key: cord-0696073-2idemgr1
authors: Vu, Hoang Lan; Ng, Kelvin Tsun Wai; Richter, Amy; Kabir, Golam
title: The use of a Recurrent Neural Network model with separated time-series and lagged daily inputs for waste disposal rates modeling during COVID-19
date: 2021-09-08
journal: Sustain Cities Soc
DOI: 10.1016/j.scs.2021.103339
sha: eba0b6f360cadcf59b2e1a9bb6eae4cdb12aecab
doc_id: 696073
cord_uid: 2idemgr1

A new modeling framework is proposed to estimate mixed waste disposal rates in a Canadian capital city during the pandemic. Different Recurrent Neural Network models were developed using climatic, socio-economic, and COVID-19 related daily variables with different input lag times and study periods. It is hypothesized that the use of distinct time series and lagged inputs may improve modeling accuracy. Considering the entire 7.5-year period from Jan 2013 to Sept 2020, multi-variate weekday models were sensitive with lag times in the testing stage. It appears that the selection of input variables is more important than waste model complexity. Models applying COVID-19 related inputs generally had better performance, with average MAPE of 10.1%. The optimized lag times are however similar between the periods, with slightly longer average lag for the COVID-19 at 5.3 days. Simpler models with least input variables appear to better simulate waste disposal rates, and both ‘Temp-Hum’ (Temperature-Humidity) and ‘Temp-New Test’ (Temperature-COVID new test case) models capture the general disposal trend well, with MAPE of 10.3% and 9.4%, respectively. The benefits of the use of separated time series inputs are more apparent during the COVID-19 period, with noticeable decrease in modeling error.

Rapid urbanization and population growth have presented significant challenges to municipal solid waste management across the globe (Heidari et al. 2019; Alam and Qiao, 2020; Lu et al. 2020) , particularly with respect to the overall system costs Richter et al. 2018 ). The need for accurate waste modeling is imperative to the efficiency of disposal operations and the well-being of sanitation workers during the global COVID-19 pandemic (Vu et al. 2021) . Waste generation characteristics and disposal behaviors are important for the planning and operation of any waste management system, and are of great practical interest and commonly reported (Azadi and Karimi-Jashni, 2016; Kumar and Samadder, 2017; Wu et al., 2020) . Improving the accuracy of waste generation and disposal models facilitates efficient waste collection and improves efficiency of municipal waste management planning and operation (Vu et al., 2019a; Hannan et al. 2020; ).

Due to the robustness of the method, machine learning approaches have been widely adopted for various environmental applications, including indoor air quality (Zhang et al. 2019) , electricity consumption (Kim et al. 2020) , and urban heat island effects (Equere et al. 2021) .

Specifically, machine learning techniques have also been applied in waste management studies in the last decade. For example, waste generation rate in Mashhad, Iran, has been studied using various machine learning techniques (Noori et al. 2009 , Abdoli et al. 2012 . Table 1 presents recent literature on municipal solid waste (MSW) prediction using machine learning approaches, and among them, Artificial Neuron Network (ANN) and ANN-based models are one of the most popular analytical tools. Noori et al. (2010) applied principal component analysis (PCA) and

Gamma Test (GT) techniques and they found that the PCA-ANN and GT-ANN models had better results compared to conventional ANN models. Shahabi et al. (2012) altered the number of neurons in the hidden layer to improve the accuracy of weekly waste generation. Vu et al. (2019b) modeled the effects of lag times on weekly yard waste time-series models and found that modelling error reduced by 50% at optimal lag times. In a Danish study, Cubillos (2020) attempted to model waste generation at household levels using a Long Short-Term Memory (LSTM) Neural Network. Wu et al. (2020) , on the contrary, explored regional scale ANN models on municipal solid waste generation in China. Niu et al. (2021) adopted a LSTM for MSW forecasting and obtained satisfactory results.

