COVID-19 heterogeneity in islands chain environment

Background It is critical to capture data and modeling from the COVID-19 pandemic to understand as much as possible and prepare for future epidemics and possible pandemics. The Hawaiian Islands provide a unique opportunity to study heterogeneity and demographics in a controlled environment due to the geographically closed borders and mostly uniform pandemic-induced governmental controls and restrictions. Objective The goal of the paper is to quantify the differences and similarities in the spread of COVID-19 among different Hawaiian islands as well as several other archipelago and islands, which could potentially help us better understand the effect of differences in social behavior and various mitigation measures. The approach should be robust with respect to the unavoidable differences in time, as the arrival of the virus and promptness of mitigation measures may vary significantly among the chosen locations. At the same time, the comparison should be able to capture differences in the overall pandemic experience. Methods We examine available data on the daily cases, positivity rates, mobility, and employ a compartmentalized model fitted to the daily cases to develop appropriate comparison approaches. In particular, we focus on merge trees for the daily cases, normalized positivity rates, and baseline transmission rates of the models. Results We observe noticeable differences among different Hawaiian counties and interesting similarities between some Hawaiian counties and other geographic locations. The results suggest that mitigation measures should be more localized, that is, targeting the county level rather than the state level if the counties are reasonably insulated from one another. We also notice that the spread of the disease is very sensitive to unexpected events and certain changes in mitigation measures. Conclusions Despite being a part of the same archipelago and having similar protocols for mitigation measures, different Hawaiian counties exhibit quantifiably different dynamics of the spread of the disease. One potential explanation is that not sufficiently targeted mitigation measures are incapable of handling unexpected, localized outbreak events. At a larger-scale view of the general spread of the disease on the Hawaiian island counties, we find very interesting similarities between individual Hawaiian islands and other archipelago and islands.


Introduction
Significant local variations in the spread of COVID-19 have been established in heterogeneous environments. For example, omas, et al., compares nineteen different cities and counties in the US [20]. ey found that small differences in network models for interdependence and social interaction as well as the effects due to uneven population distributions can lead to substantial differences in infection timing and severity, leading different areas in each city to have vastly different experiences of the pandemic. Similar pa erns associated with heterogeneity have been made for entire nations, such as the work comparing the most affected cities in China [4]. ese works are based on the premise that substantial heterogeneity in social relationships at various scales affect the viral spread. It is unclear, however, whether or not such heterogeneity is a critical factor for an island chain and such study is absent from the literature. is is of utmost importance due to islands' vulnerability to any pandemic, especially for native populations as demonstrated for example with the introduction of measles to the Pacific Islands in the 1800's [28]. Islands are smaller contained populations, and thus epidemiological models may require adjustments to properly apply them to disease containment strategies. Identifying if major local variations can be expected for an island chain in the spread of COVID-19 is crucial since it directly impacts the effectiveness of mitigation measures, vaccine distribution and health care management. We focus here on a specific island chain, the Hawaiian archipelago and take somewhat different approach by comparing the individual island differences and identifying countries exhibiting similar properties. Maui for instance behave much more similarly to Japan over the last three months than her neighbor Islands which was surprising to see. Our goal is to demonstrate that Islands in general, whether they belong to the same archipelago or not, respond differently to the pandemic and cannot be aggregated into one single class.  [6].
e Hawaiian Islands are an archipelago of eight major islands, with only seven of them being populated.
e State is divided into five counties: Hawai'i , Honolulu, Kalawao, Kaua'i , and Maui. Since Kalawao is the smallest county in all of the 50 states in terms of both population and land area, we focus here on only the four major countiesure 1 shows the main eight islands as well as the various counties. Table 1 shows that Honolulu city and county is the most populated county of the state, with 69% of the state's population. Hawai'i county has the largest land mass of 63% of the entire state, but comes second in resident population. ird by population is Maui county, which spans the islands of Maui, Moloka'i, Lanai, and Kaho'olawe. Kaua'i county, which spans the islands Kaua'i and Ni'ihau, has the smallest population. In determining heterogeneity effects and how the Hawaiian Islands might differ from each other, it is also important to compare the demographics of the four counties we study.

