COVID-19 Heterogeneity in Islands Chain Environment
Monique Chyba, Alice Koniges, Prateek Kunwar, Winnie Lau, Yuriy Mileyko, Alan Tong
CCOVID-19 Heterogeneity in Islands Chain Environment
Monique Chyba , Alice Koniges , Prateek Kunwar , Winnie Lau , Yuriy Mileyko , Alan Tong Applied and Computational Epidemiological Studies (ACES), University of Hawai ‘ i at Manoa Departmentof Mathematics, Honolulu, Hawai ‘ i , United States Hawai ‘ i Data Science Institute, University of Hawai ‘ i at Manoa, Honolulu, Hawai ‘ i , United States Abstract
As 2021 dawns, the COVID-19 pandemic is still raging strongly as vaccines finally appear and hopes for areturn to normalcy start to materialize. There is much to be learned from the pandemic’s first year datathat will likely remain applicable to future epidemics and possible pandemics. With only minor variantsin virus strain, countries across the globe have suffered roughly the same pandemic by first glance, yetfew locations exhibit the same patterns of viral spread, growth, and control as the state of Hawai’i. In thispaper, we examine the data and compare the COVID-19 spread statistics between the counties of Hawai ‘ ias well as examine several locations with similar properties to Hawai ‘ i . Introduction
Significant local variations in the spread of COVID-19 have been established in heterogeneous environ-ments. For example, Thomas, et al., compares nineteen different cities and counties in the US [20]. Theyfound that small differences in network models for interdependence and social interaction as well as theeffects due to uneven population distributions can lead to substantial differences in infection timing andseverity, leading different areas in each city to have vastly different experiences of the pandemic. Similarpatterns associated with heterogeneity have been made for entire nations, such as the work comparing themost affected cities in China [4]. These works are based on the premise that substantial heterogeneity insocial relationships at various scales affect the viral spread. It is unclear, however, whether or not suchheterogeneity is a critical factor for an island chain and such study is absent from the literature. Thisis of utmost importance due to islands’ vulnerability to any pandemic, especially for native populationsas 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 adjustmentsto properly apply them to disease containment strategies. Identifying if major local variations can beexpected for an island chain in the spread of COVID-19 is crucial since it directly impacts the effec-tiveness of mitigation measures, vaccine distribution and health care management. We focus here on aspecific island chain, the Hawaiian archipelago and take somewhat different approach by comparing theindividual island differences and identifying countries exhibiting similar properties. Maui for instancebehave much more similarly to Japan over the last three months than her neighbor Islands which wassurprising to see. Our goal is to demonstrate that Islands in general, whether they belong to the samearchipelago or not, respond differently to the pandemic and cannot be aggregated into one single class.1 a r X i v : . [ q - b i o . P E ] F e b ig 1. The State of Hawai ‘ i and its counties [6].The Hawaiian Islands are an archipelago of eight ma-jor islands, with only seven of them being populated.The State is divided into five counties: Hawai ‘ i , Hon-olulu, Kalawao, Kaua ‘ i , and Maui. Since Kalawaois the smallest county in all of the 50 states interms of both population and land area, we focushere on only the four major countiesure 1 showsthe main eight islands as well as the various coun-ties.Table 1 shows that Honolulu city and county is themost populated county of the state, with 69% of the state’s population. Hawai ‘ i county has the largestland mass of 63% of the entire state, but comes second in resident population. Third by population is Mauicounty, which spans the islands of Maui, Moloka ‘ i, Lanai, and Kaho ‘ olawe. Kaua ‘ i county, which spans theislands Kaua ‘ i and Ni ‘ ihau, has the smallest population. In determining heterogeneity effects and how theHawaiian Islands might differ from each other, it is also important to compare the demographics of thefour counties we study. Statistics Honolulu Hawai ‘ i Maui Kaua ‘ iLand Area (miles) 600.74 4,028.42 1,161.52 619.96Resident Population 974,563 201,513 167,503 72,293Resident Population State Percent 68.8% 14.2% 11.8% 5.1%Tourists (thousands per year) 5862.4 1706.2 2914.9 1388.6Tourists (as daily percent of residents) 1.64% 2.32% 4.77% 5.26% Table 1.
