integrated Moving Average (ARIMA) admissions forecast was compared with the Trust's forecast, and found to be more accurate, namely, being closer to the actual value 95.6% of the time. Furthermore, it was more precise than the Trust's. The subforecasts, as well as those for bed occupancy, tended to be less accurate compared with the overall forecasts. All of the explanatory variables improved the forecasts.

CONCLUSIONS

ARIMA models can forecast non-elective admissions in an NHS Trust accurately on a 6-week horizon, which is an improvement on the current predictive modelling in the Trust. These models can be readily applied to other contexts, improving patient flow.

Using the SARIMA Model to Forecast the Fourth Global Wave of Cumulative Deaths from COVID-19: Evidence from 12 Hard-Hit Big Countries

The COVID-19 pandemic is a serious threat to all of us. It has caused an unprecedented shock to the world’s economy, and it has interrupted the lives and livelihood of millions of people. In the last two years, a large body of literature has attempted to forecast the main dimensions of the COVID-19 outbreak using a wide set of models. In this paper, I forecast the short- to mid-term cumulative deaths from COVID-19 in 12 hard-hit big countries around the world as of 20 August 2021. The data used in the analysis were extracted from the Our World in Data COVID-19 dataset. Both non-seasonal and seasonal autoregressive integrated moving averages (ARIMA and SARIMA) were estimated. The analysis showed that: (i) ARIMA/SARIMA forecasts were sufficiently accurate in both the training and test set by always outperforming the simple alternative forecasting techniques chosen as benchmarks (Mean, Naïve, and Seasonal Naïve); (ii) SARIMA models outperformed ARIMA models in 47 out 48 metrics (in forecasting future values), i.e., on 97.9% of all the considered forecast accuracy measures (mean absolute error [MAE], mean absolute percentage error [MAPE], mean absolute scaled error [MASE], and the root mean squared error [RMSE]), suggesting a clear seasonal pattern in the data; and (iii) the forecasted values from SARIMA models fitted very well the observed (real-time) data for the period 21 August 2021–19 September 2021 for almost all the countries analyzed. This article shows that SARIMA can be safely used for both the short- and medium-term predictions of COVID-19 deaths. Thus, this approach can help government authorities to monitor and manage the huge pressure that COVID-19 is exerting on national healthcare systems.

Discrepancy between the Demand and Supply of Intensive Care Unit Beds in South Korea from 2011 to 2019: A Cross-Sectional Analysis

PURPOSE

Intensive care unit (ICU) bed availability is key to critical patient care. In many countries, older patients generally account for a significant proportion of hospitalizations and ICU admissions. Therefore, considering the rapidly increasing aging population in South Korea, it is important to establish whether the demand for critical care is currently met by available ICU beds.

MATERIALS AND METHODS

We evaluated a 9-year trend in ICU bed supply and ICU length of stay in South Korea between 2011 and 2019 in a population-based cross-sectional analysis, using data from the Korean Health Insurance Review & Assessment Service and Statistics database. We described the changes in ICU bed rates in adult (≥20 years) and older adult (≥65 years) populations. ICU length of stay was categorized similarly and was used to predict future ICU bed demands.

RESULTS

The ICU bed rate per 100000 adults increased from 18.5 in 2011 to 19.5 in 2019. In contrast, the ICU bed rate per 100000 older adults decreased from 127.6 in 2011 to 104.0 in 2019. ICU length of stay increased by 43.8% for adults and 55.6% for older adults. In 2019, the regional differences in the ICU bed rate nearly doubled, and the ICU length of stay increased six-fold. The ICU bed occupancy rate in South Korea is expected to rise to 102.7% in 2030.

CONCLUSION

The discrepancy between the demand and supply of ICU beds in South Korea requires urgent action to anticipate future ICU demands.

Forecasting waved daily COVID-19 death count series with a novel combination of segmented Poisson model and ARIMA models

Autoregressive Integrated Moving Average (ARIMA) models have been widely used to forecast and model the development of various infectious diseases including COVID-19 outbreaks; however, such use of ARIMA models does not respect the count nature of the pandemic development data. For example, the daily COVID-19 death count series data for Canada and the United States (USA) are generally skewed with lots of low counts. In addition, there are generally waved patterns with turning points influenced by government major interventions against the spread of COVID-19 during different periods and seasons. In this study, we propose a novel combination of the segmented Poisson model and ARIMA models to handle these features and correlation structures in a two-stage process. The first stage of this process is a generalization of trend analysis of time series data. Our approach is illustrated with forecasting and modeling of daily COVID-19 death count series data for Canada and the USA.

Does Climate Play Any Role in COVID-19 Spreading?-An Australian Perspective

Compared to other countries, the COVID-19 pandemic did not severely affect Australia as measured by total deaths until mid-2021. Though a substantial number of daily confirmed cases (up to 698) were reported during the second wave, most of them were from the southern state of Victoria. This study examined the possible correlations between climate variables and the number of daily confirmed COVID-19 cases in Victoria, Australia, from 25 January to 31 October 2020. Appropriate regression models and cross-correlation diagnostics were used to examine the effect of temperature, rainfall, solar exposure, and ultraviolet index (UVI) with the number of daily confirmed cases. Significant positive associations were identified for solar exposure and maximum and average UVI for confirmed cases one and 19 days later. Negative associations for these variables were found for confirmed cases five days later. Minimum temperature had a significant negative correlation one day later and a positive effect 21 days later. No significant correlation was found for maximum temperature and rainfall. The most significant relationships were found for confirmed cases 19 days after changes in the meteorological variables. A 1% increase in solar exposure, maximum UVI, and average UVI was associated with a 0.31% (95% CI: 0.13 to 0.51), 0.71% (95% CI: 0.43 to 0.98), and 0.63% (95%CI: 0.20 to 1.61) increase 19 days later in the number of confirmed cases, respectively. The implications of these results can be used in the public health management of any possible future events in Australia. It also highlights the significance of considering the climatic variables and seasonality in all kinds of epidemics and pandemics.

Forecasting COVID-19 Hospital Census: A Multivariate Time-Series Model Based on Local Infection Incidence

BACKGROUND

COVID-19 has been one of the most serious global health crises in world history. During the pandemic, health care systems require accurate forecasts for key resources to guide preparation for patient surges. Forecasting the COVID-19 hospital census is among the most important planning decisions to ensure adequate staffing, number of beds, intensive care units, and vital equipment.