Statistics
Honolulu  Table 1. e state's general statistics by county [11].  While Honolulu city and county has been dominating the COVID-19 daily cases numbers due to its larger population, the other counties are also facing the pandemic. Intuitively we might expect all counties to exhibit homogeneity with respect of impact of the virus, however this is not observed. We describe in detail commonalities and differences between the four counties. Additionally, we compare them to other non-Hawaiian islands to find similarities and differences. Our work highlights the need for localized measures and possibly targeted mitigation measures at the county level and as opposed to the state level for the most effective pandemic control. is has been already initiated to some degree with Kaua'i county implementing their more restricted travel policy on Dec. 2, 2020; on Jan. 19, 2021, Maui implemented the mandatory safe travel app for all travelers, see Fig. 3 for more details. It is critical for decision makers to take into account heterogeneity in their strategies. An important conclusion of this research is the identification of pa erns that change extremely rapidly. is is due primarily to the nonlinear behaviour of the underlying equations that simulate the spread of the pandemic. In other words, it is not sufficient to average the initial conditions of the virus spread and assume that the different islands will exhibit similar behavior in an average sense. On the contrary, nonlinear effects and clusters can take off in one of the contained populations at a different time, thus requiring different pandemic control mandates. We find that it is critical to assure that heterogeneity is included in modeling and thus decision making for adequate and effective pandemic control.

Materials and methods
ere are useful collections of Hawai'i COVID-19 data in the form of dashboards: the Hawai'i Emergency Management Agency's (HiEMA) dashboard, the State of Hawai'i 's Department of Health's Disease Outbreak Control Division's (DOCD) COVID-19 dashboard, and COVID Pau dashboard (CPD) [9,10,12]. Directly utilizing these dashboards alone is challenging. Firstly, the dashboards are not synchronized; they often display different data at various times for the same quantities, such as hospitalization data. Secondly, the availability of the dashboard data is sometimes restricted because of political concerns. Both HiEMA and DOCD provide visual data in plots, but do not allow for downloading of the data. e Hawai'i Data Collaborative dashboard [8] resolves a majority of these issues by providing a Google Spreadsheet of the local Department of Health's DOCD data. e Hawai'i Data Collaborative also works to coalesce data from the other dashboards, and even obtains data directly from the office of Lt. Governor Josh Green. Collected data and their sources are summarized in Table 2.
We also use the distribution of cases per zip code for each county whose tabulation areas are illustrated in S1 Fig. is   In this paper, we also compare the Hawaiian counties to other countries, Table 3 Table 3. e sources of COVID-19 data used in this paper for the comparison countries.

Compartmental Model
ere are two main classes of epidemiological models for this type of disease spread: compartmental models [1][2][3] and agent-based models [13,[16][17][18]. In this paper, we use a compartmentalized model inspired by [19], which is based on a standard discrete SEIR model. An extension, key to this paper, that we added to the model is a new group for travelers. Indeed, the tourist population plays a prominent role in Hawai'i and due to our isolated geographic location we are able to to collect precise information about daily arrivals and departure.
In our model, a given population is divided into four compartments: Susceptible (not currently infected), Exposed (infected with no symptoms), Infected (infected with symptoms), and Removed (recovered or deceased). Moreover, we subdivide the entire population into three additional groups: the general community (C), healthcare workers (H) and visitors (V). Visitors, who are only considered after October 15, when the safe travels Hawai'i program began, are further broken down into two categories: returning residents and tourists. While the returning residents are absorbed into the community bucket, the tourists are treated as a separate group. ese groups interact with each other, and each of them consists of the aforementioned compartments. In addition, compartments Exposed and Infected (in each population group) are split into multiple stages by day to be er reflect the progression of the disease. ere are two key dynamics of each population group: the dynamics of Susceptible individuals and the dynamics of the rest of the compartments. e time dependent hazard rate, λ(t), governs the susceptible dynamics as it determines the probability, 1 − e −λ(t) , of an individual becoming exposed at time t. e hazard rate is different for different population groups and takes into account interactions between the groups, thus coupling their dynamics.
Key to governing the spread of the disease is parameter β, capturing the basal transmission rate due to various interactions among individuals. Our model optimizes β to fit daily cases for a specific geographic location. Specifically, we use several different values of β that capture changes in COVID-19 mitigation policy. Table 4 displays the variables and parameters common to all simulations in this paper (optimized β's are given in the Results section). We introduce parameters p i as probabilities to develop symptoms on day i, and chose them such that if symptoms do develop, it takes between 2 to 14 days, with a mean between 4 and 6 days [26], while assuming that about 40% of all infections remain asymptomatic. e values of q s,i reflect the sentiment that symptomatic individuals are likely to quarantine, especially after a couple of days of symptoms. In addition, parameter r is the probability of transitioning from one stage of the illness to the next (with the final stage being recovery or death). Based on prior work [5], we chose r to yield an expected length of illness of 17 days.
In addition, we have parameters related to mitigation measures such as mask compliance as well as contact tracing that depend on the geographical location. Table 5 lists the values we use for the State of Hawai'i (those are assumed to be constant over the various counties) as well as the ones for others countries relevant to the discussion section. e parameters have been identified from dashboards/articles as well as for contact tracing. e choice of q a,i reflects the various testing and contact tracing efforts, and provide the probability for an asymptomatic individual to go into isolation as a result of testing and contact tracing.