ANN-based models are versatile and applicable to many non-linear problems, provided that a good training data set is provided (Xu et al. 2021) . Common inputs used in waste studies include socio-economic variables such as earnings and income, education level, employment status, dwelling and household characteristics, workplace and demographic parameters (Younes et al., 2015; Kannangara et al., 2018; Kontokosta et al., 2018; Wu et al., 2020) , or climatic variables such as temperature, humidity, wind speed, and precipitation (Kontokosta et al., 2018; Cubillos, 2020) . Some studies utilized both socio-economic and climatic variables on waste forecasting (Kontokosta et al., 2018; Vu at al., 2019b) . The selection of input variables, however, appears case specific. For example, Wu et al. (2020) used only 7 socio-economic parameters in their regional ANN models and obtained satisfactory modeling results in China. Kontokosta et al. (2018) , on the other hand, concluded that climatic variables were vital features in their ANN waste prediction models at New York. Recently, Jassim et al. (2021) used various environmental related parameters such as annual tourist numbers, annual electricity consumption, and total annual CO 2 emissions to model MSW generation rates in Bahrain. 

The objectives of the present study are to (i) develop mixed waste disposal RNN time series models using lagged inputs in a Canadian capital city, (ii) construct waste disposal rate models using COVID-19 related variables to address waste disposal behaviors during the pandemic, (iii) examine the use of lagged inputs and distinct datasets on RNN time-series modeling. The effect of lag time on waste generation was first explicitly studied by Vu et al. (2019b) , this work adds to the literature regarding the use of variable lag times on RNN time-series modeling.

Conventional ANN-based time series models inherently assume an immediate causal effect between input variables and the output parameter. This assumption may not be realistic when considering that COVID-19 symptoms and subsequent patient treatment take weeks (Wong et al. 2021 , Zhu et al. 2021 .

Unlike other ANN-based waste modeling studies unitizing weekly or monthly inputs, daily socio-economical and climatic input variables were used in the present work. Nabavi-Pelesaraei et al. (2017) successfully conducted a life cycle and energy flow assessments of municipal solid waste in Iran using daily waste data. Some socio-economic variables, such as disposal rates in a city landfill, change markedly depends on the day of the week (weekday or weekend/holiday).

The periodicity of these socio-economic inputs would introduce unnecessary bias to the modeling results. As such, the 7.5-year waste disposal dataset (January 2013 to September 2020) is divided into three distinct sets (weekday, weekend, and week-long) for model construction and result comparisons. Vu et al. (2021) modeled waste disposal rates during COVID by considering multiple waste streams separately and obtained promising results. It is hypothesized that the use of separated weekday and weekend time series may improve modeling accuracy. The proposed modeling approach (with the use of daily values and lagged inputs, together with distinct timeseries) requires more work; however, they are more appropriate with respect to the study objectives. The use of lagged input variables and distinct time-series are original and they fill the knowledge gap in ANN-based modeling. Instead of estimated waste generation rates, recorded waste disposal rates at landfill were used in this study to provide more reliable modeling inputs.

An original analytical approach for RNN waste disposal rate modeling during a pandemic is proposed. It is important to note that the proposed framework was developed for waste disposal rate estimation only, and changes in waste generation behaviors were not explicitly considered.

The capital city of Saskatchewan, Regina, was selected as the study area. The city is a typical mid-sized prairie city with a population of 236,500 (Statistics Canada, 2016). The average temperature in Regina was 3.4 o C during the 7.5-year study period (January 2013 to September 2020) (WU, 2020). The Regina landfill is the sole municipal landfill in the area and accepts wastes from nearby towns. Canadian landfill design embraces a wide variety of design principles as each jurisdiction have slightly different regulations and design guidelines (Richter et al. 2019 ).