The state’s general statistics by county [11].Figure 2 left provides the age demographic distribution per county. Honolulu county has a largerpercentage of individuals between 20 and 40 years old while Hawai ‘ i county is more represented in the55-80 years old age group. From Fig. 2 (right) it can be observed that the Honolulu county has a largerrelative Asian population compared to the other counties and a smaller relative Native Hawaiian and PacificIslander population. Fig 2.
Left: Age demographic per county. Right: Ethnicity distribution per county [8].While Honolulu city and county has been dominating the COVID-19 daily cases numbers due to itslarger population, the other counties are also facing the pandemic. Intuitively we might expect all countiesto exhibit homogeneity with respect of impact of the virus, however this is not observed. We describein detail commonalities and differences between the four counties. Additionally, we compare them toother non-Hawaiian islands to find similarities and differences. Our work highlights the need for localized2easures and possibly targeted mitigation measures at the county level and as opposed to the state levelfor the most effective pandemic control. This has been already initiated to some degree with Kaua ‘ i countyimplementing their more restricted travel policy on Dec. 2, 2020; on Jan. 19, 2021, Maui implemented themandatory safe travel app for all travelers, see Fig. 3 for more details. It is critical for decision makers totake into account heterogeneity in their strategies. Fig 3.
Safe travel protocols per counties. Kaua ‘ i county has the most restricted travel regulations since Dec.2, 2020 following a significant initial surge in cases with the introduction of the Safe Travel program onOctober 15, 2020.An important conclusion of this research is the identification of patterns that change extremely rapidly.This is due primarily to the nonlinear behaviour of the underlying equations that simulate the spread of thepandemic. In other words, it is not sufficient to average the initial conditions of the virus spread and assumethat the different islands will exhibit similar behavior in an average sense. On the contrary, nonlineareffects and clusters can take off in one of the contained populations at a different time, thus requiringdifferent pandemic control mandates. We find that it is critical to assure that heterogeneity is included inmodeling and thus decision making for adequate and effective pandemic control. Materials and methods
There are useful collections of Hawai ‘ i COVID-19 data in the form of dashboards: the Hawai ‘ i EmergencyManagement Agency’s (HiEMA) dashboard, the State of Hawai ‘ i ’s Department of Health’s Disease OutbreakControl Division’s (DOCD) COVID-19 dashboard, and COVID Pau dashboard (CPD) [9, 10, 12]. Directlyutilizing these dashboards alone is challenging. Firstly, the dashboards are not synchronized; they oftendisplay 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 HiEMAand DOCD provide visual data in plots, but do not allow for downloading of the data. The Hawai ‘ i DataCollaborative dashboard [8] resolves a majority of these issues by providing a Google Spreadsheet of thelocal Department of Health’s DOCD data. The Hawai ‘ i Data Collaborative also works to coalesce data fromthe other dashboards, and even obtains data directly from the office of Lt. Governor Josh Green. Collecteddata 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 illustratedin S1 Fig. This data proved even more challenging to gather, since those numbers are not compiled in anyopen source spreadsheet; they need to be fetched from the Disease Outbreak Control Division Dashboard3tatistic SourceDaily Cases Hawai ‘ i Data Collaborative [8]Deaths Hawai ‘ i Data Collaborative [8]Testing Data Hawai ‘ i State Department of Health [12]Hospitalization Hawai ‘ i Data Collaborative [8]Infections by County Hawai ‘ i State Department of Health [12]Mobility Index Hawai ‘ i State Department of Health [12]Traveler Data Hawai ‘ i Data Collaborative [8] Table 2.