OBJECTIVE

The goal of this study was to explore the potential utility of local COVID-19 infection incidence data in developing a forecasting model for the COVID-19 hospital census.

METHODS

The study data comprised aggregated daily COVID-19 hospital census data across 11 Atrium Health hospitals plus a virtual hospital in the greater Charlotte metropolitan area of North Carolina, as well as the total daily infection incidence across the same region during the May 15 to December 5, 2020, period. Cross-correlations between hospital census and local infection incidence lagging up to 21 days were computed. A multivariate time-series framework, called the vector error correction model (VECM), was used to simultaneously incorporate both time series and account for their possible long-run relationship. Hypothesis tests and model diagnostics were performed to test for the long-run relationship and examine model goodness of fit. The 7-days-ahead forecast performance was measured by mean absolute percentage error (MAPE), with time-series cross-validation. The forecast performance was also compared with an autoregressive integrated moving average (ARIMA) model in the same cross-validation time frame. Based on different scenarios of the pandemic, the fitted model was leveraged to produce 60-days-ahead forecasts.

RESULTS

The cross-correlations were uniformly high, falling between 0.7 and 0.8. There was sufficient evidence that the two time series have a stable long-run relationship at the .01 significance level. The model had very good fit to the data. The out-of-sample MAPE had a median of 5.9% and a 95th percentile of 13.4%. In comparison, the MAPE of the ARIMA had a median of 6.6% and a 95th percentile of 14.3%. Scenario-based 60-days-ahead forecasts exhibited concave trajectories with peaks lagging 2 to 3 weeks later than the peak infection incidence. In the worst-case scenario, the COVID-19 hospital census can reach a peak over 3 times greater than the peak observed during the second wave.

CONCLUSIONS

When used in the VECM framework, the local COVID-19 infection incidence can be an effective leading indicator to predict the COVID-19 hospital census. The VECM model had a very good 7-days-ahead forecast performance and outperformed the traditional ARIMA model. Leveraging the relationship between the two time series, the model can produce realistic 60-days-ahead scenario-based projections, which can inform health care systems about the peak timing and volume of the hospital census for long-term planning purposes.

Forecasting fully vaccinated people against COVID-19 and examining future vaccination rate for herd immunity in the US, Asia, Europe, Africa, South America, and the World

Coronavirus disease 2019 (COVID-2019) has spread rapidly all over the world and it is known that the most effective way to eliminate the disease is vaccination. Although the traditional vaccine development process is quite long, more than ten COVID-19 vaccines have been approved for use in about a year. The COVID-19 vaccines that have been administered are highly effective enough, but achieving herd immunity is required to end the pandemic. The motivation of this study is to contribute to review the countries’ vaccine policies and adjusting the manufacturing plans of the vaccine companies. In this study, the total number of people fully vaccinated against COVID-19 was forecasted in the US, Asia, Europe, Africa, South America, and the World with the Autoregressive Integrated Moving Average (ARIMA) model, which is a new approach in vaccination studies. Additionally, for herd immunity, the percentage of fully vaccinated people in these regions at the beginning of 2021 summer was determined. ARIMA results show that in the US, Asia, Europe, Africa, South America, and the World will reach 139 million, 109 million, 127 million, 8 million, 38 million, and 441 million people will be fully vaccinated on 1 June 2021, respectively. According to these results, 41.8% of the US, 2.3% of Asia, 17% of Europe, 0.6% of Africa, 8.8% of South America, and 5.6% of the World population will be fully vaccinated people against the COVID-19. Results show that countries are far from the herd immunity threshold level desired to reach for safely slow or stop the COVID-19 epidemic.

How New Mexico Leveraged a COVID-19 Case Forecasting Model to Preemptively Address the Health Care Needs of the State: Quantitative Analysis

BACKGROUND

Prior to the COVID-19 pandemic, US hospitals relied on static projections of future trends for long-term planning and were only beginning to consider forecasting methods for short-term planning of staffing and other resources. With the overwhelming burden imposed by COVID-19 on the health care system, an emergent need exists to accurately forecast hospitalization needs within an actionable timeframe.

OBJECTIVE

Our goal was to leverage an existing COVID-19 case and death forecasting tool to generate the expected number of concurrent hospitalizations, occupied intensive care unit (ICU) beds, and in-use ventilators 1 day to 4 weeks in the future for New Mexico and each of its five health regions.

METHODS

We developed a probabilistic model that took as input the number of new COVID-19 cases for New Mexico from Los Alamos National Laboratory's COVID-19 Forecasts Using Fast Evaluations and Estimation tool, and we used the model to estimate the number of new daily hospital admissions 4 weeks into the future based on current statewide hospitalization rates. The model estimated the number of new admissions that would require an ICU bed or use of a ventilator and then projected the individual lengths of hospital stays based on the resource need. By tracking the lengths of stay through time, we captured the projected simultaneous need for inpatient beds, ICU beds, and ventilators. We used a postprocessing method to adjust the forecasts based on the differences between prior forecasts and the subsequent observed data. Thus, we ensured that our forecasts could reflect a dynamically changing situation on the ground.

RESULTS

Forecasts made between September 1 and December 9, 2020, showed variable accuracy across time, health care resource needs, and forecast horizon. Forecasts made in October, when new COVID-19 cases were steadily increasing, had an average accuracy error of 20.0%, while the error in forecasts made in September, a month with low COVID-19 activity, was 39.7%. Across health care use categories, state-level forecasts were more accurate than those at the regional level. Although the accuracy declined as the forecast was projected further into the future, the stated uncertainty of the prediction improved. Forecasts were within 5% of their stated uncertainty at the 50% and 90% prediction intervals at the 3- to 4-week forecast horizon for state-level inpatient and ICU needs. However, uncertainty intervals were too narrow for forecasts of state-level ventilator need and all regional health care resource needs.

CONCLUSIONS

Real-time forecasting of the burden imposed by a spreading infectious disease is a crucial component of decision support during a public health emergency. Our proposed methodology demonstrated utility in providing near-term forecasts, particularly at the state level. This tool can aid other stakeholders as they face COVID-19 population impacts now and in the future.