Results
In this section we provide the results of simulations of our model for the four counties of the State of Hawai'i under analysis. In our plots we use the raw daily cases and not the 7 day average because our model fit plots the sum over all groups of the newly isolated and quarantined daily exposed and infected individuals, see S1 Appendix, Model Dynamics.

Initial Conditions.
e initial values of most variables are zero. e only non-zero values are the number of susceptible individuals in the general community and the healthcare worker community, the values of which are listed in Table 6, as well as a single not quarantined symptomatic individual, I c,0 (0) = 1.

Region
S c (0) S h (0) Date for I c,0 (0) = 1  Honolulu 937711 15000  Mar 06  Maui  167417 1500  Mar 15  Hawai'i 201513 1500 Mar 16 Table 6. Susceptible population for each region and first detected symptomatic individual. All other variables have an initial value of 0. Figure 5 displays the model fit for the Honolulu county. e dots represents the daily cases and the curve is the model fit. e vertical lines corresponds to mitigation measures that had an impact on the curve and for which we optimized the β. Table 7 explicit the different β's. e maximal daily case for Honolulu county was 342 and happened on August 12, 2020. We see two major exponential growths, one early in March that was crushed through a stay-at-home order and one in August followed by a second stay-at-home order. However the second lockdown was lifted before daily cases reached single digits in the hope to save the local economy. It can be seen on Table 7 that the first lockdown was more efficient. e largest peak is a ributed to the July 4 festivities, the transmission rate β was however quite smaller than for the first peak, but the State was much slower to call for a second stay-at-home order which resulted in the significantly higher counts. On October 15, 2020 the state of Hawai'i introduced the safe travel program which prompted an influx of tourists and traveling residents, this influx varies with time which explains the waving shape of the fit. For more details on incorporation of travelers in our model see S1 Appendix. Since the Safe travel program the daily cases have been fluctuating quite a lot which makes a fit difficult (some high daily cases came from a correctional facility cluster for instance). e overall trend as of January 15, 2021 is shown to be slightly increasing (the 7-day average can be found in Fig.6).  Table 7. Optimized transmission rates to fit Honolulu county data. ey reflect the State and Honolulu non-pharmaceutical mitigation measures. e top of Fig.6 shows the total number of tests, the test positivity rate (i.e. the percent of tests for COVID-19 that came back positive) as well as the daily cases for the Honolulu County. To create this overlayed plot, the shown metrics have been normalized by calculating each data point as a percent of the maximum of the corresponding metric over the whole observation period and using the 7-day rolling average. It can be seen that, as anticipated, test positivity correlates strongly with daily cases. e noticeably large initial values of the test positivity rate (also present for other counties) are likely caused by the a small number of test that have been administered to a very narrow slice of the population with much higher chances of having the virus. When interpreting these plots, it should also be noted that even later in the pandemic the sample of people receiving tests was not unbiased, since the State of Hawai'i has been administering tests to people who satisfy criteria which make them more likely to have the virus. e bo om plot of Fig.6 displays the mobility for Honolulu County, it shows the major dip in mobility triggered by the first stay-at-home order back in March 2020, coming back up in May to peak again in August before the second stay-at-home order. e mobility data clearly suggests why the second lockdown was not as efficient as the first one. In addition to the daily cases, we represents in Fig.7 the cumulative daily counts for Honolulu county distributed per zip code from the onset of daily cases to January 18, 2021. It can be observed that Honolulu downtown as well as the West Coast (Waianae) have been the most affected in terms of daily cases. For the West Coast it is mostly due to its high pacific islanders population and the fact that they have been disproportionately impacted. While they form about 4% of the total Hawai'i population they account for more than 27% of total cases [15].