The sources of COVID-19 statistics for this paper. The Hawai ‘ i State Department of Health data isoriginal, while the Hawai ‘ i Data Collaborative takes a large portion of it’s data from the Department ofHealth.under their Hawai ‘ i COVID-19 Maps daily. To obtain mobility data we used the open source SafeGraphCOVID-19 Data Consortium [27] that provides social distancing metrics illustrating the daily view ofmovement between census block groups.The transmission rate in our model is optimized to reflect non pharmaceutical mitigation interven-tionsure 4 displays the timeline from March 6 to September 24. Primary events impacting the curve afterSeptember 24 are due to the safe travel program and can be seen in Fig. 3. In addition, the State moved toTier 2 on October 22, 2020 and has stated in that phase since. Note also that the State of Hawai ‘ i startedvaccines administration on Dec 15, 2020. As of January 17, 2021 the State recorded 76’498 administeredvaccines doses. The deadliest day since September 24, and global maximum happened on October 14, 2020with a count of 14 individual. Fig 4.
Timeline of events related to the pandemic in the State of Hawai ‘ i from March 6, 2020 to September24, 2020.In this paper, we also compare the Hawaiian counties to other countries, Table 3 summarizes the sourcesfor the data we used. 4tatistic SourceDaily Cases Iceland COVID-19 in Iceland - Statistics [7]Daily Cases Japan Japan COVID-19 Coronavirus Tracker [14]Daily Cases Puerto-Rico The COVID Tracking Project [29] Table 3.
The sources of COVID-19 data used in this paper for the comparison countries.
Compartmental Model
There are two main classes of epidemiological models for this type of disease spread: compartmentalmodels [1–3] and agent-based models [13, 16–18]. In this paper, we use a compartmentalized model inspiredby [19], which is based on a standard discrete SEIR model. An extension, key to this paper, that we addedto the model is a new group for travelers. Indeed, the tourist population plays a prominent role in Hawai ‘ iand due to our isolated geographic location we are able to to collect precise information about daily arrivalsand 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 ordeceased). Moreover, we subdivide the entire population into three additional groups: the general com-munity (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: returningresidents and tourists. While the returning residents are absorbed into the community bucket, the touristsare treated as a separate group. These groups interact with each other, and each of them consists of theaforementioned compartments. In addition, compartments Exposed and Infected (in each population group)are split into multiple stages by day to better reflect the progression of the disease. There are two keydynamics of each population group: the dynamics of Susceptible individuals and the dynamics of the rest ofthe compartments. The time dependent hazard rate , λ ( t ) , governs the susceptible dynamics as it determinesthe probability, − e − λ ( t ) , of an individual becoming exposed at time t . The hazard rate is different fordifferent population groups and takes into account interactions between the groups, thus coupling theirdynamics.Key to governing the spread of the disease is parameter β , capturing the basal transmission rate due tovarious interactions among individuals. Our model optimizes β to fit daily cases for a specific geographiclocation. Specifically, we use several different values of β that capture changes in COVID-19 mitigationpolicy. Table 4 displays the variables and parameters common to all simulations in this paper (optimized β ’sare 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 4and 6 days [26], while assuming that about 40% of all infections remain asymptomatic. The values of q s,i reflect the sentiment that symptomatic individuals are likely to quarantine, especially after a couple of daysof symptoms. In addition, parameter r is the probability of transitioning from one stage of the illness tothe next (with the final stage being recovery or death). Based on prior work [5], we chose r to yield anexpected length of illness of 17 days.In addition, we have parameters related to mitigation measures such as mask compliance as well ascontact tracing that depend on the geographical location. Table 5 lists the values we use for the State ofHawai ‘ i (those are assumed to be constant over the various counties) as well as the ones for others countriesrelevant to the discussion section. The parameters have been identified from dashboards/articles as well asfor contact tracing. The choice of q a,i reflects the various testing and contact tracing efforts, and providethe probability for an asymptomatic individual to go into isolation as a result of testing and contact tracing.For more information regarding dynamics equations of the model, see S1 Appendix.5 able 4. Variable and parameters common for all geographic locationsParameter, meaning Value β , basal transmission rates optimized to fit dataFactors modifying transmission rate ε , asymptomatic transmission 0.75 ρ , reduced healthcare worker interactions 0.8 ρ v , reduced visitor-communityinteraction 0.5 γ , quarantine 0.2 γ v , quarantine for visitor 0.3 κ , hospital precautions 0.5 η , healthcare worker precautions . Population fractions p i , i = i q s,i , i = i C: 0.1, 0.4, 0.8, 0.9, 0.99;H: 0.2, 0.5, 0.9, 0.98, 0.99r, transition to next symptomaticday/stage 0.2 ν , symptomatic hospitalization 0.075 ι , icu admission rate of hospitalizedpatients 0.2 Table 5.