Prognosticating the Spread of Covid-19 Pandemic Based on Optimal Arima Estimators

COVID-19 cases have been reported as a global threat and several studies are being conducted using various modelling techniques to evaluate patterns of disease dispersion in the upcoming weeks. Here we propose a simple statistical model that could be used to predict the epidemiological extent of community spread of COVID-19 from the explicit data based on optimal ARIMA model estimators. Raw data was retrieved on confirmed cases of COVID-19 from Johns Hopkins University (https://github.com/CSSEGISandData/COVID-19) and the Auto-Regressive Integrated Moving Average (ARIMA) model was fitted based on cumulative daily figures of confirmed cases aggregated globally for ten major countries to predict their incidence trend. Statistical analysis was completed by using R 3.5.3 software. The optimal ARIMA model having the lowest Akaike information criterion (AIC) value for US (0,2,0); Spain (1,2,0); France (0,2,1); Germany (3,2,2); Iran (1,2,1); China (0,2,1); Russia (3,2,1); India (2,2,2); Australia (1,2,0) and South Africa (0,2,2) imparted the nowcasting of trends for the upcoming weeks. These parameters are (p, d, q) where p refers to the number of autoregressive terms, d refers to the number of times the series has to be differenced before it becomes stationary, and q refers to the number of moving average terms. Results obtained from the ARIMA model showed a significant decrease in cases in Australia; a stable case for China and rising cases have been observed in other countries. This study predicted the possible proliferate of COVID-19, although spreading significantly depends upon the various control and measurement policy taken by each country.

Deep learning-based forecasting model for COVID-19 outbreak in Saudi Arabia

COVID-19 outbreak has become a global pandemic that affected more than 200 countries. Predicting the epidemiological behavior of this outbreak has a vital role to prevent its spreading. In this study, long short-term memory (LSTM) network as a robust deep learning model is proposed to forecast the number of total confirmed cases, total recovered cases, and total deaths in Saudi Arabia. The model was trained using the official reported data. The optimal values of the model's parameters that maximize the forecasting accuracy were determined. The forecasting accuracy of the model was assessed using seven statistical assessment criteria, namely, root mean square error (RMSE), coefficient of determination (R2), mean absolute error (MAE), efficiency coefficient (EC), overall index (OI), coefficient of variation (COV), and coefficient of residual mass (CRM). A reasonable forecasting accuracy was obtained. The forecasting accuracy of the suggested model is compared with two other models. The first is a statistical based model called autoregressive integrated moving average (ARIMA). The second is an artificial intelligence based model called nonlinear autoregressive artificial neural networks (NARANN). Finally, the proposed LSTM model was applied to forecast the total number of confirmed cases as well as deaths in six different countries; Brazil, India, Saudi Arabia, South Africa, Spain, and USA. These countries have different epidemic trends as they apply different polices and have different age structure, weather, and culture. The social distancing and protection measures applied in different countries are assumed to be maintained during the forecasting period. The obtained results may help policymakers to control the disease and to put strategic plans to organize Hajj and the closure periods of the schools and universities.

A time series-based statistical approach for outbreak spread forecasting: Application of COVID-19 in Greece

The aim of this paper is the generation of a time-series based statistical data-driven procedure in order to track an outbreak. At first are used univariate time series models in order to predict the evolution of the reported cases. Moreover, are considered combinations of the models in order to provide more accurate and robust results. Additionally, statistical probability distributions are considered in order to generate future scenarios. Final step is the build and use of an epidemiological model (tSIR) and the calculation of an epidemiological ratio (R₀) for estimating the termination of the outbreak. The time series models include Exponential Smoothing and ARIMA approaches from the classical models, also Feed-Forward Artificial Neural Networks and Multivariate Adaptive Regression Splines from the machine learning toolbox. Combinations include simple mean, Newbolt-Granger and Bates-Granger approaches. Finally, the tSIR model and the R₀ ratio are used for estimating the spread and the reversion of the pandemic. The suggested procedure is used to track the COVID-19 epidemic in Greece. This epidemic has appeared in China in December 2019 and has been widespread since then to all over the world. Greece is the center of this empirical study as is considered an early successful paradigm of resistance against the virus.

Forecasting COVID-19 Confirmed Cases Using Empirical Data Analysis in Korea

From November to December 2020, the third wave of COVID-19 cases in Korea is ongoing. The government increased Seoul's social distancing to the 2.5 level, and the number of confirmed cases is increasing daily. Due to a shortage of hospital beds, treatment is difficult. Furthermore, gatherings at the end of the year and the beginning of next year are expected to worsen the effects. The purpose of this paper is to emphasize the importance of prediction timing rather than prediction of the number of confirmed cases. Thus, in this study, five groups were set according to minimum, maximum, and high variability. Through empirical data analysis, the groups were subdivided into a total of 19 cases. The cumulative number of COVID-19 confirmed cases is predicted using the auto regressive integrated moving average (ARIMA) model and compared with the actual number of confirmed cases. Through group and case-by-case prediction, forecasts can accurately determine decreasing and increasing trends. To prevent further spread of COVID-19, urgent and strong government restrictions are needed. This study will help the government and the Korea Disease Control and Prevention Agency (KDCA) to respond systematically to a future surge in confirmed cases.

Forecasting national and regional level intensive care unit bed demand during COVID-19: The case of Italy

Given the pressure on healthcare authorities to assess whether hospital capacity allows properly responding to outbreaks such as COVID-19, there is a need for simple, data-driven methods that may provide accurate forecasts of hospital bed demand. This study applies growth models to forecast the demand for Intensive Care Unit admissions in Italy during COVID-19. We show that, with only some mild assumptions on the functional form and using short time-series, the model fits past data well and can accurately forecast demand fourteen days ahead (the mean absolute percentage error (MAPE) of the cumulative fourteen days forecasts is 7.64). The model is then applied to derive regional-level forecasts by adopting hierarchical methods that ensure the consistency between national and regional level forecasts. Predictions are compared with current hospital capacity in the different Italian regions, with the aim to evaluate the adequacy of the expansion in the number of beds implemented during the COVID-19 crisis.

Using multivariate long short-term memory neural network to detect aberrant signals in health data for quality assurance

BACKGROUND

The data quality of electronic health records (EHR) has been a topic of increasing interest to clinical and health services researchers. One indicator of possible errors in data is a large change in the frequency of observations in chronic illnesses. In this study, we built and demonstrated the utility of a stacked multivariate LSTM model to predict an acceptable range for the frequency of observations.