The Regina landfill has an active gas management system Bruce et al., 2018) and a comprehensive groundwater monitoring program (Pan et al., 2019a; Pan et al., 2019b) . The landfill is open 7 days/week in summer and 6 days/week in winter. The Regina landfill receives mixed solid waste, construction and demolition waste, asphalt, grit, and treated biomedical wastes (City of Regina, 2020). Mixed solid waste represents over 62% of the waste stream disposed of at the landfill by weight, and is considered in the present study. Mixed solid waste consists mostly wastes collected from residential, industrial, commercial and institutional sources. The average mixed waste disposal in Regina was 440.2 tonnes/day during the study period.

The first confirmed COVID-19 case was reported in Regina on March 12 th , 2020 (Government of Saskatchewan, 2020a), and a provincial state of emergency was declared six days later on March 18 th . During the initial lockdown phase, most bars and restaurants in the city were closed except for takeout service. According to Goddard (2020) , online grocery shopping in Canada has increased significantly, and consumer stockpiling behavior was observed.

Unemployment rates in Saskatchewan increased from 6.0% in January 2020 to 12.5% in May 2020 (Government of Saskatchewan, 2020c). The number of COVID-19 cases in Saskatchewan has stabilized, and the government has partially lifted restrictions according to the provincial "reopen Saskatchewan" plan. On May 29 th , 2021, the total number of COVID-19 cases in the city was 11,636 (Government of Saskatchewan, 2020b).

The details of the methodology are shown in Figure 1 , as separately discussed in the following sub-sections from Sections 2.2 to 2.5.

Note: (*) -Those models using the results obtained from the models under Objective 1  ► Climatic data (temperature, humidity, wind speed)  ► COVID-19 data (new test cases, total cases, active cases, number of patients in hospitals)  Data processing:

 ► Create three separate time series: "weeklong", "weekday", and "weekends" sets  ► Calculate upper and lower bounds based on IQR, and eliminate data with extremely low value (less than 1 tonne/day)

Variables screening using correlation analysis ► Conduct correlation analysis on all variables during entire study period (Jan 2013 to Sep 2020) and the COVID-19 period (Mar 2020 to Sep 2020) ► Identify highly correlated input variables (with correlation coefficient greater than 0.95) to reduce multi-collinearity of input variables ► Identify significant input variables on waste disposal to develop multiple waste disposal rate models during entire study period and COVID-19 period variables were collected from official records published by the Government of Saskatchewan (2020b). Socio-economic and climatic variables were widely applied to predict waste generation (Johnson et al., 2017; Kannangara et al., 2018; Abbasi et al., 2018; Vu et al., 2019b) , whereas the COVID-19 related variables were specifically selected in this study to capture the scale of the pandemic in Saskatchewan. Studies suggested that the pandemic may have affected waste disposal behavior in the city (Richter et al. 2021a; 2021b) . Evidence from Spain suggests that people have been using more single use products and personal protection equipment during the COVID-19 pandemic, according to Kalina and Tilley (2020) . Similar findings were observed in South Korea (Rhee, 2020) .

Mixed waste disposal of extremely low value (less than one tonne/day) were removed.

These are likely due to landfill scale calibrations or emergency disposals during landfill closure.

Upper and lower boundaries derived by Interquartile Range (IQR) were used to eliminate the outliers (Equations 1-3). Data points that were higher than the upper bound or below the lower bound were removed (Kannangara et al. 2018; Fallah et al. 2020; Niu et al. 2021 ). If the computed lower bound is negative, then one tonne/day is taken as the lower bound.

Where: IQR=Interquartile Range; Q1=First Quartile of the data set; Q3=Third Quartile of the data set.

Two periods for time series were specifically defined for modeling purposes: the 7.5-year entire study period (January 1 st , 2013 to September 12 th , 2020) and the 6-month COVID-19

period (March 18 th , 2020 to September 12 th , 2020). The periods were selected based on the availability of landfill disposal data. A provincial state of emergency was declared on March 18 th , 2020 and was selected to define the starting date of the COVID-19 period in Regina.

in disposal behaviors at Regina. To overcome the periodicity of the waste disposal rates and to minimize unnecessary input fluctuations, three distinct time-series were considered: "weeklong", "weekday", and "weekend". The "week-long" set contains continuous daily disposal data with no distinction between workdays and weekends. The "weekday" set consists of truncated time-series from Mondays to Fridays in a given period, and the "weekend" set consists of truncated time-series from only Saturdays and Sundays in a given period.