Hawai'i County
Daily cases for Hawai'i county were very small until the aftermath of the July 4 celebrations which generated a large spike. e second stay-at-home order on Maui was extremely efficient but immediately followed by an exponential increase in the form of a few clusters. e maximum value is 51 and happened on October 25, 2020 during the third peak with a very close value during the second peak of 39 on August 29, 2020. One can observe a somewhat puzzling decrease in the number of daily cases after the start of the safe travel program. A potential explanation is that the spike in the number of cases that happened at that time was an isolated event unrelated to other activities on the island.  Table 9. Optimized transmission rates to fit Hawai'i county data. ey reflect the State and Hawai'i non-pharmaceutical mitigation measures. e mobility for Hawai'i county did not show a decline as steep as for Honolulu county, and it shows good correlation with the daily cases and testing data.     inhabitants  96720  48339  594  12  96740  42069  615  15  96749  17308  122  7  96778  14885  100  7  Table 10. e four zip codes with the largest cumulative distribution of daily cases.

Maui County
Maui county started the pandemic with a relatively low number of daily cases, but then entered an alarming state of a high number of cases per hundred thousand of population even reaching a a maximum of 56 cases on January 6, 2021. It can be seen clearly the trigger with the introduction of the safe travel program on October 15, 2020. e influx of travelers is not constant through time and because the ratio tourists versus residents is high on Maui we see as a result the wavy increasing curve. In addition to the effect of additional tourists there was a large outbreak in relatively high population density condominium complex. e initial increase after October 15 was solely due to travelers which is why we see a rise in daily cases even though the basal transmission rate β stays small.  Table 11. Optimized transmission rates to fit Maui county data. ey reflect the State and Maui non-pharmaceutical mitigation measures.
Tests, positivity and daily cases are represented on Fig.14 and show a strong correlation between the three. e mobility for Maui County seems correlating well until the introduction of the safe travel program.   e four zip codes with the largest counts can be found in 12 and their daily behavior is displayed in Fig.16. ere was a large outbreak in a multistory in early 2021 located in zip code 96732. e residents in this complex used elevators more than residents in other complexes in other areas with fewer stories.
ere are relatively larger number of tourists compared to local residents in zip codes 96761 and 96753 as compared to most other zip code areas. is is possible reason these two zip code area had larger increases in December than other areas.

Kaua'i County
Due to the low numbers on Kaua'i a model fit using our compartmental model could not be achieved. It can be observed on Fig.17 that the daily cases started following an exponential growth, it was a ributed to travelers which prompted the mayor of Kaua'i to request authorization to opt-out from the safe travel program. It was followed by a decrease in numbers and stabilization. A new peak can be observed right after the safe travel program was authorized reinstated by Kaua'i for intercounty travelers. e numbers are so small that is it extremely difficult to draw any additional conclusion. We still represent tests, positivity and daily cases on Fig.18 and see as for Maui a strong correlation between the three. e mobility for Kaua'i County is very flat after the initial decrease in March and even went a bit down after the safe travel program started. Fig 18. Top: e number of daily cases and test positivity rate are still well correlated, even though the raw numbers are small. Similar to Hawai'i county, we can see a jump in the daily case numbers that correlates with the increased number of tests rather than the test positivity rate, which is likely due to the biased nature of the population sample on which the tests are performed. Bo om: Overall mobility for Kaua'i County from March 2020 to January 2021 does not correlate well with the daily cases.