METHODS

We applied the LSTM approach to a large EHR dataset with over 400 million total encounters. We computed sensitivity and specificity for predicting if the frequency of an observation in a given week is an aberrant signal.

RESULTS

Compared with the simple frequency monitoring approach, our proposed multivariate LSTM approach increased the sensitivity of finding aberrant signals in 6 randomly selected diagnostic codes from 75 to 88% and the specificity from 68 to 91%. We also experimented with two different LSTM algorithms, namely, direct multi-step and recursive multi-step. Both models were able to detect the aberrant signals while the recursive multi-step algorithm performed better.

CONCLUSIONS

Simply monitoring the frequency trend, as is the common practice in systems that do monitor the data quality, would not be able to distinguish between the fluctuations caused by seasonal disease changes, seasonal patient visits, or a change in data sources. Our study demonstrated the ability of stacked multivariate LSTM models to recognize true data quality issues rather than fluctuations that are caused by different reasons, including seasonal changes and outbreaks.

Modeling and forecasting of COVID-19 using a hybrid dynamic model based on SEIRD with ARIMA corrections

The outbreak of novel coronavirus (COVID-19) attracted worldwide attention. It has posed a significant challenge for the global economies, especially the healthcare sector. Even with a robust healthcare system, countries were not prepared for the ramifications of COVID-19. Several statistical, dynamic, and mathematical models of the COVID-19 outbreak including the SEIR model have been developed to analyze the infection its transmission dynamics. The objective of this research is to use public data to study the properties associated with the COVID-19 pandemic to develop a dynamic hybrid model based on SEIRD and ascertainment rate with automatically selected parameters. The proposed model consists of two parts: the modified SEIRD dynamic model and ARIMA models. We fit SEIRD model parameters against historical values of infected, recovered and deceased population divided by ascertainment rate, which, in turn, is also a parameter of the model. Residuals of the first model for infected, recovered, and deceased populations are then corrected using ARIMA models. The model can analyze the input data in real-time and provide long- and short-term forecasts with confidence intervals. The model was tested and validated on the US COVID statistics dataset from the COVID Tracking Project. For validation, we use unseen recent statistical data. We use five common measures to estimate model prediction ability: MAE, MSE, MLSE, Normalized MAE, and Normalized MSE. We proved a great model ability to make accurate predictions of infected, recovered, and deceased patients. The output of the model can be used by the government, private sectors, and policymakers to reduce health and economic risks significantly improved consumer credit scoring.

Testing the Accuracy of the ARIMA Models in Forecasting the Spreading of COVID-19 and the Associated Mortality Rate

Background and objectives: The current pandemic of SARS-CoV-2 has not only changed, but also affected the lives of tens of millions of people around the world in these last nine to ten months. Although the situation is stable to some extent within the developed countries, approximately one million have already died as a consequence of the unique symptomatology that these people displayed. Thus, the need to develop an effective strategy for monitoring, restricting, but especially for predicting the evolution of COVID-19 is urgent, especially in middle-class countries such as Romania. Material and Methods: Therefore, autoregressive integrated moving average (ARIMA) models have been created, aiming to predict the epidemiological course of COVID-19 in Romania by using two statistical software (STATGRAPHICS Centurion (v.18.1.13) and IBM SPSS (v.20.0.0)). To increase the accuracy, we collected data between the established interval (1 March, 31 August) from the official website of the Romanian Government and the World Health Organization. Results: Several ARIMA models were generated from which ARIMA (1,2,1), ARIMA (3,2,2), ARIMA (3,1,3), ARIMA (3,2,2), ARIMA (3,1,3), ARIMA (2,2,2) and ARIMA (1,2,1) were considered the best models. For this, we took into account the lowest value of mean absolute percentage error (MAPE) for March, April, May, June, July, and August (MAPE_March = 9.3225, MAPE_April = 0.975287, MAPE_May = 0.227675, MAPE_June = 0.161412, MAPE_July = 0.243285, MAPE_August = 0.163873, MAPE_{March – August} = 2.29175 for STATGRAPHICS Centurion (v.18.1.13) and MAPE_March = 57.505, MAPE_April = 1.152, MAPE_May = 0.259, MAPE_June = 0.185, MAPE_July = 0.307, MAPE_August = 0.194, and MAPE_{March – August} = 6.013 for IBM SPSS (v.20.0.0) respectively. Conclusions: This study demonstrates that ARIMA is a useful statistical model for making predictions and provides an idea of the epidemiological status of the country of interest.

COVID-19 prevalence estimation: Four most affected African countries

The world at large has been confronted with several disease outbreak which has posed and still posing a serious menace to public health globally. Recently, COVID-19 a new kind of coronavirus emerge from Wuhan city in China and was declared a pandemic by the World Health Organization. There has been a reported case of about 8622985 with global death of 457,355 as of 15.05 GMT, June 19, 2020. South-Africa, Egypt, Nigeria and Ghana are the most affected African countries with this outbreak. Thus, there is a need to monitor and predict COVID-19 prevalence in this region for effective control and management. Different statistical tools and time series model such as the linear regression model and autoregressive integrated moving average (ARIMA) models have been applied for disease prevalence/incidence prediction in different diseases outbreak. However, in this study, we adopted the ARIMA model to forecast the trend of COVID-19 prevalence in the aforementioned African countries. The datasets examined in this analysis spanned from February 21, 2020, to June 16, 2020, and was extracted from the World Health Organization website. ARIMA models with minimum Akaike information criterion correction (AICc) and statistically significant parameters were selected as the best models. Accordingly, the ARIMA (0,2,3), ARIMA (0,1,1), ARIMA (3,1,0) and ARIMA (0,1,2) models were chosen as the best models for SA, Nigeria, and Ghana and Egypt, respectively. Forecasting was made based on the best models. It is noteworthy to claim that the ARIMA models are appropriate for predicting the prevalence of COVID-19. We noticed a form of exponential growth in the trend of this virus in Africa in the days to come. Thus, the government and health authorities should pay attention to the pattern of COVID-19 in Africa. Necessary plans and precautions should be put in place to curb this pandemic in Africa.