Geographically dependent factors modifying transmission rateParameter, meaning HI Counties Japan Puerto Rico IcelandFactors modifying transmission rate p mp , maskcompliance 0.2 beforeAug 27, 0.7thereafter 0.2 beforeMay 04, 0.8thereafter 0.2 beforeAug 21, 0.7thereafter 0.2 beforeOct 20, 0.5thereafter p me , mask efficiency 0.25 0.25 0.25 0.25Population fractions q a,i , i = i q = q = q = q = q = q = q = q = q = q = q = q = Results
In this section we provide the results of simulations of our model for the four counties of the State ofHawai ‘ i under analysis. In our plots we use the raw daily cases and not the 7 day average because ourmodel fit plots the sum over all groups of the newly isolated and quarantined daily exposed and infectedindividuals, see S1 Appendix, Model Dynamics. Initial Conditions.
The initial values of most variables are zero. The only non-zero values are the numberof susceptible individuals in the general community and the healthcare worker community, the values of6hich are listed in Table 6, as well as a single not quarantined symptomatic individual, I c, (0) = 1 .Region S c (0) S h (0) Date for I c, (0) = 1 Honolulu 937711 15000 Mar 06Maui 167417 1500 Mar 15Hawai ‘ i 201513 1500 Mar 16 Table 6.
Susceptible population for each region and first detected symptomatic individual. All othervariables have an initial value of 0.
Honolulu County
Figure 5 displays the model fit for the Honolulu county. The dots represents the daily cases and the curve isthe model fit. The vertical lines corresponds to mitigation measures that had an impact on the curve and forwhich we optimized the β . Table 7 explicit the different β ’s. The maximal daily case for Honolulu countywas 342 and happened on August 12, 2020. We see two major exponential growths, one early in March thatwas 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 thelocal economy. It can be seen on Table 7 that the first lockdown was more efficient. The largest peak isattributed 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 significantlyhigher counts. On October 15, 2020 the state of Hawai ‘ i introduced the safe travel program which promptedan influx of tourists and traveling residents, this influx varies with time which explains the waving shapeof the fit. For more details on incorporation of travelers in our model see S1 Appendix. Since the Safe travelprogram the daily cases have been fluctuating quite a lot which makes a fit difficult (some high daily casescame from a correctional facility cluster for instance). The overall trend as of January 15, 2021 is shown tobe slightly increasing (the 7-day average can be found in Fig.6).7 ig 5. City and county of Honolulu: COVID-19 daily count and key events reflecting a change in behavior.The star shows the beginning of safe travel program.Transmission ratesMarch 6 - April 1 April 2 - May 19 May 20 - May 29 May 30 - Jul 3 β = 0 . β = 0 . β = 0 . β = 0 . Jul 4 - Aug 10 Aug 11 - Sep 23 Sep 24 - Oct 14 Oct 15 - Oct 21 β = 0 . β = 0 . β = 0 . β = 0 . Oct 22 - Nov 23 Nov 24 - Dec 9 Dec 10 - Jan 15 β = 0 . β = 0 . β = 0 . Table 7.