Discussion
ere is clearly major differences among the four counties. Fig.19 shows on the same plot normalized model fits for Honolulu, Hawai'i and Maui counties as well as the daily raw numbers for Kaua'i . It can observed that beside Kaua'i for which numbers have been very low to draw comparison, the other three counties correlates well until when the Safe Travel program began on October 15, 2020. Hawai'i county displays an increase in daily numbers right before which were a ributed to a couple of clusters (one in Hilo and one in Ocean View). Maui also had a few clusters, including a major one around October 20 on Lanai and another major one in early January in Kahului. After October 15, 2020 both Honolulu county and Hawai'i county show a slight increase in contrast with Maui county that displays a very sharp increase. Looking at Tables 7, 9 and 11 we observe that the exponential growths and decays for Hawai'i and Maui counties require typically larger value for the basal transmission rate than for Honolulu county. e reason is that changes occurred more rapidly in the outer-islands, for instance the peak for Honolulu county is based on a build-up starting in June while for Hawai'i county the peaks are much more narrower. For Maui county the decay due to the second stay-at-home order was extremely efficient at the beginning and then slowed down which requested an increase in β. Fig 19. Honolulu, Maui and Kaua'i counties with normalized model fit, Kaua'i with normalized daily cases. It is clearly observed that counties started to differ in respond to the spread of COVID-19 after the safe travel program opened.
We analyze similarity by using the L 2 -norm for the difference between two normalized given model fits. One comparison was done over the entire length from March 6, 2020 to January 15, 2021. Results are displayed in Table 13 Table 13. Normalized L 2 norm between hawaiian counties measuring similarity. Show the impact of the different county's regulations for travel since the dissimilarity between the counties grows when we add the period October 15, 2020 to January 15, 2021. In particular, before travel was instated Honolulu and Maui counties were the most similar, situation that reversed afterwards.
In regards to mobility and movement of the counties from the bo om halves of Fig. 6, 10, 14, and 18, we acknowledge that the counties behavior follow a pa ern that following the onset of the pandemic, movement dramatically slowed down. Afterwards, it began to plateau towards a movement index between the shutdown and normal. Curiously, the correlation between the mobility index and the daily case is far from strong, and in the case of Kaua'i county the picture is more similar to anti-correlation (see Fig.17). It suggests that the spread of the virus among households, especially large and multi-generational, could significantly contribute to the overall daily cases. As we can observe from the 3D zip code maps, the cases are very localized. Not surprisingly, they are higher in urban locations and towns where the population density, as well as the probability of indoor gatherings, is higher.
We use three other Islands: Japan, Iceland, Puerto-Rico for comparison with our counties. We ran a fit with our compartmental model for the three countries and analyze similarity by looking at the qualitative structure of the results as captured by merge trees (see e.g. [30]). e la er construct is a topological descriptor of functions, and is constructed by tracking how connected components of the sublevel sets appear and merge as the threshold for the sublevel sets increases. is comparison is favored to a standard L 2 metric due to time shifts in the course of the pandemic for the various countries. An easy way to visualize this process is to move a horizontal line from the bo om to the top of the graph of a function and keep track of the function values at which a new connected component of the graph appears under the line or two existing components get merged. e actual horizontal locations of the branches, which represent the connected components, is not important, just their relative (left-right) positions. e merge trees for our three counties and the aforementioned countries are shown in Fig.20. ey were computed using the normalized time series for the daily cases numbers starting from June 15. We also slightly simplified the structure (for illustration purposes) by removing very small branches. We can see that the Honolulu county merge tree is most similar to the Iceland merge tree and the Maui county merge tress is most similar to the Japan merge tree. e complexity of the Hawai'i county merge tree makes it more similar to the Puerto Rico merge tree, although these two are not as good of a match as the other pairs.

Honolulu Iceland
Maui Japan Hawai'i Puerto Rico  Table 14 provides the initial values for Iceland, Japan and Puerto-Rico used by our model. travel restrictions vary widely between countries, see Table 15 for the estimate made for Iceland, Japan and Puerto-Rico.
Iceland, most similar to Honolulu County, detected their first case in February and had a significant first wave, but then controlled the spread beside a super spreader event trigger by two travelers. Traveling has then be very restricted which is why the daily cases are mostly in the single digits at the end of the fit. Hawai'i county is most similar to Puerto-Rico. e accuracy of the data for Puerto-Rico is unclear and it was very difficult to find the travel restrictions. e primary difference is the peak in December that Puerto-Rico suffered. Maui and Japan display a very similar qualitative curve, especially when travelers are ignored for Maui. e reason for Japan explosive growth at the end of the year is a ributed to a few factors, including a controversial encouraging domestic travel policy that is as of January more restrictive and a possible COVID-19 fatigue by the population.  Table 14. Susceptible population for the three countries.