Analysis and Estimation of COVID-19 Spreading in Russia Based on ARIMA Model

Russia has been currently in the "hard-hit" area of the COVID-19 outbreak, with more than 396,000 confirmed cases as of May 30. It is necessary to analyze and predict its epidemic situation to help formulate effective public health policies. Autoregressive integrated moving average (ARIMA) models were developed to predict the cumulative confirmed, dead, and recovered cases, respectively. R 3.6.2 software was used to fit the data from January 31 to May 20, 2020, and predict the data for the next 30 days. The COVID-19 epidemic in Russia was divided into two stages and reached its peak in May. The epidemic began to stabilize on May 19. The case fatality rate has been at an extremely low level. ARIMA (2,2,1), ARIMA (3,2,0), and ARIMA (0,2,1) were the models of cumulative confirmed, dead, and recovered cases, respectively. After testing, the mean absolute percentage error (MAPE) of three models were 0.6, 3.9, and 2.4, respectively. This paper indicates that Russia's health system capacity can effectively respond to the COVID-19 pandemic. Three ARIMA models have a good fitting effect and can be used for short-term prediction of the COVID-19 trend, providing a theoretical basis for Russia to formulate new intervention policies.

Modeling and Forecasting of COVID-19 Growth Curve in India

In this article, we analyze the growth pattern of COVID-19 pandemic in India from March 4 to July 11 using regression analysis (exponential and polynomial), auto-regressive integrated moving averages (ARIMA) model as well as exponential smoothing and Holt–Winters models. We found that the growth of COVID-19 cases follows a power regime of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({t}^{2}, t,...)$$\end{document}(t2,t,...) after the exponential growth. We found the optimal change points from where the COVID-19 cases shifted their course of growth from exponential to quadratic and then from quadratic to linear. After that, we saw a sudden spike in the course of the spread of COVID-19 and the growth moved from linear to quadratic and then to quartic, which is alarming. We have also found the best fitted regression models using the various criteria, such as significant p-values, coefficients of determination and ANOVA, etc. Further, we search the best-fitting ARIMA model for the data using the AIC (Akaike Information Criterion) and provide the forecast of COVID-19 cases for future days. We also use usual exponential smoothing and Holt–Winters models for forecasting purpose. We further found that the ARIMA (5, 2, 5) model is the best-fitting model for COVID-19 cases in India.

Estimation of COVID-19 prevalence in Italy, Spain, and France

At the end of December 2019, coronavirus disease 2019 (COVID-19) appeared in Wuhan city, China. As of April 15, 2020, >1.9 million COVID-19 cases were confirmed worldwide, including >120,000 deaths. There is an urgent need to monitor and predict COVID-19 prevalence to control this spread more effectively. Time series models are significant in predicting the impact of the COVID-19 outbreak and taking the necessary measures to respond to this crisis. In this study, Auto-Regressive Integrated Moving Average (ARIMA) models were developed to predict the epidemiological trend of COVID-19 prevalence of Italy, Spain, and France, the most affected countries of Europe. The prevalence data of COVID-19 from 21 February 2020 to 15 April 2020 were collected from the World Health Organization website. Several ARIMA models were formulated with different ARIMA parameters. ARIMA (0,2,1), ARIMA (1,2,0), and ARIMA (0,2,1) models with the lowest MAPE values (4.7520, 5.8486, and 5.6335) were selected as the best models for Italy, Spain, and France, respectively. This study shows that ARIMA models are suitable for predicting the prevalence of COVID-19 in the future. The results of the analysis can shed light on understanding the trends of the outbreak and give an idea of the epidemiological stage of these regions. Besides, the prediction of COVID-19 prevalence trends of Italy, Spain, and France can help take precautions and policy formulation for this epidemic in other countries.

Comparison of Growth Patterns of COVID-19 Cases through the ARIMA and Gompertz Models. Case Studies: Austria, Switzerland, and Israel

On May 19, 2020, data confirmed that coronavirus 2019 disease (COVID-19) had spread worldwide, with more than 4.7 million infected people and more than 316,000 deaths. In this article, we carry out a comparison of the methods to calculate and forecast the growth of the pandemic using two statistical models: the autoregressive integrated moving average (ARIMA) and the Gompertz function growth model. The countries that have been chosen to verify the usefulness of these models are Austria, Switzerland, and Israel, which have a similar number of habitants. The investigation to check the accuracy of the models was carried out using data on confirmed, non-asymptomatic cases and confirmed deaths from the period February 21-May 19, 2020. We use the root mean squared error (RMSE), the mean absolute percentage error (MAPE), and the regression coefficient index R2 to check the accuracy of the models. The experimental results provide promising adjustment errors for both models (R2>0.99), with the ARIMA model being the best for infections and the Gompertz best for mortality. It has also been verified that countries are affected differently, which may be due to external factors that are difficult to measure quantitatively. These models provide a fast and effective system to check the growth of pandemics that can be useful for health systems and politicians so that appropriate measures are taken and countries' health care systems do not collapse.

Epidemiological features and time-series analysis of influenza incidence in urban and rural areas of Shenyang, China, 2010-2018

In recent years, there have been a significant influenza activity and emerging influenza strains in China, resulting in an increasing number of influenza virus infections and leading to public health concerns. The aims of this study were to identify the epidemiological and aetiological characteristics of influenza and establish seasonal autoregressive integrated moving average (SARIMA) models for forecasting the percentage of visits for influenza-like illness (ILI%) in urban and rural areas of Shenyang. Influenza surveillance data were obtained for ILI cases and influenza virus positivity from 18 sentinel hospitals. The SARIMA models were constructed to predict ILI% for January–December 2019. During 2010–2018, the influenza activity was higher in urban than in rural areas. The age distribution of ILI cases showed the highest rate in young children aged 0–4 years. Seasonal A/H3N2, influenza B virus and pandemic A/H1N1 continuously co-circulated in winter and spring seasons. In addition, the SARIMA (0, 1, 0) (0, 1, 2)₁₂ model for the urban area and the SARIMA (1, 1, 1) (1, 1, 0)₁₂ model for the rural area were appropriate for predicting influenza incidence. Our findings suggested that there were regional and seasonal distinctions of ILI activity in Shenyang. A co-epidemic pattern of influenza strains was evident in terms of seasonal influenza activity. Young children were more susceptible to influenza virus infection than adults. These results provide a reference for future influenza prevention and control strategies in the study area.