Optimized transmission rates to fit Honolulu county data. They reflect the State and Honolulunon-pharmaceutical mitigation measures.The top of Fig.6 shows the total number of tests, the test positivity rate (i.e. the percent of tests forCOVID-19 that came back positive) as well as the daily cases for the Honolulu County. To create thisoverlayed plot, the shown metrics have been normalized by calculating each data point as a percent ofthe maximum of the corresponding metric over the whole observation period and using the 7-day rollingaverage. It can be seen that, as anticipated, test positivity correlates strongly with daily cases. The noticeablylarge initial values of the test positivity rate (also present for other counties) are likely caused by the asmall number of test that have been administered to a very narrow slice of the population with muchhigher chances of having the virus. When interpreting these plots, it should also be noted that even later inthe pandemic the sample of people receiving tests was not unbiased, since the State of Hawai ‘ i has beenadministering tests to people who satisfy criteria which make them more likely to have the virus. Thebottom plot of Fig.6 displays the mobility for Honolulu County, it shows the major dip in mobility triggeredby the first stay-at-home order back in March 2020, coming back up in May to peak again in August beforethe second stay-at-home order. The mobility data clearly suggests why the second lockdown was not asefficient as the first one. 8 ig 6. Top: A sharp increase in the test positivity rate (along with the daily cases) in July indicates anoutbreak of the disease. The later decrease in the positivity rate with the increased number of testsindicates a substantial slowdown of the spread of the disease. Bottom: Overall mobility for HonoluluCounty from March 2020 to January 2021 suggest a modest correlation with the number of daily cases.In addition to the daily cases, we represents in Fig.7 the cumulative daily counts for Honolulu countydistributed per zip code from the onset of daily cases to January 18, 2021. It can be observed that Honoluludowntown as well as the West Coast (Waianae) have been the most affected in terms of daily cases. Forthe West Coast it is mostly due to its high pacific islanders population and the fact that they have beendisproportionately impacted. While they form about 4% of the total Hawai ‘ i population they account formore than 27% of total cases [15]. 9 ig 7. Honolulu county cumulative daily counts distributed per zip code from March 2020 to January 18,2021.Table 8 highlights the numbers for the seven highest zip codes. Zip code 96819 dominates the countper 100 inhabitants, containing Moanalua, Kalihi, Kapalama, and Daniel K. Inouye International Airporton the south side of Oahu. The second one is 96792 of the Waianae area on the west side of Oahu. FromFig.8, we see that zip code 96701 displays a cluster behavior and that almost all its cases happened betweenDecember 16, 2020 to January 6, 2021. This was due to a cluster at Halawa Correctional Facility. There is noreal immediate visible pattern from the other zip codes.Honolulu CountyZip code PopulationEstimate Cumulative Dailycases Cum. Dailycases per 100inhabitants96701 40857 1156 2896706 74592 1562 2196707 46928 850 1896792 49971 1534 3196797 73579 2038 2896817 56144 1493 26.596819 52981 2342 44
Table 8.
The seven zip codes with the largest cumulative distribution of daily cases.10 ig 8.
Honolulu county cumulative daily counts distributed per zip code from October 2020 to January 18,2021.
Hawai ‘ i County Daily cases for Hawai ‘ i county were very small until the aftermath of the July 4 celebrations which generateda large spike. The second stay-at-home order on Maui was extremely efficient but immediately followed byan exponential increase in the form of a few clusters. The maximum value is 51 and happened on October25, 2020 during the third peak with a very close value during the second peak of 39 on August 29, 2020. Onecan observe a somewhat puzzling decrease in the number of daily cases after the start of the safe travelprogram. A potential explanation is that the spike in the number of cases that happened at that time wasan isolated event unrelated to other activities on the island. Fig 9.
Hawai ‘ i county: COVID-19 daily count and key events reflecting a change in behavior. The starshows the beginning of the safe travel program.On Fig.10 top we represent for the Hawai ‘ i county the normalized total number of tests, the normalizedtests positivity rate and normalized daily cases. Again test positivity correlates strongly with daily cases.11ransmission ratesMar 16 - Mar 24 Mar 25 - Apr 29 Apr 30 - Jul 3 β = 0 . β = 0 . β = 0 . Jul 4 - Aug 10 Aug 11 - Aug 26 Aug 27 - Sep 23 β = 0 . β = 0 . β = 0 . Sep 24 - Oct 14 Oct 15 - Dec 09 Dec 10 - Jan 15 β = 0 . β = 0 . β = 0 . Table 9.
Optimized transmission rates to fit Hawai ‘ i county data. They reflect the State and Hawai ‘ inon-pharmaceutical mitigation measures.The mobility for Hawai ‘ i county did not show a decline as steep as for Honolulu county, and it shows goodcorrelation with the daily cases and testing data. Fig 10.
