key: cord-0926420-ny8fnh4b authors: Haridy, Salah; Maged, Ahmed; Baker, Arthur W.; Shamsuzzaman, Mohammad; Bashir, Hamdi; Xie, Min title: Monitoring Scheme for Early Detection of Coronavirus and Other Respiratory Virus Outbreaks date: 2021-03-16 journal: Comput Ind Eng DOI: 10.1016/j.cie.2021.107235 sha: 319abb4b2b7477ba9c8953d0f9233f10b238b07b doc_id: 926420 cord_uid: ny8fnh4b In December 2019, an outbreak of pneumonia caused by a novel coronavirus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) began in Wuhan, China. SARS-CoV-2 exhibited efficient person-to-person transmission of what became labeled as COVID-19. It has spread worldwide with over 83,000,000 infected cases and more than 1,800,000 deaths to date (December 31, 2020). This research proposes a statistical monitoring scheme in which an optimized np control chart is utilized by sentinel metropolitan airports worldwide for early detection of coronavirus and other respiratory virus outbreaks. The sample size of this chart is optimized to ensure the best overall performance for detecting a wide range of shifts in the infection rate, based on the available resources, such as the inspection rate and the allowable false alarm rate. The effectiveness of the proposed optimized np chart is compared with that of the traditional np chart with a predetermined sample size under both sampling inspection and 100% inspection. For a variety of scenarios including a real case, the optimized np control chart is found to substantially outperform its traditional counterpart in terms of the average number of infections. Therefore, this control chart has potential to be an effective tool for early detection of respiratory virus outbreaks, promoting early outbreak investigation and mitigation. In December 2019, an outbreak of mysterious pneumonia from an unidentified origin occurred in Wuhan, China. Chinese health authorities identified a novel coronavirus (severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) that was responsible for the outbreak (World Health Organization, 2020b) . Coronaviruses are a large family of viruses that cause illnesses ranging from the common cold to more severe diseases, such as middle east respiratory syndrome (MERS-CoV) and severe acute respiratory syndrome (SARS-CoV). SARS-CoV-2 exhibited efficient person-to-person transmission of what became labeled as coronavirus disease 2019 , which quickly led to a worldwide outbreak of potentially fatal viral pneumonia. COVID-19 has spread around the world with over 83,000,000 infected cases and more than 1,800,000 deaths to date (December 31, 2020) , and further dissemination through air travel is likely (Goscé, Phillips, Spinola, Gupta, & Abubakar, 2020) . As a result, the World Health Organization (WHO) declared COVID-19 a pandemic on March 11, 2020 (World Health Organization, 2020a . A timeline of crucial early events related to SARS-CoV-2 is shown in Figure 1 (CNN Health, 2020; National Health Commission of China 2020). [Please insert Figure 1 here] The attack rate (i.e., how rapidly the disease is spreading) of a virus is indicated by its reproductive number (R 0 ). A recent study estimated the R 0 for COVID-19 to be between 2.24 and 3.58 (Zhao et al., 2020) . Per this estimate, on average, every case of COVID-19 would create two to three new cases, exhibiting 2 to 3 times greater transmissibility than seasonal influenza viruses (Zhang et al., 2017) . Furthermore, the mortality rate of COVID-19 is currently estimated at around 3% (Wang, Horby, Hayden, & Gao, 2020) . For comparison, the mortality rate of seasonal flu is less than 0.1% (Centers of Disease Control and Prevention, 2019), but the mortality rate is approximately 10% for SARS-CoV and 34% for MERS (Jiang, Rayner, & Luo, 2020) . Early detection and response to epidemics and pandemics, including quarantine of patients with confirmed infections and observation of those who have had close contact with infected patients, can help to mitigate outbreaks, lowering the attack rate and the total number of deaths (Bauer, 2015) . In this analysis, we present how early detection of important respiratory virus outbreaks could be achieved through use of an optimized np control chart at a worldwide network of sentinel airports to improve the quality of surveillance. Using effective surveillance tools is essential for the early detection of outbreaks of coronaviruses and other respiratory viruses. When used for outbreak detection, statistical process control (SPC) charts have been proven to be effective, easy to implement, and inexpensive (Wiemken et al., 2017; Woodall, 2006) . SPC charts were originally developed by Walter Shewhart in the 1920s for monitoring production processes (Montgomery, 2013) . Since the early 1990s, there has been a growing interest in applying these charts to healthcare (Ahamed, Campbell, Horan, & Rosen, 2018; Lawson, Hall, Esnaola, & Ko, 2012) , including those related to the detection and monitoring of outbreaks (e.g., Baker et al. (2018); Shu, Su, Jiang, and Tsui (2014) ; Sogandi, Aminnayeri, Mohammadpour, and Amiri (2019); Xie, Tsui, Xie, and Goh (2010)). Sogandi et al. (2019) proposed a Bernoulli state-space model for monitoring multi-stage medical processes. The proposed model performed well under different shifts and was able to identify the out-of-control stage efficiently. Grigg (2019) discussed the problem of maintaining patient ordering according to the treatment timeline for different charts. They recommended that compromising on the fullness of presentation of the historical data is the best way to preserve patient ordering on any chart. Gould and Wang (2017) proposed an effective method for routine monitoring of safety information for programs that include blinded trials. A comprehensive literature review of the various applications of SPC charts in healthcare can be found in Suman and Prajapati (2018) , Tennant, Mohammed, Coleman, and Martin (2007) , and May, Simpson, Hart, Rowett, and Perrier (2009) . A control chart is a visual tool that can provide early identification of statistically significant changes in data. For effective process monitoring, several studies have proposed to optimize the parameters of different types of charts in various applications. For instance, Rahim and Khalaf (1997) presented an optimal design of exponentially weighted moving average (EWMA) chart parameters using genetic algorithms. The results showed that the optimal design reduces the false alarm probability (i.e., the probability that the control chart gives an out-ofcontrol signal, while the process is actually in control) and is powerful in detecting serious shifts. Haridy, Wu, Khoo, and Yu (2012) proposed an algorithm for the optimal design of a Syn-np chart which combines the synthetic chart and the np chart. The proposed chart was more effective than the np chart by 73% and the synthetic by 31%. Shamsuzzaman, Khoo, Haridy, and Alsyouf (2016) proposed an optimization design of the combined Shewhart chart and X EWMA chart. The charting parameters and the allocation of detection power between the elements of both charts were optimized based on the loss function. Muhammad, Yeong, Chong, Lim, and Khoo (2018) developed an algorithm for the optimization of coefficient of variation (CV) control chart. The results revealed that the proposed optimized CV chart outperforms five existing CV charts in literature in almost all scenarios. For the early detection of outbreaks of coronaviruses and other respiratory viruses, this study proposes a monitoring scheme that utilizes an attribute chart -namely, the np chart -with optimized parameters. Furthermore, we introduce the average number of infections (ANI) as an effective measure of the overall detection speed of the control chart for monitoring the infection rate. Finally, the use of the proposed monitoring scheme is illustrated by different scenarios. The proposed monitoring scheme, which is shown in Figure 2 , can be used as a monitoring tool at selected metropolitan airports where checkpoints are established. Sampling is actually a common practice in airports when 100% is impossible due to the limited resources (Bauer, 2015; Civil Aviation Authority, 2017) . By the proposed scheme, airports would screen passengers to detect fevers potentially related to respiratory viruses. A typical screening procedure would include thermal screening by measuring the skin temperature using various tools, such as thermal cameras, thermal imaging, or forehead thermometer guns (Air Technology, 2020). Alternatively, if available, airports could use automated temperature screenings using artificial intelligence (GovInsider, 2020) . Surveillance for other symptoms, such as cough or shortness of breath, might also be incorporated into the model to determine the likelihood of respiratory virus infection. If outbreak onset is already known to have occurred, it would be important to increase the inspection rate (i.e., increase the sample size n and decrease the sampling interval h) if 100% inspection is impossible so that a greater percentage of infected passengers could be evaluated. However, the proposed monitoring scheme can also be used continuously where either rational subgrouping or 100% inspection is adopted. [Please insert Figure 2 here] The np control chart is an attribute chart that can be used to monitor the number of infections 2. The resulting d is plotted for each sample on the np chart. 