COVID-19 Case Prediction and Outbreak Control of Navy Cluster in Sri Lanka: Effectiveness of SIR Model

Introduction: Infectious diseases such as coronavirus disease 2019 (COVID-19) can spread dangerously fast in semi-conned places. Nevertheless, it has been found that rapid public health interventions such as isolation and quarantine could successfully curtail such outbreaks. An outbreak of COVID-19 was reported within a cluster of Navy personnel in the Western Province of Sri Lanka commencing from 22 nd April 2020. An epidemiological investigation followed by aggressive public health measures were implemented by the Epidemiology Unit of the Ministry of Health with the support of the Sri Lanka Navy in response to the above outbreak. The objective of this research was to predict possible number of cases within the susceptible population in Sri Lanka Navy, to be used primarily for operational planning purpose by the Ministry of Health in control of outbreak in Sri Lanka. Methods: COVID-19 Hospital Impact Model for Epidemics (CHIME) developed by Predictive Health Care Team at Penn Medicine, which was a Susceptibility, Infected and Removed (SIR) model was used. The model was run on 20.05.2020 for a susceptible population of 10400, with number of hospitalized patients on the day of running the model being 357, rst case hospitalized on 22.04.2020 and social distancing being implemented on 26.04.2020. Social distancing scenarios of 0, 25, 50 and 74% were run with 10 days of infectious period and 30 days of projection period. Results: With increasing social distancing measures, the peak number of infected persons decreased, as well as the duration of the curve extended. The number of infected cases from the rst case ranged from 49 th day to 54 th day under social distancing scenarios from 0% to 74%. The doubling time increased from 3.1 days to 4.1 days from no social distancing to application of 74% social distancing, with corresponding decrease of Ro from 3.54 to 2.83. Expected daily growth rate of COVID-19 cases has decreased from 25.38 % to 18.53% under aforementioned increasing social distancing scenarios. The observed or actually experienced number of cases were well above the projected number of cases up to 07.05.2020, however, since this date the reported number of cases were lower than the projected number of cases from the model under four social distancing scenarios considered. Similar pattern was noted for the observed or actually experienced number of cases until the 20.05.2020, however, since then it was continuing at a very low intensity until the end of the modelling period. The number of COVID-19 cases prevented as per the model ranged from 2.3 – 21.1 %, compared to the base line prediction of no social distancing. However, based on the observed number of cases and the baseline model with no social distancing, 90.3% reduction was observed by the time of the model application date.


Introduction
Infectious diseases in semi-con ned places such as Cruise Ships, Military Barracks, and College Dormitories can have rapid spread, coronavirus disease 2019  being no exception (1). The COVID-19 outbreak among navy servicemen in USS Theodore Roosevelt was characterized by widespread transmission with mostly young and healthy sailors, in close and congregate exposure showing mild or no symptoms (2). During the outbreak of COVID-19 in the Diamond Princess cruise ship reported a basic reproduction rate (Ro) 4 times higher on-board compared to the that in the epicenter in Wuhan. However, with the preventive measures implemented in the Diamond Prince cruise ship, it was possible to reduce the Ro of 14.8 to 1.78 (3).
While security forces are essential to stay in such con ned places as per their operational requirements, spread of COVID-19 could have serious repercussions not only on the staff of the forces, but also on national security. Sri Lanka being an island nation, the role played by Sri Lanka Navy is pivotal, especially in a scenario of high transmission rates in the neighboring countries. On 22 nd of April, a new case from Polonnaruwa district, a navy sailor attached to the Sri Lanka Navy Base at Welisara, who was on leave tested positive for COVID-19 (4). Subsequently increasing number of COVID-19 cases were diagnosed from the same Naval Base. Having con rmed an outbreak in the Naval Base, several public health measures were implemented by the Sri Lanka Navy and together with the Epidemiology Unit of the Ministry of Health based on the ndings of epidemiological investigations.