Correlation analysis of the mixed waste disposal rates, as well as the identified 8 socioeconomic, climatic, COVID-19 related variables were conducted for both the entire study period and the COVID-19 period to examine the interrelationships between the variables. The input variables having the highest Pearson correlation coefficients with p < 0.05 during their respective periods were selected as the core input variables to build the models. On the other hand, highly intercorrelated input pairs with a large correlation coefficient were identified. Only one of the correlated inputs will be used for model building to avoid multicollinearity of the inputs. In the current study, the correlation coefficient cutoff of |0.95| was adopted, similar to Abdoli et al. week-long models (Figure 1 ). The "weekday" model used the daily data on weekdays and the "weekend model" used the daily data on weekends. The "week-long" model used the continuous daily input data including both weekday and weekend data.

A total of four weekday multi-variate models were developed for the entire 7.5-year study period (Figure 1 ). The lag time of the models ranged from 1 -12 days. One hidden layer with 128 neurons was used for the multi-variates models. The accuracy of the multi-variate models was compared and their model structure studied with respect to lag time (Output 1, Figure 1 ).

In this part, the weekend set is ignored and only the more representative weekday set is considered. Two periods (the entire study period and the 6-month COVID-19 period) are considered for waste disposal prediction in the COVID-19 period, as separately discussed below.

A total of five models were developed for waste disposal prediction using the entire dataset: a single feature model and four multi-variate models (Output 2a, Figure 1 ). The single feature model (SingleWaste1) had four layers: an input layer, two hidden layers, and an output layer. The number of neurons of each hidden layer was selected at 600. On the other hand, a single hidden layer with 128 neurons is adopted for the four multi-variate models. Both singlehidden layer and double hidden layers are commonly applied in ANN-based waste studies (Xu et al. 2021) . The narrower range of lag times (1-6 days) are studied for both single and multivariate models. The disposal rates obtained from the single feature model and the four multivariate models were then compared with those of the models using the COVID-19 period data set (Output 2a vs. 2b, Figure 1 ).

A total of four models were developed using the COVID-19 period data set: a single feature model and three multi-variate models (output 2b, Figure 1 ).The single feature model (SingleWaste2) had four layers: an input layer, two hidden layers, and an output layer. The number of neurons of each hidden layer was selected at 600. The defined COVID-19 period was about 6 months, and a shorter range of lags (1-6 days) were studied. The structure of the three multi-variate models (number of hidden layersand neurons) using the COVID-19 period data was identical to that of the multi-variate models using the entire dataset ( Figure 1 ).

In this part, the model accuracy between the use of a continuous time-series and the two distinct time series covering the entire study period was examined. The analysis is conducted using the optimized models in the entire study period (output 1, Figure 1 ). Three different RNN models were developed to simulate daily mixed waste disposal in the entire study period: weeklong, weekday, and weekend models. The week-long model used the continuous daily input data including weekday and weekend data with a total of 2,390 daily disposal data. The weekday model consists of 2,002 data points, and the weekend model consists of 388 data points. The results from the optimized weekday model (output 3a, Figure 1 ) and weekend model(output 3b, Figure 1 ) are then stitched together to form a complete set, and then compared with the optimized week-long waste model (output 3c, Figure 1 ). All models have one hidden layer with 128 neurons. The lag time of the weekday and week-long models ranged from 1 -12 days, whereas the lag time of the weekend models varied from 1 to 2 weeks (Figure 1 ).