3. If d ≥ UCL, then a potential outbreak is declared and in this case, a 100% inspection is recommended. Otherwise, the process is in control, and step 1 is repeated for the next sample. The charting parameters (i.e., n, h and UCL) need to be decided in an optimal and effective way. With the aim of carrying out the optimal design for the np chart, several specifications need to be set. The design specifications of this study are summarized below:  is the in-control infection rate; 0  τ is the allowable minimum value of the in-control average time to signal ( ); 0  r is the inspection rate; and  is the maximum out-of-control infection rate The abovementioned specifications are commonly used to design attribute control charts (Bourke, 1991; Gan, 1993; Reynolds & Stoumbos, 1998; Wu, Xie, & Tian, 2002) . The in-control infection rate is assumed to be known, as it is considered to be the 0 baseline or expected infection rate that does not require investigation. In addition, the value of τ is set based on the requirements of the false alarm rate that is deemed to be acceptable and can be managed by airports. The sampling rate r is determined according to the availability of resources such as manpower and inspection tools (e.g., thermometers and testing kits). The maximum out-of-control infection rate, , is decided based on the shift size the authority is interested to detect. The performance of a control chart is often evaluated using different measures of performance. A measure called the average time to signal (ATS), which is the expected time from when a shift with a particular size occurred until the control chart indicates an out-of-control signal (i.e., outbreak), is usually recommended (Li, Zou, Gong, & Wang, 2014) . Nevertheless, it is not easy to predict the size of an outbreak. Therefore, in this study, we introduce a performance measure that is the average number of infections (ANI) to evaluate the overall performance of the proposed np chart over a wide range of shifts in the infection rate. The ANI is actually a weighted average of the out-of-control ATS values over different shifts in an infection rate, hence it is a better measure for the overall performance of a control chart. When an increasing shift in the infection rate occurs, the infection rate will change from p 0 to p. The ANI is the average number of infections that occurred over a shift range of 0 prior to control chart detection. The infection rate is considered to be in control < ≤ when p = p 0 and out of control when with a maximum infection rate at p = 0 < ≤ p max . If N is the number of arrivals per unit time and ATS(p) is the out-of-control ATS value that corresponds to a particular infection rate p, then the ANI produced by a control chart across the p range ( ) can be calculated as follows: is the probability density function of p which is assumed to follow uniform distribution in this research and can be estimated as follows: (2) The out-of-control ATS(p) at a particular infection rate p can be calculated as follows: (1) is assumed to be constant. As a result, it may be removed while not affecting the optimization design and comparative study. This section presents the optimization model and algorithm for the np chart. The optimal design is carried out based on the four design specifications listed in Section 2. The optimization procedure to compute the optimal parameters of the np chart in minimizing ANI as the objective function is given as follows: Objective: Minimize ANI Constraints: where n is the independent variable, while the h and UCL are the dependent variables on the n, r and specified value of τ, respectively. The above-mentioned model will provide the optimal values of n, h and UCL that will minimize ANI over a shift range of ( ), and ≤ ≤ meanwhile, ensure that the in-control ATS 0 is greater than or equal to a predefined value of τ. The ATS 0 represents the expected time the control chart takes to give a false alarm signal. The ATS 0 of the np chart can be calculated as follows: where α is the probability that the np chart gives an out-of-control signal when the infection rate is actually in-control. α can be determined as follows: The optimization design of np chart is implemented as follows: 1. Specify the design specifications p 0, τ , r and p max. 2. Initiate ANI min variable to store the minimum value of ANI and set the initial value of ANI min to very large number. 3. Search the optimal value of n, starting with n = 1 and increase its value in an increment of 1. 4. For each n, find h (= n / r) that satisfies constraint (5).  For each pair of (n, h), find α using Equation (6) where ATS 0 = τ (i.e., α = h / τ) and then the value of UCL using Equation (7) so that constraint (4) can be fulfilled.  For the identified n, h and UCL, find the corresponding value of ANI using Equation (1).  If the calculated ANI is less than the current ANI min , replace the latter by the former and the current values of n, h and UCL are stored as temporary optimal solution. 