It was necessary to predict how the outbreak would spread among the con ned space of the Navy base, in order to understand the health system demand from the infected individuals, as well as to quantify the effects on operational continuity of the Navy. The objective of this exercise was to predict possible number of cases within the susceptible population in Sri Lanka Navy Base at Welisara and their associated operational units in the Western Province, to be used primarily for operational planning purposed by the Ministry of Health in control of outbreak in Sri Lanka. The speci c objectives of the study were to predict the number of COVID-19 cases among the exposed population under suggested different social distancing scenarios and to compare the actual number of cases reported with those predicted by the model based on the preventive measures implemented by the Epidemiology Unit, Ministry of Health Sri Lanka Navy, and Ministry of Defense as a collaborative effort.

Methodology
Mathematical models could be a key tool in response to outbreaks such as COVID-19 (5-7). Susceptibility, Infected and Removed (SIR) Model is one of the simplest compartmental models, and many models are derivatives of this basic form (8)(9)(10)(11)(12). Nesteruk used this popular SIR model to get optimal values for the model parameters with the use of statistical approach (13). The SIR model has been widely used by many in modelling disease control activities among others (14,15).
As described by Kermack and McKendrick, the SIR model consists of three compartments: S for the number of susceptible, I for the number of infectious, and R for the number of removed (recovered and thus immune or deceased) individuals) of which the relationship is explained below. N = S+I+R ß = the average number of contacts per person per time λ = Number of infected individuals As per the SIR model shown in Figure 1, the population can be seen as con ned to three compartments, susceptible, infected or recovered. An individual may move between compartment as the disease continues to spread in the community, however, at a given time, one person could be only in one of the three compartments (16).
The number of susceptible persons will gradually decrease as the number of infected persons gradually rise, peak and decline. Parallel to that, the number of recovered persons will gradually increase. It is only applicable during the period prior to a region's peak infections, and it accounts only for a single signi cant social distancing policy. COVID-19 Hospital Impact Model for Epidemics (CHIME) developed by Predictive Health Care Team at Penn Medicine which uses a Monte Carlo simulation instantiation of a susceptible, infected, removed (SIR) model with a 1-day cycle (17). The CHIME model is used to predict hospital capacity needs during COVID-19 using local model inputs, which has an easy to use public web (17). We chose the CHIME model since it was simple and ready to be deployed even by busy, on the job outbreak response teams.
The CHIME model is speci cally developed to assess hospital capacity needs during COVID-19. In the Sri Lankan context, we have to rethink some of the model inputs. In the CHIME model, hospital market share needs to be provided. In Sri Lanka, all patients who are diagnosed with COVID-19 are centrally and dynamically allocated case-by case to a designated hospital. These designated state-owned hospitals are providing services free of charge and do not have rigid catchment area boundaries. Hence, we used the model to the whole of the hospital system of Sri Lanka which could be used to admitted COVID-19 con rmed persons. Hence, both hospital market share and percentage of hospital admissions were kept as 100%. Further, epidemiological pattern from the time of onset of the outbreak to the point of running the CHIME model has shown that most of the COVID-19 patients were healthy and asymptomatic Navy personnel. Hence, it was decided that there was no requirement to model in the ICU admission and ventilated proportions during the current exercise.
We ran the model on 20.05.2020 using the following model inputs given in Table 1: Projected days 30 CHIME Model * Highest social distancing percentage that the web-interphase provided (74%) was used.
The excel les generated through the CHIME model was analyzed using IBM SPSS Statistics 21 to prepare the diagrams.
It should be noted that the susceptible population of 10400 persons consisted of Navy personnel as well as their close family contacts of them. In addition, we plotted the daily number of cases from the Sri Lanka Navy Cluster as reported daily in the Daily Situational Report issued by the Epidemiological Unit.
It should also be noted that some of the preventive measures were commenced as early as 23.04.2020, however, for the modelling purposes, the date from which the full-scale social distancing commenced was taken as 26.04.2020.