Mean absolute error ( 

The upper and lower bounds of the weekday data set were calculated at 815.17 tonnes/day and 63.21 tonnes/day, respectively, using equations (2) and (3). Only a single outlier of 886.96 tonnes/day was eliminated from the weekday data set in the entire 7.5-year study period. There is no data point below the calculated lower bound. As shown in 

The upper and lower bounds of the weekend data set were computed and a total of 10 outliers were identified (six data points larger than 142.92 tonnes/day, and four data points below 1 tonne/day) in the weekend data set during the entire study period. After removal of the outliers, the weekend set contained 388 data points. The average mixed waste disposal on weekends was 42.72 tonnes/day ( (Table 2) .

The COVID-19 data set is a weekday set with 128 data points, covering the period from

March 18 th , 2020 to September 12 th , 2020 ( Table 2 ). The average mass of mixed disposal waste in the COVID-19 period was 488.27 (tonnes/day), slightly higher than the weekday set during the entire period. However, the overall effect of COVID-19 on waste disposal is not definite, as the COVID-19 period occurred in spring and summer, a period with historically higher waste disposal in Regina (Figure 2) . A noticeable decrease in the variability of the waste disposal data is observed, with a standard deviation of 81.09 tonnes/day, and a higher min-to-max ratio of 0.29 (Table 2 ). The coefficient of variation of the disposal rate in the COVID-19 period is the lowest in the present study (0.166). It appears that COVID-19 improved the consistency of the disposal behaviors by the Regina residents, probably due to newly established social norms (avoid large in-person gatherings and social distancing) and the widely adopted work-form-home practices.

The average unemployment rates increased from 5.60-5.65% to 9.99% during the COVID-19 period ( Table 2) . Four waste disposal rate models were built in the COVID-19 period, including a single feature model (SingleWaste 2) using mixed waste disposal as the sole input, and three multivariate models. Temperature and number of new test cases had the highest and second highest correlation with mass of mixed waste disposal. They were used as the core variables to develop the multi-variate models in the COVID-19 period (Table 5 ). There were three multi-variate models developed in this period including Temp-New Test, Temp-New Test-Unemp, and Temp-New Test-New Case-Active Case-Patient-Unemp. Table 5 summarizes the models in both periods. The daily mass of waste disposal in the period from Jan 2013 to Sep 2020 was selected to build the single feature model. This model will be applied for calculating waste disposal in the COVID-19 period.

Climatic group (2) Waste disposal prediction model with the inputs containing temperature and humidity at the study area Two parameters including daily temperature and humidity in the period from Jan 2013 to Sep 2020 were selected for the model as they have the highest and second highest correlation coefficient with the waste disposal rates. This model will be used to predict:(i) week-long waste disposal; (ii) weekday waste disposal in the entire study period and the COVID-19 period, and (iii) weekend waste disposal in the entire study period.

(3) Waste disposal prediction model with the inputs containing temperature, humidity, and unemployment rate at the study area This model was created using the core daily temperature and humidity variables in the entire study period. The socio-economic parameter of unemployment rates was added in the model inputs. This model will be used to predict weekday waste disposal in the entire study period and the COVID-19 period.

(4) Waste disposal prediction model with the inputs containing temperature, humidity, and total COVID-19 cases at the study area This model was created using the core daily temperature and humidity variables. The total number of COVID-19 cases was added in the model inputs as it has the highest correlation coefficient with the waste disposal compared to others in the COVID-19 variables group (Table 3) . This model will be used to predict weekday waste disposal in the entire study period and the COVID-19 period.

Temp-Hum-Total Case (5) Waste disposal prediction model with the inputs containing temperature, humidity, wind speed, unemployment rates, new tests and total COVID-19 cases at the study area This model was created using the variables having six highest correlation coefficients with waste disposal. They are temperature, humidity, wind speed, unemployment rates, total cases, and new test cases. This model will be used to predict weekday waste disposal in the entire study period and the COVID-19 period.

►Single feature model (6) Waste disposal prediction model with the input containing a single feature of mass of waste disposal

The daily mass of waste disposal in the period from Mar 2020 to Sep 2020 was selected to build the single feature model.

