key: cord-0784310-k6mlrrxx authors: Saidan, Motasem N.; Shbool, Mohammad A.; Arabeyyat, Omar Suleiman; T Al-Shihabi, Sameh; Abdallat, Yousef Al; Barghash, Mahmoud A.; Saidan, Hakam title: Estimation of the probable outbreak size of novel coronavirus (COVID-19) in social gathering events and industrial activities date: 2020-07-04 journal: Int J Infect Dis DOI: 10.1016/j.ijid.2020.06.105 sha: 9475ed9a2189d8990a0fed998079f6d1acd7af4f doc_id: 784310 cord_uid: k6mlrrxx Abstract Background The reproduction number (R0) is vital in epidemiology to estimate the number infected people and trace the close contacts. The R0 values varies depending on social activity and type of gathering events that induce infection transmissibility, in addition to its pathophysiology dependence. Objectives In this study, we estimated the probable outbreak size of COVID-19 at clusters mathematically using a simple model that can predict the number of COVID-19 cases, as a function of time. Methods We proposed mathematical model to estimate the R0 of COVID-19 in the outbreak occurring in both of local and international clusters in light of published data. Different types of clusters (religious, wedding, and industrial activity) were selected based on reported events in different countries between February and April 2020. Results The highest R0 values were found in wedding party events (5), followed by religious gathering events (2.5), while the lowest value was found in the industrial cluster (2). This in return, shall enable us to assess the trend coronavirus spread by comparing the model results and observed patterns.. Conclusions This study provides a predictive COVID-19 transmission patterns in different clusters types based on different R0 values. This model offers the decision makers in the contact-tracing task the predicted number of cases, which would help them in epidemiology investigations by knowing when to stop. The reproduction number (R0) is a measure used in epidemiology to estimate the number of cases, infected people, that are caused by contacting one infected person in the population (Zhao et al., 2020; Liu, 2020) . If R0 is more than one, infections will continue to spread; while, if R0 is less or equal one the infection will eventually diminish; however, virus is still new, many assumptions are needed to calculate Covide-19 R0, and researchers do not have a consensus about this value. According to the published literature, R0 of COVID-19 ranges between 1.4 to 6.49 (Liu et al., 2020a; Wu et al., 2020; Shen et al., 2020; Liu et al., 2019; Read et al., 2020; Majumder et al., 2020; Cao et al., 2020; Zhao et al., 2020; Imai, 2020; Julien and Althaus, 2020; Tang et al., 2020; . The variations in the estimated values of R0 for COVID-19 indicates that it is situationdependent. Furthermore, R0 for COVID-19 varies based on the time of the outbreak and the measures that are imposed by the countries to combat the virus spread. To date, most of the virus outbreaks in several countries can be attributed to events that had several people present, such as wedding parties, religious events, scientific conferences, national festivals, etc. Henceforth, we use the word cluster to describe any event that involved the presence of an infected person with a group of susceptible people. The main objective of this study is to estimate (R0) of COVID-19 at clusters mathematically. We rely on published data from several events and countries to estimate R0. Using the estimated R0, we develop a simple model that can predict the number of COVID-19 cases, as a function of time, where these cases emerge from such clusters. We validate our prediction model by applying it to religious, socials, and industrial clusters. Results show that decision-makers can rely on our model in estimating possible cases related to such cluster, which would help them in epidemiology investigations by knowing when to stop. We use dynamical modelling to capture and predict the number of cases with time. Unlike previous research that relies on the classical SIR (susceptible-infectious-recovered) model and its extension (Calafiore et al., 2020) , we have a new definition for the different J o u r n a l P r e -p r o o f compartments into which people in the cluster are divided (Fanelli et al., 2020) . Moreover, we present a new set of transition equations among the compartments. We assume that our mathematical model is only valid when the COVID-19 infection is transmitted in a cluster event of homogeneous population and with the same social contact pattern. For instance, infected individuals are infected with the same transmission probability from the susceptible group of individuals. This can help in the contact tracing while undertaking epidemiological investigation. However, to track the COVID-19 spread in heterogeneous populations with no-contact social pattern, our model cannot model and perform this situation with reasonable accuracy. Other mathematical models were proposed to do so. For example, Liu et al. (2020b) developed the contact network and no-contact models to keep track of the disease spread in and contact patterns, such as unprotected and protected contact and airborne spread. This in fact