Top: A sharp increase in the test positivity rate around August indicates an outbreak the disease.The later decrease in the positivity rate with the number of tests hovering around the same value indicatesa welcome slowdown of the spread of the disease. Bottom: Overall mobility for Hawai ‘ i county fromMarch 2020 to January 2021 indicates a mild correlation with the number of daily cases.Figure 11 shows the cumulative daily counts for Hawai ‘ i county distributed per zip code from the onsetof daily cases to January 18, 2021. Clearly the vast majority of cases are located in one of the two maintown: Kona (West) and Hilo (East). 12 ig 11. Hawai ‘ i county cumulative daily counts distributed per zip code.Table 10 summarizes the numbers for the four highest zip codes. Zip codes 96720 and 9674, respectivelyHilo and Kona, clearly dominate the counts. We can see on Fig.12 that Kona had consistently larger numberthan Hilo for the exception of the few days before Christmas. This can be explained that overall theperiod October 15 to January 18, air traffic was quite more significant in Kona than in Hilo. Total (Tourist,Returning resident): Kona (76189,23824), Hilo (15808, 8800).Hawai ‘ i CountyZip code PopulationEstimate Cumulative Dailycases Cum. Dailycases per 100inhabitants96720 48339 594 1296740 42069 615 1596749 17308 122 796778 14885 100 7 Table 10.
The four zip codes with the largest cumulative distribution of daily cases.13 ig 12.
Hawai ‘ i county cumulative daily counts distributed per zip code from October 2020 to January 18,2021. Maui County
Maui county started the pandemic with a relatively low number of daily cases, but then entered an alarmingstate of a high number of cases per hundred thousand of population even reaching a a maximum of 56cases on January 6, 2021. It can be seen clearly the trigger with the introduction of the safe travel programon October 15, 2020. The influx of travelers is not constant through time and because the ratio touristsversus residents is high on Maui we see as a result the wavy increasing curve. In addition to the effect ofadditional tourists there was a large outbreak in relatively high population density condominium complex.The initial increase after October 15 was solely due to travelers which is why we see a rise in daily caseseven though the basal transmission rate β stays small.14 ig 13. Maui county: COVID-19 daily count and key events reflecting a change in behavior.Transmission ratesMar 15 - Mar 24 Mar 25 - Apr 29 Apr 30 - Jun 7 β = 0 . β = 0 . β = 0 . Jun 8 - Aug 26 Aug 27 - Sep 23 Sep 24 - Oct 14 β = 0 . β = 0 . β = 0 . Oct 15 - Nov 23 Nov 24 - Dec 19 Dec 20 - Jan 15 β = 0 . β = 0 . β = 0 . Table 11.
Optimized transmission rates to fit Maui county data. They reflect the State and Mauinon-pharmaceutical mitigation measures.Tests, positivity and daily cases are represented on Fig.14 and show a strong correlation between thethree. The mobility for Maui County seems correlating well until the introduction of the safe travel program.15 ig 14.
Top: A series of ups and downs in the test positivity rate and the number of daily cases indicate theoccurrences of outbreaks of the disease. The significant increase in these numbers at the beginning of thisyear suggests a serious spread of the virus. A noticeable jump in the daily case number that does notcorrelate with the positivity rate can be explained by a jump in the number of tests, since the latter areperformed for people with higher chances of having the virus. Bottom: Overall mobility for Maui Countyfrom March 2020 to January 2021 does not correlate well with the number of daily cases.Figure 15 shows the cumulative daily counts for Maui county distributed per zip code from the onsetof daily cases to January 18, 2021. The low counts on the eastern half of Maui are associated with lowpopulation density of local residents and relatively few tourists.16 ig 15.
Maui county cumulative daily counts distributed per zip code.The four zip codes with the largest counts can be found in 12 and their daily behavior is displayed inFig.16. There was a large outbreak in a multistory in early 2021 located in zip code 96732. The residentsin this complex used elevators more than residents in other complexes in other areas with fewer stories.There are relatively larger number of tourists compared to local residents in zip codes 96761 and 96753 ascompared to most other zip code areas. This is possible reason these two zip code area had larger increasesin December than other areas.Maui County Zipcode PopulationEstimate Cumulative Dailycases Cum. Dailycases per 100inhabitants96732 29075 278 9.596753 28737 259 996761 22301 240 1196768 18529 90 596793 34036 211 6
Table 12.