After Less Than 2 Months, the Simulations That Drove the World to Strict Lockdown Appear to be Wrong, the Same of the Policies They Generated

Here, we review modeling predictions for Covid-19 mortality based on recent data. The Imperial College model trusted by the British Government predicted peak mortalities above 170 deaths per million in the United States, and above 215 deaths per million in Great Britain, after more than 2 months from the outbreak, and a length for the outbreak well above 4 months. These predictions drove the world to adopt harsh distancing measures and forget the concept of herd immunity. China had peak mortalities of less than 0.1 deaths per million after 40 days since first deaths, and an 80-day-long outbreak. Italy, Belgium, the Netherlands, Sweden, or Great Britain flattened the curve at 13.6, 28.6, 9.0, 10.6, and 13.9 deaths per million after 40, 39, 33, 44, and 39 days from first deaths, or 31, 29, 24, 38, and 29 days since the daily confirmed deaths reached 0.1 per million people, respectively. The declining curve is much slower for Italy, the Netherlands, or Great Britain than Belgium or Sweden. Opposite to Great Britain, Italy, or Belgium that enforced a complete lockdown, the Netherlands only adopted an "intelligent" lockdown, and Sweden did not adopt any lockdown. However, they achieved better results. Coupled to new evidence for minimal impact of Covid-19 on the healthy population, with the most part not infected even if challenged, or only mild or asymptomatic if infected, there are many good reasons to question the validity of the specific epidemiological model simulations and the policies they produced. Fewer restrictions on the healthy while better protecting the vulnerable would have been a much better option, permitting more sustainable protection of countries otherwise at risk of second waves as soon as the strict measures are lifted.

Decoding and modelling of time series count data using Poisson hidden Markov model and Markov ordinal logistic regression models

Hidden Markov models are stochastic models in which the observations are assumed to follow a mixture distribution, but the parameters of the components are governed by a Markov chain which is unobservable. The issues related to the estimation of Poisson-hidden Markov models in which the observations are coming from mixture of Poisson distributions and the parameters of the component Poisson distributions are governed by an m-state Markov chain with an unknown transition probability matrix are explained here. These methods were applied to the data on Vibrio cholerae counts reported every month for 11-year span at Christian Medical College, Vellore, India. Using Viterbi algorithm, the best estimate of the state sequence was obtained and hence the transition probability matrix. The mean passage time between the states were estimated. The 95% confidence interval for the mean passage time was estimated via Monte Carlo simulation. The three hidden states of the estimated Markov chain are labelled as 'Low', 'Moderate' and 'High' with the mean counts of 1.4, 6.6 and 20.2 and the estimated average duration of stay of 3, 3 and 4 months, respectively. Environmental risk factors were studied using Markov ordinal logistic regression analysis. No significant association was found between disease severity levels and climate components.

Time series modelling to forecast prehospital EMS demand for diabetic emergencies

BACKGROUND

Acute diabetic emergencies are often managed by prehospital Emergency Medical Services (EMS). The projected growth in prevalence of diabetes is likely to result in rising demand for prehospital EMS that are already under pressure. The aims of this study were to model the temporal trends and provide forecasts of prehospital attendances for diabetic emergencies.

METHODS

A time series analysis on monthly cases of hypoglycemia and hyperglycemia was conducted using data from the Ambulance Victoria (AV) electronic database between 2009 and 2015. Using the seasonal autoregressive integrated moving average (SARIMA) modelling process, different models were evaluated. The most parsimonious model with the highest accuracy was selected.

RESULTS

Forty-one thousand four hundred fifty-four prehospital diabetic emergencies were attended over a seven-year period with an increase in the annual median monthly caseload between 2009 (484.5) and 2015 (549.5). Hypoglycemia (70%) and people with type 1 diabetes (48%) accounted for most attendances. The SARIMA (0,1,0,12) model provided the best fit, with a MAPE of 4.2% and predicts a monthly caseload of approximately 740 by the end of 2017.

CONCLUSIONS

Prehospital EMS demand for diabetic emergencies is increasing. SARIMA time series models are a valuable tool to allow forecasting of future caseload with high accuracy and predict increasing cases of prehospital diabetic emergencies into the future. The model generated by this study may be used by service providers to allow appropriate planning and resource allocation of EMS for diabetic emergencies.

Impact of weather factors on hand, foot and mouth disease, and its role in short-term incidence trend forecast in Huainan City, Anhui Province

Hand, foot, and mouth disease (HFMD) is one of the most common communicable diseases in China, and current climate change had been recognized as a significant contributor. Nevertheless, no reliable models have been put forward to predict the dynamics of HFMD cases based on short-term weather variations. The present study aimed to examine the association between weather factors and HFMD, and to explore the accuracy of seasonal auto-regressive integrated moving average (SARIMA) model with local weather conditions in forecasting HFMD. Weather and HFMD data from 2009 to 2014 in Huainan, China, were used. Poisson regression model combined with a distributed lag non-linear model (DLNM) was applied to examine the relationship between weather factors and HFMD. The forecasting model for HFMD was performed by using the SARIMA model. The results showed that temperature rise was significantly associated with an elevated risk of HFMD. Yet, no correlations between relative humidity, barometric pressure and rainfall, and HFMD were observed. SARIMA models with temperature variable fitted HFMD data better than the model without it (sR ² increased, while the BIC decreased), and the SARIMA (0, 1, 1)(0, 1, 0)₅₂ offered the best fit for HFMD data. In addition, compared with females and nursery children, males and scattered children may be more suitable for using SARIMA model to predict the number of HFMD cases and it has high precision. In conclusion, high temperature could increase the risk of contracting HFMD. SARIMA model with temperature variable can effectively improve its forecast accuracy, which can provide valuable information for the policy makers and public health to construct a best-fitting model and optimize HFMD prevention.

Data-driven outbreak forecasting with a simple nonlinear growth model

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We present EpiGro, a simple data-driven method to forecast the scope of an ongoing outbreak.

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We provide general hypotheses for expected model validity and also discuss model limitations.

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We propose an automated parameter estimation method that can be used for forecasting.

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We test our approach on 9 different outbreaks and show robustness over multiple systems and over noisy data sets.