not our objective. Our mathematical model is only predicting the spread in a homogenous population (event attendees) based on contact model to mainly offer the decision maker in the contact-tracing task the predicted number of cases, which would help them in epidemiology investigations by knowing when to stop. The population that we target in our model is only the people attending an event, those in the cluster. The different compartments in which we divide the targeted population are: 1) suspected individuals (S) who is exposed to positive infected individuals with symptoms of COVID-19 infection, where, θ is empirically estimated as 0.035 for COVID-19 in the present study to best fit the actual cases (i.e. with accuracy more than 80% given as a constraint to the model), which represents the average transmissibility. Liu et al. estimated θ to equal 0.026 under no quarantine measure. The R0 range given to the model was between 2 to 5.; and N is 14 days for COVID-19 (range, 2 to 14 days) (Lauer et al., 2020; Linton et al., 2020) . At the time of the event, we divided attendees into S0 and I0 to show the starting numbers of susceptible and infected individuals. I0 is either a given number or is a percentage of S0, 2% to 4% of the S0, depending on the infection source country. For example, for the religious event that took place in South Korea and caused thousands of infections, the source of infection was a single individual; consequently, I0=1 and S0 is equal to all the event attendees, except the infected individual. The number of suspected and infected cases in the first day (n=1) can be calculated using Equations 2 and 3, respectively. Two to 14 days after the event, the number of suspected and infected cases are found using Equations 4 and 5, respectively. Si=n= Si=n-1 + Ii=n-1 -Ii=n (4) Ii=n= Ii=n-1 + (Si=n-1*ri) In order to calculate the suspected cases per day after identification of infected cases and removing them (the infected cases) from the susceptible population for treatment, then equation (5) is substituted in Equation (4), as shown in Equation (6) Si=n= Si=n-1 -(Si=n-1*ri) The clusters types are selected in the present study because they are considered as a homogenous sample with running contact-based model in specific time and location. The cluster event is bounded and well identified. Accordingly, the social pattern and communication intensity is relatively varied, hence, it is expected that the R0 is varied J o u r n a l P r e -p r o o f too. Most importantly, these clusters events were in the initial beginning of the virus spread worldwide and played a role in causing outbreaks in each of the considered countries in the present study. We searched for data reported in the news and public health reports, official website (WHO), and governmental reports that reported the situation of COVID-19 infection in the selected study cases. For each case, we extracted from the news and other sources the number of the positive cases recorded each day after the event. In most cases, the interval of possible COVID-19 virus exposure was selected at the time between the time of the event held, and the latest reported positive cases related to the event. We assumed that the transmission is proceeding until the epidemiological teams are reaching all cases (generations) of the infection chains. Two religious events are analysed in our work. The first event took place in the Malaysian mosque while the second event took place in South Korean church. A four-day Tablighi Jamaat event was held at Jamek Mosque in Sri Petaling, Kuala Lumpur, from February 27 to March 1, where 16000 attendees (including about 1,500 from outside Malaysia (Barker, 2020) ) were invited and at least 10,500 guests have attended this event. The event was socially active (including sharing of foods, sitting close to each other's, and holding hands, while no COVID-19 precautions were officially declared), but most attendees washed their hands during the event (The New York Times, 2020). The Tabligh assembly is considered the largest cluster that kicked off the second wave of COVID-19 infections in Malaysia. On March 16, 553 positive cases were reported and linked to this Tabligh assembly in Malaysia, in addition to 620 people, including those from other countries, who attended the event have tested positive, making it the largest-known center of COVID-19 transmission in Southeast Asia (Beech, 2020) . Hence, various containment measures were introduced in mid-March, and major restrictions on movement followed in late March. After suppressing the infection rate to below 1%, parts of Australia started easing restrictions (i.e. social distancing); consequently, a relatively small COVID-19 cluster has emerged on April 2 2020 at a meat factory in Victoria (Kelly, 2020) . After that, 49 positive cases were reported in a meat processing plant, with 350 employees, on April 29 2020. The physical layout of meat factories is relatively challenging the physical distancing since the workers have to be in relative proximity. To evaluate the transmissibility of COVID-19 in the selected clusters and events, as stated before, we applied the mathematical model to estimate the R0 in such types