5. For each trail n value, step 4 will be repeated until ANI cannot be further minimized. The optimization algorithm is terminated if the ANI keeps increasing for 60 consecutive iterations. The optimal np charting parameters n, h and UCL will be the values that produce the minimum ANI, while satisfying constraints (4) and (5). The optimization algorithm of the np chart is summarized as shown in Figure 3 . [Please insert Figure 3 here] The above search mechanism is reliable and straightforward as the only independent design variables, n, is integral, and therefore all its possible values can be examined. It can complete the optimization design of the np chart in a few seconds of CPU time on a personal computer. In addition, the results can be used to study the effect of the sample size on the performance of the np chart. C programming language was used to code the design algorithm of the np chart. It can be obtained from authors upon request. This section shows the results of optimizing the charting parameters of the np chart, including n, h and UCL. It also conducts a comparative study between the optimized np chart and the traditional np chart for one real case and five simulated scenarios. The optimized np chart proposed in this study is named as np optimal chart whereas, the traditional np chart is referred to as the np traditional chart. Both ANI and ATS are used as measures of performance to compare the np optimal and np traditional charts and to attain a clear conclusion on how the sample size affects the performance of the monitoring chart. This study is conducted from late December 2019 through January 2020 at an international airport with limited resources that do not allow 100% inspection. The name of the airport is not disclosed due to confidentiality reasons. The screening procedure is performed by checking the temperature using thermometer guns. A symptomatic passenger will be detected if he has a significant fever (i.e., his temperature exceeds 100.4 F). Based on the available resources, the airport can only inspect 100 arrivals every hour (i.e., r =100/hour) and it can handle one false alarm signal every 27 days on average (i.e., τ = 648 hours). The in-control infection rate that does not reflect a potential outbreak ( , whereas the maximum out-of-control value ) = 0.01 of the infection rate the airport is interested to detect is 10 times the in-control infection rate ). It is worthy to mention that the shift is assumed to follow a uniform = 10 o distribution. Fixed values of n and h are used as design specification for the np traditional chart without any optimization. Thus, we can consider that np traditional inspects a sample of 100 arrivals per hour. Contradictory, both n and h are optimized under the given inspection rate r in this study. As highlighted previously, the optimal design of the np chart came up with the optimal combination of n, h and UCL, which produces the minimum ANI while satisfying the constraints (7) and (8). Applying the optimization algorithm, we found that the optimal charting parameters of the np optimal chart are to inspect a sample of size 185 (i.e., n = 185) at every time interval of 1.85 hour (i.e., h = 1.85hr) using UCL = 6. The values of the charting parameters and the corresponding ANI values for both charts are shown below: np traditional chart: n = 100, h = 1, UCL = 5 and ANI = 0.2469. np optimal chart: n = 185, h = 1.85, UCL = 6 and ANI = 0.1248. Figure 4 shows the effect of n on the ANI values. It can be seen that the ANI values have a decay and rise pattern till they reach one point (i.e., the optimal sample size n = 185) where the ANI value does not go lower any further. Figure 4 also shows that the proposed np optimal chart outperforms np traditional chart in terms of ANI under the same design specifications. [Please insert Figure 4 here] The values of ANI are compared based on a defined relative performance index (RPI) which can be calculated as: the ANI of the np optimal chart compared to that of the np traditional chart. One interpretation of this result is that inspecting a sample of 185 every 111 minutes can detect an outbreak almost two times faster than inspecting a sample of 100 every hour while satisfying the same constraints on the false alarm rate and inspection rate. As shown in Figure 4 , there are several valley points (VP i ). These valley points are always the local minima on the curve of ANI against n, and ANI is actually a concave-upward function of n at these valley points. This is due to the fact that the UCL at a valley point is always the tightest, and the corresponding ATS 0 is just slightly larger than the specified τ. It also results in the smallest ANI in the neighborhood of a valley point. If the sample size n is increased by one from the sample size at a valley point, the UCL has to be increased by one in order to meet