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In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Recent events have thrown the spotlight on infectious disease outbreak response. We developed a data-driven method, EpiGro, which can be applied to cumulative case reports to estimate the order of magnitude of the duration, peak and ultimate size of an ongoing outbreak. It is based on a surprisingly simple mathematical property of many epidemiological data sets, does not require knowledge or estimation of disease transmission parameters, is robust to noise and to small data sets, and runs quickly due to its mathematical simplicity. Using data from historic and ongoing epidemics, we present the model. We also provide modeling considerations that justify this approach and discuss its limitations. In the absence of other information or in conjunction with other models, EpiGro may be useful to public health responders.

Historical Data Analysis of Hospital Discharges Related to the Amerithrax Attack in Florida

Interrupted time-series analysis (ITSA) can be used to identify, quantify, and evaluate the magnitude and direction of an event on the basis of time-series data. This study evaluates the impact of the bioterrorist anthrax attacks ("Amerithrax") on hospital inpatient discharges in the metropolitan statistical area of Palm Beach, Broward, and Miami-Dade counties in the fourth quarter of 2001. Three statistical methods-standardized incidence ratio (SIR), segmented regression, and an autoregressive integrated moving average (ARIMA)-were used to determine whether Amerithrax influenced inpatient utilization. The SIR found a non-statistically significant 2 percent decrease in hospital discharges. Although the segmented regression test found a slight increase in the discharge rate during the fourth quarter, it was also not statistically significant; therefore, it could not be attributed to Amerithrax. Segmented regression diagnostics preparing for ARIMA indicated that the quarterly data time frame was not serially correlated and violated one of the assumptions for the use of the ARIMA method and therefore could not properly evaluate the impact on the time-series data. Lack of data granularity of the time frames hindered the successful evaluation of the impact by the three analytic methods. This study demonstrates that the granularity of the data points is as important as the number of data points in a time series. ITSA is important for the ability to evaluate the impact that any hazard may have on inpatient utilization. Knowledge of hospital utilization patterns during disasters offer healthcare and civic professionals valuable information to plan, respond, mitigate, and evaluate any outcomes stemming from biothreats.

Forecast analysis of any opportunistic infection among HIV positive individuals on antiretroviral therapy in Uganda

Background

Predicting future prevalence of any opportunistic infection (OI) among persons infected with the human immunodeficiency virus (HIV) on highly active antiretroviral therapy (HAART) in resource poor settings is important for proper planning, advocacy and resource allocation. We conducted a study to forecast 5-years prevalence of any OI among HIV-infected individuals on HAART in Uganda.

Methods

Monthly observational data collected over a 10-years period (2004–2013) by the AIDS support organization (TASO) in Uganda were used to forecast 5-years annual prevalence of any OI covering the period 2014–2018. The OIs considered include 14 AIDS-defining OIs, two non-AIDS defining OIs (malaria & geohelminths) and HIV-associated Kaposi’s sarcoma. Box-Jenkins autoregressive integrated moving average (ARIMA) forecasting methodology was used.

Results

Between 2004 and 2013, a total of 36,133 HIV patients were enrolled on HAART of which two thirds (66 %) were female. Mean annual prevalence for any OI in 2004 was 57.6 % and in 2013 was 27.5 % (X²_trend = 122, b = −0.0283, p <0.0001). ARIMA (1, 1, 1) model was the most parsimonious and best fit for the data. The forecasted mean annual prevalence of any OI was 26.1 % (95 % CI 21.1–31.0 %) in 2014 and 15.3 % (95 % CI 10.4–20.3 %) in 2018.

Conclusions

While the prevalence of any OI among HIV positive individuals on HAART in Uganda is expected to decrease overall, it’s unlikely that OIs will be completely eliminated in the foreseeable future. There is therefore need for continued efforts in prevention and control of opportunistic infections in all HIV/AIDS care programmes in these settings.

Electronic supplementary material

The online version of this article (doi:10.1186/s12889-016-3455-5) contains supplementary material, which is available to authorized users.

Forecasting Daily Patient Outflow From a Ward Having No Real-Time Clinical Data

Background: Modeling patient flow is crucial in understanding resource demand and prioritization. We study patient outflow from an open ward in an Australian hospital, where currently bed allocation is carried out by a manager relying on past experiences and looking at demand. Automatic methods that provide a reasonable estimate of total next-day discharges can aid in efficient bed management. The challenges in building such methods lie in dealing with large amounts of discharge noise introduced by the nonlinear nature of hospital procedures, and the nonavailability of real-time clinical information in wards.

Time series analysis of influenza incidence in Chinese provinces from 2004 to 2011

Influenza as a severe infectious disease has caused catastrophes throughout human history, and every pandemic of influenza has produced a great social burden. We compiled monthly data of influenza incidence from all provinces and autonomous regions in mainland China from January 2004 to December 2011, comprehensively evaluated and classified these data, and then randomly selected 4 provinces with higher incidence (Hebei, Gansu, Guizhou, and Hunan), 2 provinces with median incidence (Tianjin and Henan), 1 province with lower incidence (Shandong), using time series analysis to construct an ARIMA model, which is based on the monthly incidence from 2004 to 2011 as the training set. We exerted the X-12-ARIMA procedure for modeling due to the seasonality these data implied. Autocorrelation function (ACF), partial autocorrelation function (PACF), and automatic model selection were to determine the order of the model parameters. The optimal model was decided by a nonseasonal and seasonal moving average test. Finally, we applied this model to predict the monthly incidence of influenza in 2012 as the test set, and the simulated incidence was compared with the observed incidence to evaluate the model's validity by the criterion of both percentage variability in regression analyses (R) and root mean square error (RMSE). It is conceivable that SARIMA (0,1,1)(0,1,1)12 could simultaneously forecast the influenza incidence of the Hebei Province, Guizhou Province, Henan Province, and Shandong Province; SARIMA (1,0,0)(0,1,1)12 could forecast the influenza incidence in Gansu Province; SARIMA (3,1,1)(0,1,1)12 could forecast the influenza incidence in Tianjin City; and SARIMA (0,1,1)(0,0,1)12 could forecast the influenza incidence in Hunan Province. Time series analysis is a good tool for prediction of disease incidence.