Hybrid group (7) Waste disposal prediction model with the inputs containing temperature and new test cases at the study area Two parameters including daily temperature and number of new test cases in the COVID-19 period from Mar 2020 to Sep 2020 were selected for the model as they have the highest and second highest correlation coefficient with the waste disposal in this period. This model will be used to predict weekday waste disposal in the COVID-19 period. Figure 3 shows the stability of the multi-variate weekday models with different lagged inputs (1 to 12 days) using weekday data from the entire study period. In the training stage, it is clear that the performances of the Temp-Hum, Temp-Hum-Unemp, Temp-Hum-Total Case, and 

performance in the testing stage will be used to evaluate their relative performance. As shown in Figure 4a , a lag time of 5 days and 10 days had similar MAPE (11.98% and 11.99%, respectively). A closer look at MSE, however, suggest that the model error is minimized at a lag time of 10 days at 6,004 tonnes/day.

The Temp-Hum model generally simulates the waste disposal behaviors in Regina well.

Irrespective of the lag times applied, R was generally greater than 0.74 and IA was greater than 0.83 in the testing stage (Figure 4b ). R is also maximized (0.807) at a lag of 10 days. IA values show similar result, with optimized lags of about 10-11 days (IA = 0.866, 0.867, respectively).

By increasing the lag time from 1 day to the optimum of 10 day, the accuracy is improved and reduces the MSE by 21.8% (from 7,020 to 5,493 tonnes/day) in the training stage, and 25.3%

(from 8,033 to 6,004 tonnes/day) in the testing stage ( Figure 4a ). 45 16.31 15.94 15.72 15.81 15.88 16.06 15.95 15.31 15.38 15.32 MAPE (test) 12.36 12.37 12.56 12.50 11.98 12.07 12.20 12.24 12.43 11.99 12.04 12.12 MSE (train) 7, 020 6, 487 6, 247 5, 992 5, 763 5, 730 5, 789 5, 809 5, 750 5, 493 5, 505 5, 544 MSE (test) 8 Table 6 compares the model performances at the optimized lag when using data from the entire study period and the COVID-19 period to simulate waste disposal rates during the COVID-19 period. In general, the models applying COVID-19 period inputs had better performance than those of the models applying entire study period inputs. The average MSE of models applying entire study period inputs was 7,770 tonnes/day. The average MSE of models applying COVID-19 period inputs was only about 3,382 tonnes/day, or about 43.5% of its counterpart. The average MAPE of models applying COVID-19 period inputs was 10.1%, considerably lower than its counterpart at 14.5%. R and IA values of the models applying COVID-19 period inputs were also better ( Table 6 ). The findings confirm that waste disposal behaviors during COVID-19 were changed, and the use of COVID-19 variables on waste modeling can better capture the spread and severity of the pandemic. The optimized lag times between the periods were however similar, with a slightly longer average lag for the COVID-19 period at 5.3 days.

In both periods, MSE was much higher for the hexa-variate models and the single feature models using historical disposal rate as sole input. On the other hand, the uni-variate and trivariate models appear to simulate waste disposal rates better. The Temp-Hum model and the Temp-NewTest-Unemp model have the lowest MSE for the entire period and COVID-19 period, respectively. The lag times for both models were 5 days. Among all models in both periods, Temp-Hum-Wind-Total Case-New Test-Unemp has the highest MSE (15,573 tonnes/day), probably due to the high correlations between New Test and Total Case (Table 3) . Figure 5 ) generally predicts a higher disposal rate than Temp-Hum. Consistency between the models was highest when there was more scattering in the actual disposal data (from April 29th to Aug 5th). Although the models were able to capture the general disposal trend well, none of the optimized models could identify precisely the peaks and troughs on daily basis. Three Temp-Hum models were developed and optimized using weekday, weekend, and