Results
The SIR models under different social distancing scenarios obtained through the CHIME model are presented in gure 2. In addition, the peak number of infected cases under different social distancing scenarios as well as the day of the peak number of cases under different social distancing scenarios were compared as shown in Table 2. As per Figure 2 and table 2, it is evident that with increasing social distancing measure, the peak number of infected persons decreases, as well as the duration of the curve prolongs. The day of peak number of infected cases from the rst case ranged from 49 th day to 54 th day under social distancing scenarios from 0% to 74%. The peak number of infected cases varied from 3658 to 2555. The doubling time R 0 and growth rate under different social distancing scenarios are shown in Table 3. Next, we plotted the number of daily COVID-19 cases as projected under different social distancing scenarios for the susceptible Navy population along with the observed or actually reported number of COVID-19 cases on a daily basis in line with the outbreak control measures. This was intended to examine how the epidemiological curves of projected and observed or actually reported cases would relate to each other ( Figure 3).
As per gure 3, it could be seen that the observed or actually reported number of cases were well above the projected number of cases up to 07.05.2020. However, since this date the reported number of cases were lower than the projected number of cases from the model under four social distancing scenarios considered. The typical bell-shaped epidemiological curve was not observed among the observed or the actual COVID-19 cases. Next, we plotted the cumulative number of cases predicted by different social distancing scenarios along with the observed cumulative number of cases among the Navy cluster cases.
As per Figure 4, the cumulative number of observed cases was overriding the cumulative number of projected cases from the model till 20.05.2020. Then, it was continuing at a very low intensity until the end of the modelling period. A steady decrease in the peak of projected curves is seen with the application of increasing social distancing levels.  (20). The assistance from the security forces was received to complement the work by the health sector in curtailing the COVID-19 outbreak. Prior to the emergence of the Navy cluster, there were several other clusters of COVID-19 patients which were successfully managed in Sri Lanka. However, the Navy cluster was quite unique. Firstly, it marked the occurrence of the largest number of cases within a con ned population. Secondly, if the COVID-19 cluster within the Navy personnel was not successfully managed, it would have led to the paralysis of the functional capacity of the Sri Lanka Navy. This would have had serious repercussions on border security concerns, as an island nation.
The Epidemiology Unit in collaboration with the Sri Lanka Navy conducted a detailed epidemiological investigation on the outbreak in the Navy cluster experienced in the Sri Lanka Navy Base at Welisara and their associated operational units. However, as per the preliminary investigations, a susceptible population of 10400 Navy personnel were identi ed and considered for the running of the model. As a part of the operational response, the SIR model was used to predict the probable number of infected persons amongst the Navy Cluster.
Under the (0) social distancing scenario, the daily case load was predicted to peak up to 3658 cases on the 49th day. Further, under the best predictable social distancing scenario (74%), the number of daily cases would peak to 2555 on the 54th day. The network of designated hospitals and preventive health services were ready to anticipate and receive a large in ux of COVID-19 con rmed cases from the Sri Lanka Navy based on this case prediction scenario. A series of COVID-19 treatment hospitals with increasing bed capacity was identi ed as a response activity. However, country was able to control this outbreak situation in a very effective manner, implementing different preventive strategies, in addition to the social distancing, probably accounting to more stringent than even 74%.
It was also found that the observed number of daily cases and observed cumulative number of cases seems to be much higher at the initial stages of the outbreak than the predicted number of daily cases and the predicted cumulative number of cases. This may signal the dangerous levels that the outbreak would have escalated into, if not successful control measures were implemented. However, subsequently, both the projected number of daily cases and the cumulative number of cases became lower than the reported number of daily cases and the cumulative number of reported cases.
More ever, the predicted number of COVID-19 cases within the Navy Cluster based on all four different social distancing scenarios were much higher than the actual number observed. When comparing the proportion of cases prevented in relation to the no social distancing scenario, 2.3%, 7.9% and 21.1% were prevented by 25%, 50% and 74% social distancing scenarios. However, when comparing the proportion of actual number of cases prevented compared to the no social distancing scenario, the prevented percentage rose to 90.3.