of clusters and accordingly fitted the expected infected cases while comparing its accuracy with the actual reported cases in these aforementioned events. We assumed the interval values of the corresponding parameter (R0) of this mathematical model, by which COVID-19 at the early stage of spread in each country, without intervention scenarios (curfew, lockdown, restricted social distancing, etc) are modeled. The R0 values were selected in the interval between 2 to 5.5, and then the best fit R0 value was determined for each event. Wedding party events Two wedding events, which were held in Jordan and Uruguay, as stated before, were selected to evaluate the transmissibility of COVID-19 in such types of clusters. There was insufficient information about these two cluster cases, so we relied on limited daily data which were published in official reports and daily news websites, and hence, this limited the capability to undertake sound statistical analysis. Using the existing data of reported cases and the mathematical model incorporating these data, we provide an estimation of the R0 of COVID-19 in these wedding events. We estimated that R0 was about 5, as shown in Figures (1) and (2) while modeling different ranges of R0 (2.0-5.5) where the values of modeled cases are shown in the bars above the modeled cases of R0=5. Figure ( 3) compares the modeled (predicted) and actual cases at the wedding events in both Jordan and Uruguay, at R0=5. The correlation coefficient between the two is 0.7303. It is noteworthy that it is quite difficult to precisely calculate the R0 since it is challenging to determine the actual daily cases during any cluster due to the delay in epidemiological tasks, cases sampling, and PCR testing, as well as, other parameters that might delay cases reporting such as demographic variations, etc (Delamater et al., 2019; Zhang et al., 2020) . Moreover, our model assumes that all suspected cases (exposed cases and cases who had close contact with confirmed cases) have been identified and PCR-tested, including those asymptomatic cases. Two religious gathering events, which were held in Malaysia and South Korea, as stated before, were selected to evaluate the transmissibility of COVID-19 in such types of clusters. There was insufficient information about these two cluster cases, so we relied on limited daily data which were published in official reports and daily news websites, and hence, this limited the capability to undertake sound statistical analysis. As shown in Figures (4) and (5), the R0 estimates based on the officially reported cases and after incorporating these data in our mathematical model, while modeling different ranges of R0 (2.0-5.5) as shown in the bars above the modeled cases. We estimated that R0 was about 2.5, which fits the actual data in good agreement. Figure (6) compares the modeled (predicted) and actual cases at the religious gathering events in both of Malaysia and South Korea, at R0=2.5. The correlation coefficient between the two is 0.8755. The meat and poultry processing industry is considered among the medium to large industries worldwide, and an essential component of any country's food infrastructure. Hence, it is of great importance to predict the COVID-19 spread in such industrial sector. Therefore, we incorporated the existing data of reported cases in Australia, as stated before, and accordingly, we provided an estimation of the R0 of COVID-19 in the meat processing case. We estimated that R0 was about 2, as shown in Figures (7) , while modeling different ranges of R0 (2.0-5.5) where the values of modeled cases are shown in the bars above the modeled cases of R0=2. Since most of increasingly transmitted COVID-19 outbreaks started with clustering events as stated before, then the transmission trends analysis based on daily positive cases data using mathematical modeling is of crucial significance. Hence, it can be employed as early warning system for non-pharmaceutical interventions and needs for imposing restricted measures (i.e., lockdown, confinement or quarantine), to combat and weaken the outbreak chains. Our proposed model might be used as a conventional tool to track the COVID-19 by testing and reporting changes overtime, and benchmark the cases mainly within and after imposing of measures (i.e. restricted or intermittent). Despite of the limited data at the beginning of any cluster-causing-outbreak, however, the timely prediction of pattern variations might provide the responsible agencies with more information on the varied J o u r n a l P r e -p r o o f spread momentum, trend pattern, and outbreak size. Thus, this helps to make decisions of measures ahead of time that lead to flatten the COVID-19 epidemic curve. The R0 estimates for different types of clusters events, accordingly, our model can be used for predictive purposes, and based on this the healthcare authorities can assess their capabilities and resilience to absorb such events outbreak wave. Our findings indicated that the daily predicted infected cases and the size of the outbreak are drastically dependent on the R0 value. When no lockdown measures were imposed, the R0 value was relatively high at the early beginning of