Conclusion
In this paper, using the Hawaiian archipelago, we explore the importance of taking into account local variations in island chains. Ratios between residents and tourists as well as age demographic and other specificity call for targeted mitigation measures and Safe Travel program when in a pandemic. (Implementation of the Safe Travel program varies between the different Hawaiian counties.) e State of Hawai'i has launched an aggressive mass vaccination campaign starting in December but the effects of which are only now starting to impact the daily case rate. During the period of our study the very small impact of vaccination was neglected. As of February 2, 2021 we have 202,200 doses administered. e State policy is to keep the vaccination plan as originally planned to 2 doses per individuals even though two cases of the more transmissible B1.1.7 have been detected in Hawai'i . As of February 8, 2021 cases have been decreasing in all four counties.
Not studied in this paper is hospital beds capacity, for the State of Hawai'i . e county of Honolulu is home to most of the hospital facilities and healthcare workers. e primary reason we did not discuss this here is the lack of consistent and clear data regarding hospitalisations. Similarly, quantification of COVID-19 related fatalities in the State of Hawai'i is delicate, indeed for instance in January about 60 deaths have been reclassified and added to the cumulative count.
It is critical to conduct studies such as those presented here and capture critical data to be used in future pandemics. We are now working with the Hawai'i government on scenarios to understand impact of lifting some of the mitigation measures. rates into quarantine may be different between the three groups.
• Variable S(t). e number of susceptible individuals.
• Variables E i (t). e number of asymptomatic infected individuals i days after exposure who are not quarantined.
• Variables E q,i (t). e number of quarantined asymptomatic infected individuals i days after exposure.
• Variables I j (t), i = 0, 1. e number of symptomatic infected individuals i days after the onset of symptoms who are not quarantined.
• Variables I j (t), j = 3, 4, 5. e number of symptomatic infected individuals at the nominal stage i of the illness. Note that a person can stay at a given stage for several days.
• Variables I q,j (t), j = 0, 1. e number of quarantined symptomatic infected individuals, with j representing either the number of days after the onset of the symptoms (j = 0, 1), or the stage of the illness (j = 2, 3, 4).
• Variable R(t). e number of removed (recovered or deceased) individuals. Spli ing exposed individuals into multiple stages, E i , allows us to capture possible differences in the progression of the asymptomatic phase of the disease. Importantly, it allows us to take into account that, according to the Centers for Disease Control and Prevention (CDC) as well as other sources, about 40% of people who contract SARS-CoV-2 remain asymptomatic, and the incubation period for those who do develop symptoms is somewhere between 2 to 14 days after exposure, with the mean incubation period between 4 and 6 days [22,25,26]. Individuals who do not develop symptoms after 14 days are assumed recovered. e use of the quarantine sub-compartments, E q,i , allows us to capture the effect of contact tracing and the reduced transmission rate for quarantined individuals. Similarly, having multiple stages for infected individuals be er reflects progression of the symptomatic phase of the disease. e first two stages represent the first two days of symptoms, but the next three should be understood as phases of the immune system fighting the disease. ere is a substantial variability (due to age as well as other factors) in the number of days any given person can spend at each stage. Our model implicitly assumes that the symptomatic phase of the illness lasts at least 5 days (in the unlikely case that each stage lasts just one day).
As we mentioned, a crucial part of the dynamics relates to the hazard rate. For the general community, group C, we have λ c (t) = β(1 − p mp (1 − p me )) (I c + εE c ) + γ((1 − ν)I c,q + εE c,q )+ ρ[(I h + εE h ) + γ((1 − ν)I h,q + εE h,q )]+ ρ v [(I v + εE v ) + γ((1 − ν)I v,q + εE v,q )] /(N c + ρ v N v ), (14) and for the tourists we have where we suppressed the dependency on t on the right for convenience. We use sub-indices c (community), h (healthcare workers), and v (tourists) to indicate the appropriate group. Subscript q indicates quarantined individuals. Here p me and p mp represent mask efficiency and mask compliance. Mask efficiency is chosen to reflect a reduction in transmission of 75% for all regions. Mask compliance is set at 20% for all regions at the start of the pandemic, but this value is modified on the dates the regions introduce mask regulations.
N v denotes the mixing pool for the visitors and N c denotes the mixing pool for the general community, computed as where variables E and I here represent the sum over all the stages within these compartments. For the healthcare worker group, we have λ h (t) = ρλ c + βη (I h + εE h ) + κν(I h,q + I c,q + I v,q ) /N h , where N h (t) = S h + E h + I h + R h . e model fit plot the following value x=c,h,v 3 i=1 q x s,i I(i) + (1 − r)q x s,4 I(4) e safe travel program started on October 15, 2020 which is when travelers are implemented in the model (they were negligible before that). Based on Safe Travels Digital Platform from the State of Hawai'i, we are assuming a pre-travel testing rate of 86%, a false negative rate of 0.5%. We also assume 1% of untested visitors go into exposed quarantine (we had to remove exempt travellers) and a 5% prevalence for the virus.
e pre-testing rates for travelers to Maui county is higher, and assumed to be 95%. Traveler average influx is modeled as a piece-wise linear function over two week intervals between the aforementioned time interval. e average influx for the comparing countries is assumed for simplification to be linear over the same time period. See Table 15.

Region
Tourists