One possible reason for the large gap between the predicted and actual number of cases observed could at least be partly attributed to the assumptions on which SIR model is based on. The SIR model assumes a fully connected population, where there is homogeneous mixing of infected and susceptible population (21). If the afore mentioned mixing falls anything less than 100%, the mode will have a bias of overestimating the number of cases that would arise. Hence, during the scenario under study among the Naval personnel, one reason why the model provided overestimates could be that the level of mixing in the actual population to be less than the model assumed to be.
In addition, the observed signi cant reduction of cases could be attributed to cumulative effect of multiple, timely and rigorous outbreak control measures including social distancing implemented by the Ministry of Health and the Sri Lanka Navy. In order to reduce the congestion within the camps, susceptible population was redistributed to a series of designated centers under strict quarantine procedure. In the meantime, the close contacts including family members of the Navy personnel who returned home from the Naval base were sent for institutional quarantine. Further, testing of all susceptible individuals was carried out for COVID-19. The other forces supported the Sri Lanka Navy to collaboratively work on institutional quarantining together with public health authorities to institute relevant preventive measures on timely basis.
The COVID-19 patients were identi ed and isolated irrespective of if they were symptomatic or not. Firstly, this indicates that the number would have been lower, if only symptomatic patients were accounted for. This would have actually have contributed to an overestimating of the observed number of COVID-19 patients. Secondly, the similar strict preventive health measures were implemented in a uniform manner irrespective of if the positively diagnosed COVID-19 patients were symptomatic or not, despite contrasting evidence on infectivity of asymptomatic COVID-19 positive patients (22)(23)(24)(25). This highlights again the effects of stringent preventive health measures that would have contributed to the outbreak control.
Further, the predicted Ro under different social distancing scenarios during the current study ranged from 3.54, 3.36, 3.07 and 2.83 under zero, 25%, 50% and 74% social distancing scenarios. Such effect by social distancing on the control of the spread of the diseases has been shown elsewhere in the world. For example, a large number of COVID-19 cases have been prevented due to rigorous preventive health measures in the aircraft carrier USS Theodore Roosevelt which arrived in Guam in March 2020, which was a similar semi-con ned population (2). In the meantime, the R 0 in the Diamond Princess Cruise Ship was to be 4 times higher than to the R 0 in Wuhan. As per the modelling, it was found that the initial R 0 to be 14.8 which came down to 1.78 with the isolation and quarantine measures (3).
When considering the observed daily reported case trend of the Sri Lanka Navy Cluster, the typical bellshaped epidemiological curve was not seen. This again could explain the vigorous interventions carried out to curtail the outbreak.

Conclusions
This exercise demonstrated the practical use of a prediction model made readily available through an online open source platform for the operational aspects of controlling a COVID-19 outbreak or similar communicable disease outbreaks in a closed community such as armed forces. At the initial stages, the results of predictions could be used for understanding the magnitude of the outbreak in the Sri Lanka Navy Cluster that the country is yet to encounter. In addition, such ndings could be used for strategic planning for curtailing the outbreak and for health system preparedness. Further, lessons from such prediction modelling could be used for forecasting existing or new infectious diseases in future. While active epidemiological surveillance, contact tracing, case isolation and case management should be the cornerstone of outbreak management, epidemiological modelling could supplement above efforts.   Projected and Observed Daily Cases: The projected daily patients under 0%, 25%, 50% and 74% social distancing scenarios are shown in blue, green, brown and purple lines respectively. The projected daily patient curve attens with increasing social distancing scenarios, while the time to the peak prolongs.
The red line shows the observed daily cases which continue to be above the projected daily patient lines of all four social distancing scenarios up to 07.05.2020. However, since this date, the red line showing the observed number of cases curve goes below the projected number of cases under four social distancing scenarios considered.