Predicting the incidence of hand, foot and mouth disease in Sichuan province, China using the ARIMA model

Hand, foot and mouth disease (HFMD) is an infectious disease caused by enteroviruses, which usually occurs in children aged <5 years. In China, the HFMD situation is worsening, with increasing number of cases nationwide. Therefore, monitoring and predicting HFMD incidence are urgently needed to make control measures more effective. In this study, we applied an autoregressive integrated moving average (ARIMA) model to forecast HFMD incidence in Sichuan province, China. HFMD infection data from January 2010 to June 2014 were used to fit the ARIMA model. The coefficient of determination (R 2), normalized Bayesian Information Criterion (BIC) and mean absolute percentage of error (MAPE) were used to evaluate the goodness-of-fit of the constructed models. The fitted ARIMA model was applied to forecast the incidence of HMFD from April to June 2014. The goodness-of-fit test generated the optimum general multiplicative seasonal ARIMA (1,0,1) × (0,1,0)12 model (R 2 = 0·692, MAPE = 15·982, BIC = 5·265), which also showed non-significant autocorrelations in the residuals of the model (P = 0·893). The forecast incidence values of the ARIMA (1,0,1) × (0,1,0)12 model from July to December 2014 were 4103-9987, which were proximate forecasts. The ARIMA model could be applied to forecast HMFD incidence trend and provide support for HMFD prevention and control. Further observations should be carried out continually into the time sequence, and the parameters of the models could be adjusted because HMFD incidence will not be absolutely stationary in the future.

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.

Forecast model analysis for the morbidity of tuberculosis in Xinjiang, China

Tuberculosis is a major global public health problem, which also affects economic and social development. China has the second largest burden of tuberculosis in the world. The tuberculosis morbidity in Xinjiang is much higher than the national situation; therefore, there is an urgent need for monitoring and predicting tuberculosis morbidity so as to make the control of tuberculosis more effective. Recently, the Box-Jenkins approach, specifically the autoregressive integrated moving average (ARIMA) model, is typically applied to predict the morbidity of infectious diseases; it can take into account changing trends, periodic changes, and random disturbances in time series. Autoregressive conditional heteroscedasticity (ARCH) models are the prevalent tools used to deal with time series heteroscedasticity. In this study, based on the data of the tuberculosis morbidity from January 2004 to June 2014 in Xinjiang, we establish the single ARIMA (1, 1, 2) (1, 1, 1)₁₂ model and the combined ARIMA (1, 1, 2) (1, 1, 1)₁₂-ARCH (1) model, which can be used to predict the tuberculosis morbidity successfully in Xinjiang. Comparative analyses show that the combined model is more effective. To the best of our knowledge, this is the first study to establish the ARIMA model and ARIMA-ARCH model for prediction and monitoring the monthly morbidity of tuberculosis in Xinjiang. Based on the results of this study, the ARIMA (1, 1, 2) (1, 1, 1)₁₂-ARCH (1) model is suggested to give tuberculosis surveillance by providing estimates on tuberculosis morbidity trends in Xinjiang, China.

Outbreak detection model based on danger theory

In outbreak detection, one of the key issues is the need to deal with the weakness of early outbreak signals because this causes the detection model to have has less capability in terms of robustness when unseen outbreak patterns vary from those in the trained model. As a result, an imbalance between high detection rate and low false alarm rate occurs. To solve this problem, this study proposes a novel outbreak detection model based on danger theory; a bio-inspired method that replicates how the human body fights pathogens. We propose a signal formalization approach based on cumulative sum and a cumulative mature antigen contact value to suit the outbreak characteristic and danger theory. Two outbreak diseases, dengue and SARS, are subjected to a danger theory algorithm; namely the dendritic cell algorithm. To evaluate the model, four measurement metrics are applied: detection rate, specificity, false alarm rate, and accuracy. From the experiment, the proposed model outperforms the other detection approaches and shows a significant improvement for both diseases outbreak detection. The findings reveal that the robustness of the proposed immune model increases when dealing with inconsistent outbreak signals. The model is able to detect new unknown outbreak patterns and can discriminate between outbreak and non-outbreak cases with a consistent high detection rate, high sensitivity, and lower false alarm rate even without a training phase.

Time series modelling and forecasting of emergency department overcrowding

Efficient management of patient flow (demand) in emergency departments (EDs) has become an urgent issue for many hospital administrations. Today, more and more attention is being paid to hospital management systems to optimally manage patient flow and to improve management strategies, efficiency and safety in such establishments. To this end, EDs require significant human and material resources, but unfortunately these are limited. Within such a framework, the ability to accurately forecast demand in emergency departments has considerable implications for hospitals to improve resource allocation and strategic planning. The aim of this study was to develop models for forecasting daily attendances at the hospital emergency department in Lille, France. The study demonstrates how time-series analysis can be used to forecast, at least in the short term, demand for emergency services in a hospital emergency department. The forecasts were based on daily patient attendances at the paediatric emergency department in Lille regional hospital centre, France, from January 2012 to December 2012. An autoregressive integrated moving average (ARIMA) method was applied separately to each of the two GEMSA categories and total patient attendances. Time-series analysis was shown to provide a useful, readily available tool for forecasting emergency department demand.

Time-series analysis on human brucellosis during 2004-2013 in Shandong Province, China

Human brucellosis is a re-emerging bacterial anthropozoonotic disease, which remains a public health concern in China with the growing number of cases and more widespread natural foci. The purpose of this study was to short-term forecast the incidence of human brucellosis with a prediction model. We collected the annual and monthly laboratory data of confirmed cases from January 2004 to December 2013 in Shandong Diseases Reporting Information System (SDRIS). Autoregressive integrated moving average (ARIMA) model was fitted based on the monthly human brucellosis incidence from 2004 to 2013. Finally, monthly brucellosis incidences in 2014 were short-term forecasted by the obtained model. The incidence of brucellosis was increasing from 2004 to 2013. For the ARIMA (0, 2, 1) model, the white noise diagnostic check (x(2) = 5.58 P = 0.35) for residuals obtained was revealed by the optimum goodness-of-fit test. The monthly incidences that fitted by ARIMA (0, 2, 1) model were closely consistent with the real incidence from 2004 to 2013. And forecasting incidences from January 2014 to December 2014 were, respectively, 0.101, 0.118, 0.143, 0.166, 0.160, 0.172, 0.169, 0.133, 0.122, 0.105, 0.103 and 0.079 per100 000 population, with standard error 0.011-0.019 and mean absolute percentage error (MAPE) of 58.79%.