The four zip codes with the largest cumulative distribution of daily cases.17 ig 16.
Maui county cumulative daily counts distributed per zip code from October 2020 to January 18,2021. There were a few clusters on Maui which is the explanation for some of the higher spikes, inparticular in early January in Kahului which is zip code 96732.
Kaua ‘ i County Due to the low numbers on Kaua ‘ i a model fit using our compartmental model could not be achieved. Itcan be observed on Fig.17 that the daily cases started following an exponential growth, it was attributedto travelers which prompted the mayor of Kaua ‘ i to request authorization to opt-out from the safe travelprogram. It was followed by a decrease in numbers and stabilization. A new peak can be observed rightafter the safe travel program was authorized reinstated by Kaua ‘ i for intercounty travelers. The numbersare so small that is it extremely difficult to draw any additional conclusion. Fig 17.
Kaua ‘ i county: COVID-19 daily count (orange) and 7-day average (red). The Opt-in Safe Travel onJan 5 is only for intercounty travelers.We still represent tests, positivity and daily cases on Fig.18 and see as for Maui a strong correlation18etween the three. The mobility for Kaua ‘ i County is very flat after the initial decrease in March and evenwent a bit down after the safe travel program started. Fig 18.
Top: The number of daily cases and test positivity rate are still well correlated, even though the rawnumbers are small. Similar to Hawai ‘ i county, we can see a jump in the daily case numbers that correlateswith the increased number of tests rather than the test positivity rate, which is likely due to the biasednature of the population sample on which the tests are performed. Bottom: Overall mobility for Kaua ‘ iCounty from March 2020 to January 2021 does not correlate well with the daily cases. Discussion
There is clearly major differences among the four counties. Fig.19 shows on the same plot normalizedmodel fits for Honolulu, Hawai ‘ i and Maui counties as well as the daily raw numbers for Kaua ‘ i . It canobserved that beside Kaua ‘ i for which numbers have been very low to draw comparison, the other threecounties correlates well until when the Safe Travel program began on October 15, 2020. Hawai ‘ i countydisplays an increase in daily numbers right before which were attributed to a couple of clusters (one inHilo and one in Ocean View). Maui also had a few clusters, including a major one around October 20 onLanai and another major one in early January in Kahului. After October 15, 2020 both Honolulu countyand 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 Mauicounties require typically larger value for the basal transmission rate than for Honolulu county. The reason19s that changes occurred more rapidly in the outer-islands, for instance the peak for Honolulu county isbased on a build-up starting in June while for Hawai ‘ i county the peaks are much more narrower. For Mauicounty the decay due to the second stay-at-home order was extremely efficient at the beginning and thenslowed 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 safetravel program opened.We analyze similarity by using the L -norm for the difference between two normalized given modelfits. One comparison was done over the entire length from March 6, 2020 to January 15, 2021. Results aredisplayed in Table 13. Mar 06 - October 15 Mar 06 - Jan 15Honolulu - Maui 2.05353346 4.49831756Honolulu - Hawai ‘ i 3.30655235 3.81229319Hawai ‘ i - Maui 3.53488371 4.23234035 Table 13.