the constraint (4). Consequently, the in-control ATS 0 , as well as the ANI, will increase sharply. Therefore, the optimal sample size (n optimal ) is identified as one of the valley points. For instance, the optimal sample size (n optimal = 185) is associated with the 4th valley point (VP 4 ). Moreover, the np traditional and np optimal charts are compared in terms of the out-of-control average time to signal ATS. Figure 5 shows the performance of both np charts in terms of the normalized ATS (ATS np traditional / ATS np optimal ). As can be seen from Figure 5 , the np optimal chart is more effective than np traditional chart for detecting p shifts over almost the whole given range. Also, it can be noted that as the shift increases, the np traditional chart performs roughly similar to the np optimal chart. In other words, the superiority of the np optimal chart over the np traditional chart decreases with increasing the shift size in the infection rate. [Please insert Figure 5 here] In most processes, the process shift usually follows a specific probability distribution. However, as Siddall (1983) pointed out, if there is uncertainty about a random variable except for its bounds, then uniform distribution might be an excellent option to represent that variable. Many researchers designed control charts assuming that the process shift follows uniform distribution (Castagliola, Celano, & Psarakis, 2011; Domangue & Patch, 1991; Sparks, 2000) , while others used beta distribution (Ou, Wu, & Goh, 2011) and Rayleigh distribution (Wu, Shamsuzzaman& Pan, 2004; Haridy, Maged, Kaytbay, & Araby, 2017) to describe the process shift. In this section, a sensitivity analysis is conducted for the case in Section 5.1 (i.e., τ = 648 hours, p 0 = 0.01, r =100/hour and p max = 10p 0 ) to study how the charts will perform if the estimated distribution of the p shift is not uniform. The np traditional and np optimal charts are designed for three other cases in which p shift follows a beta distribution as shown in cases 1, 2 and 3 of Table 1 . The probability density function of the beta distribution can be determined as follows: Table 1 here] The skewness of a beta distribution depends primarily on the parameters a and b. If (a < b), the probability distribution of the p shift will be skewed to right (Figure 6(a) ) and most of the shifts cluster to the lower end. If (a > b) , the probability distribution of the p shift will be skewed to the left (Figure 6 (c)), and most of the shifts cluster to the upper end. Finally, if (a = b), the distribution of the p shift will be symmetric (Figure 6(b) ). Cases 1, 2, and 3 in Table 1 serve as representatives of different types of non-uniform probability distributions of p shift. [Please insert Figure 6 here] The RPI values in Table 1 show that, under any probability distributions of p shift, the np optimal chart always outperforms the np traditional chart. The superiority of the np optimal chart over the np chart is more significant when f p (p) is skewed to the right (case 1). This finding is justifiable as the np optimal chart uses a relatively large sample size (n = 100), making it less sensitive for detecting large p shifts. When the beta distribution is symmetrical (case 2), it can also be observed that the RPI value for case 2 when the beta distribution is symmetric is close to that of the uniform distribution in Section 5.1. It can be concluded that the np optimal chart always considerably outperforms the np traditional chart regardless of the probability distribution of the p shift. The distribution of p shift may only influence the degree of the superiority of the p optimal chart over the np traditional chart. The performance of the np traditional and np optimal charts is further compared under five more scenarios with different design specifications to demonstrate the improvement that can be achieved by optimizing n. The overall improvement is represented in terms of RPI, which is calculated using Equation (8). The results are shown in Table 2 . [Please insert Table 2 here] As it can be observed from Table 2 , the RPI values shows the superiority of the np optimal chart over the np traditional chart throughout the five scenarios. For instance, in case 4 where r = 20, τ = 900, p 0 = 0.03 and p max = 5p 0 , the np optimal chart is able to make a reduction by 505% in the average number of infections (ANI) compared to the np traditional chart. This indicates that the np optimal chart is substantially more powerful for detecting the entire range of the shifts under such design specifications. This section shows a comparison of the detection speed of the np traditional and np optimal charts under the same scenarios shown in Table 2 . For each scenario, 30 samples with a random number of infections (d) are generated by simulation using inverse