the COVID-19 spread, despite of the fact of awareness dissemination campaigns and directives that were unleashed by governments worldwide. Based on different values of R0 (according to cluster type), we carried out a prediction of daily incidence and the probable size of the outbreak for 14 days at least for each selected case. Our mathematical modeling results show the values of R0 for the selected outbreaks clusters are 2 for industrial activity, 2.5 for religious events, and 5 for wedding events. All of these values are within the range of 2-5.5, and these values are acceptable when compared to other published literatures. However, the estimated cases presented in Figures 2, 4 , 5, 7 are also modeled for varied R0 values between 2-5.5 and this is shown in the bars, while the actual cases are within these bars values above the selected predicted value. In cluster types of outbreak infection, normally the susceptible population is more and less the same as the exposed population, which is decreasing rapidly. Hence, the modeling period is relatively short (i.e. less than a month) depending on the contacts tracing, epidemiological activity and performance. Moreover, the prediction of new cases cannot be performed until some cases are identified as infected cases, and removed from the susceptible population for treatment, hence, this might affect the infection transmission within the modeling period, and R0 is expected to change but its variation cannot be though modelled. Since our mathematical model is aimed to be used as a tool for the contacts-tracing team in the epidemiological investigation, then the target is to give the overall cumulative infected cases after 14 days (or the modeling period). Accordingly, the R0 was estimated by the model to give very good compatibility between the actual and predicted cases in the last days of the modeling period. To compare with the actual, reported cases cannot be done on a daily basis due to the delay in positive cases sampling, testing, and officially declared. This might influence the accuracy between the actual and predicted cases on a daily basis, as well as, the precision of R0 value estimation. However, the R0 was selected to reflect the overall and cumulative cases after 14 days or the modeling period. Regarding the sensitivity analysis of our model, only one parameter is used in our model which is θ is empirically estimated as 0.035 for COVID-19 in the present study to best fit the actual cases (i.e. with accuracy more than 80% given as a constraint to the model). The value estimation of θ was based on the reported infection rate in the Lombardi city (Italy) and New York (USA), while comparing the number of infected bases to the total population of the aforementioned cities (Lombardi and New York), and after subtraction the infected cases from the total susceptible population of these cities. The transmissibility is believed to relatively have high value in the initial beginning of any outbreak because of the lack of public awareness of COVID-19 throughout Feb-March 2020 in the selected cases in the present study. It is noteworthy, that θ influences the infection rate (ri) in our mathematical model. However, based on the actual data reported, θ = 0.035 was found to be the best fit (i.e. Liu et al. (2020) estimated θ to equal 0.026 under no quarantine measure). Finally, to enhance the accuracy of our model, there is a need to show the testing capacities for each country corresponding to the outbreak timing in these countries and situations. Unfortunately, we could not find a reliable source of references or data to rely on while investigating these points (i.e. testing capacities at outbreak timing, bias reporting, etc) at that outbreak timing (Feb-March 2020). The present study provides a predictive COVID-19 transmission patterns clusters with different types of activities (i.e. wedding party, religious events, industrial activity, etc.) based on different R0 values, respectively. Moreover, the proposed mathematical model offers a tool to benchmark the impacts of non-pharmaceutical interventions measures and operational responses, and their spread pattern towards flattening the epidemic curve for specific outbreaks induced by such types of clusters activity. Our findings showed that the R0 is higher in wedding type of clusters, followed by religious gathering events, and the lowest value was found in the industry cluster. Accordingly, the present model can be used as a tool to predict the expected number of infected cases, based on the outbreaks cluster, so to enhance the plan for close contacts tracing of the positive PCR cases; hence, the epidemiological activities can be directed efficiently towards exposed cases with optimal logistics as expected. Funding source: "This research received no external funding" Conflicts of Interest: "The authors declare no conflict of interest." Ethical Approval: Not required any ethical approval for this study Declaration of interests ☒ 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. J o u r n a l P r e -p r o o f Coronavirus COVID-19 cases spiked across Asia after a mass gathering in Malaysia. 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