week-long waste disposal data. The results of weekdays and weekends were stitched together to compared with the optimized week-long model. Figure 6 shows the model accuracy of the optimized Temp-Hum models. The performance of both models is acceptable, with MAE generally less than 150 tonnes/day. Figure 6a shows that the use of separated sets of time series data (blue circles, Figure 6a ) has resulted in approximately 1.45 times lower MAE than that of the week-long model at the training stage. The relatively high MAE shown in Figure 6a occurred mostly on weekends in the winter, especially when the mass of mixed waste disposal dropped to lower than 15 tonnes/day (Figure 2c ). Figure 6b shows the performances of the models in the testing stage. It can be seen that the Temp-Hum model with separated time series had approximately 2.13 times lower MAE than that of the model using week-long data. The advantage of using separated time series for waste disposal is more apparent during the COVID-19 period, when the MAE is significantly lower (typically under 100 tonnes/day). It is probably due to the lower data variability, together with the reduction of unnecessary bias between workdays and weekends. The finding supports the use of separated data sets for time series modeling if strong data periodicity is observed. 

In this study, an original RNN time series modeling framework is developed to simulate waste disposal rate in Regina, the capital city of Saskatchewan. The objectives are to develop a RNN modeling framework using lagged climatic, socio-economical, and COVID-19 related inputs and to examine the use of distinct time-series on RNN modeling. The disposal behaviors of the residents during the pandemic are also simulated and compared with the historical data.

Unlike other studies, this work explicitly examines the effects of the use of daily values, lagged inputs, and distinct time-series on RNN modeling. A total of 104 scenarios were considered. The proposed framework focuses on waste disposal rate modeling, and no attempt is made to include changes in waste generation behaviors.

Historical disposal trends reveal that disposal behaviors are different between weekdays and weekends. As such, distinct time series were used to reduce unnecessary biases and uncertainties in the waste disposal rate modeling. A noticeable decrease in variability of the waste disposal data is observed in the COVID-19 period, with a coefficient of variation of 0.166. It appears that COVID-19 improved the consistency of disposal behaviors.

Correlation results suggest that temperature and humidity are correlated with the mass of mixed waste disposal during the entire period. During COVID-19, however, temperature and new test cases have the highest correlations with waste disposal. Considering the entire period, multi-variate weekday models were more sensitive with lag times in the testing stage. It appears that the selection of input variables is more important than model complexity in RNN time series modeling. The Temp-Hum model generally simulates the waste disposal behaviors in Regina well. By increasing the lag time from 1 day to the optimum of 10 day, it helped to reduce 21.8%

of MSE in the training stage, and 25.3% of MSE in the testing stage.

In general, models applying COVID-19 period inputs had better performance than those of the models applying entire study period inputs. The optimized lag times are however similar between the periods, with slightly longer average lag for the COVID-19 period at 5.3 days.

Simpler models appear to simulate waste disposal rates more accurately.

Both Temp-Hum (entire period) and Temp-New Test (COVID-19 period) were able to capture the average disposal rate in Regina during COVID-19, however, both optimized models fail to fully capture the peaks and troughs of the waste disposal data. The benefits of the use of separated time series are more apparent during the COVID-19 period, when the MAE is significantly lower. This could be due to the lower waste disposal data variability, and the reduction of unnecessary bias.

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Joint prediction and time estimation of COVID-19 developing severe symptoms using chest CT scan

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

 Table 1 : Recent studies on waste quantity modeling using machine learning approaches  Table 2 : Data characteristics during the entire study period (Jan 2013 to Sep 2020) and the COVID-19 period (Mar 2020 to Sep 2020)  Table 3 : Correlation coefficient matrix of input variables and waste disposal rates during the entire study period from Jan 2013 to Sep 2020  Table 4 : Correlation coefficient matrix of input variables and waste disposal rates during the COVID-19 period from Mar 2020 to Sep 2020  Table 5 : Summary of daily waste disposal rate models during the entire study period (Jan 2013 to Sep 2020) and the COVID-19 period (Mar 2020 to Sep 2020)  Table 6 : Comparison of optimized model performance using different inputs and study periods