transform method. It only requires the sample size and infection rate in order to simulate d. The first 15 samples are generated to satisfy the in-control condition, and the rest are generated to be out of control. Both samples follow a binomial distribution with the same n but different infection rates (i.e., p 0 for the in-control and ip 0 for the out-of-control where i represents the increase in the shift). The values of i are indicated in Table 3 . For each chart, the same sample size in Table 2 is used. For example, the first 15 samples in scenario I when using the np traditional chart are generated using a binomial distribution B(40, 0.03), while the other 15 samples are generated with B(40, 0.06) (i.e., using a sample size of n = 40 and an infection rate of p = 20.03=0.06). Table 3 shows the sample at which both charts will detect the shift (i.e., the detection sample). The detection sample in Table 3 indicates that the np optimal chart always gives an outof-control signal faster than the np traditional chart. This demonstrates that the former has a better detection speed than the latter and consequently it is adopted for the early detection of an outbreak. Figure 7 illustrates the detection speed of both the np traditional and np optimal charts under the settings given in scenarios I-V in Table 3 . It is obvious that the np optimal chart always gives an out-of-control signal before the np traditional chart. This demonstrates that the former has a better detection speed than the latter and consequently it is adopted for the early detection of an outbreak. [Please insert Table 3 here] [Please insert Figure 7 here] In this section, the performance of the np traditional and np optimal charts is compared under 100% inspection using the same design specification in Section 5.1 (i.e., τ = 648 hours, p 0 = 0.01 and p max = 10p 0 ) and assuming that the airport has sufficient resources to carry out such inspection. A predetermined n of 100 arrivals is used for the np traditional chart, while it is optimized in the design of the np optimal chart. In 100% inspection, optimizing the sample size n means adjusting the grouping of the inspected units (Montgomery, 2013; Reynolds Jr & Stoumbos, 1999 The values of the charting parameters and corresponding ANI values for both np traditional and np optimal charts are indicated below: np traditional chart: n = 100, UCL = 2 and ANI = 6.4344. np optimal chart: n = 40, UCL = 1 and ANI = 3.4073. The RPI = indicates that the np optimal chart has a better overall 6.4344 -3.4073 3.4073 ≈ 89% performance than the np traditional chart by 89%. Figure 8 shows the performance of both np charts in terms of the normalized ATS (ATS np traditional / ATS np optimal ). It is clear that the np optimal chart outperforms the np traditional chart for detecting the whole range of p shifts. In the meantime, Figure 8 indicates that the superiority of the np optimal chart over the np traditional chart increases with increasing the shift size in the infection rate. This result is justifiable because the np optimal chart uses a sample size (n = 40) smaller than that of the np traditional chart (n = 100). [Please insert Figure 8 here] The performance of the np traditional and np optimal charts is further compared under the same five scenarios in Section 5.2 under 100% inspection. The same design specifications (τ, p 0 and p max ) for each scenario are used. The design specifications, charting parameter, ANI and RPI of both charts are all shown in Table 4 for each scenario. [Please insert Table 4 here] The overall performance of the np optimal chart, in terms of ANI, is always better than, or at least equal to, that of the np traditional chart across the five scenarios. RPI values illustrate the improvement in the overall detection effectiveness that can be achieved when the np optimal chart is used instead of the np traditional chart for each scenario. This paper proposes a monitoring scheme for early detection of outbreaks caused by coronaviruses and other important respiratory viruses. For respiratory viruses with high transmissibility and mortality rates, such as SARS-CoV-2, early detection of important clusters of infections provides critical information to public health representatives and policymakers. Table 3 . A comparison of the detection speed of the np traditional and np optimal charts Table 4 . A comparison of the np traditional and np optimal charts for 100% inspection under five different scenarios  Monitoring scheme is proposed for early detection of coronavirus virus outbreaks. The sample size is optimized to ensure the best overall performance of the scheme. False alarm rate and inspection rate are used as constrains. The proposed scheme substantially outperforms its traditional counterpart. 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