Normalized L norm between hawaiian counties measuring similarity. Show the impact of thedifferent county’s regulations for travel since the dissimilarity between the counties grows when we addthe period October 15, 2020 to January 15, 2021. In particular, before travel was instated Honolulu andMaui counties were the most similar, situation that reversed afterwards.In regards to mobility and movement of the counties from the bottom halves of Fig. 6, 10, 14, and 18,we acknowledge that the counties behavior follow a pattern that following the onset of the pandemic,movement dramatically slowed down. Afterwards, it began to plateau towards a movement index betweenthe shutdown and normal. Curiously, the correlation between the mobility index and the daily case is farfrom 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, couldsignificantly contribute to the overall daily cases. As we can observe from the 3D zip code maps, the casesare very localized. Not surprisingly, they are higher in urban locations and towns where the populationdensity, as well as the probability of indoor gatherings, is higher.20e use three other Islands: Japan, Iceland, Puerto-Rico for comparison with our counties. We ran a fitwith our compartmental model for the three countries and analyze similarity by looking at the qualitativestructure of the results as captured by merge trees (see e.g. [30]). The latter construct is a topologicaldescriptor of functions, and is constructed by tracking how connected components of the sublevel setsappear and merge as the threshold for the sublevel sets increases. This comparison is favored to a standard L metric due to time shifts in the course of the pandemic for the various countries. An easy way tovisualize this process is to move a horizontal line from the bottom to the top of the graph of a function andkeep track of the function values at which a new connected component of the graph appears under the lineor two existing components get merged. The actual horizontal locations of the branches, which representthe connected components, is not important, just their relative (left-right) positions. The merge trees forour three counties and the aforementioned countries are shown in Fig.20. They were computed using thenormalized time series for the daily cases numbers starting from June 15. We also slightly simplified thestructure (for illustration purposes) by removing very small branches. We can see that the Honolulu countymerge tree is most similar to the Iceland merge tree and the Maui county merge tress is most similar to theJapan merge tree. The complexity of the Hawai ‘ i county merge tree makes it more similar to the PuertoRico merge tree, although these two are not as good of a match as the other pairs. H o n o l u l u I ce l a nd M a u i J a p a n H a w a i‘i P u e rt o R i c o Fig 20.
Merge trees elucidate the qualitative structure of the daily case numbers over time.Figures 21, 22 and 23 display the model fit as well as the β values for Honolulu, Hawai ‘ i and Mauicounties with their most similar Islands using the merge trees similarity of Fig.20. Table 14 provides theinitial values for Iceland, Japan and Puerto-Rico used by our model. travel restrictions vary widely betweencountries, 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 significant21irst wave, but then controlled the spread beside a super spreader event trigger by two travelers. Travelinghas then be very restricted which is why the daily cases are mostly in the single digits at the end of the fit. Fig 21.
Top: Comparison between the daily cases between Honolulu County and Iceland. The blue fit forHonolulu correspond to not taking into account the travelers. Bottom: Superposition of the transmissionrate values optimized for the fits above.Hawai ‘ i county is most similar to Puerto-Rico. The accuracy of the data for Puerto-Rico is unclear andit was very difficult to find the travel restrictions. The primary difference is the peak in December thatPuerto-Rico suffered. 22 ig 22. Top: Comparison between the daily cases between Hawai ‘ i County and Puerto Rico. The blue fitfor Hawai ‘ i county is a smoothing occurring by neglecting the travelers. Bottom: Superposition of thetransmission rate values optimized for the fits above.Maui and Japan display a very similar qualitative curve, especially when travelers are ignored forMaui. The reason for Japan explosive growth at the end of the year is attributed to a few factors, includinga controversial encouraging domestic travel policy that is as of January more restrictive and a possibleCOVID-19 fatigue by the population. 23 ig 23. Top: Comparison between the daily cases between Maui County and Japan. Blue fit for Maui iswithout travelers. Bottom: Superposition of the transmission rate values optimized for the fits above.Region S c (0) S h (0) Date for I c, (0) = 1 Japan 126500000 1673518 Feb 01Iceland 356991 1404 Feb 21Puerto Rico 3194000 89000 Mar 04
Table 14.
Susceptible population for the three countries.
Conclusion
In this paper, using the Hawaiian archipelago, we explore the importance of taking into account localvariations in island chains. Ratios between residents and tourists as well as age demographic and otherspecificity call for targeted mitigation measures and Safe Travel program when in a pandemic. (Implemen-tation of the Safe Travel program varies between the different Hawaiian counties.) The State of Hawai ‘ ihas launched an aggressive mass vaccination campaign starting in December but the effects of which areonly now starting to impact the daily case rate. During the period of our study the very small impact ofvaccination was neglected. As of February 2, 2021 we have 202,200 doses administered. The State policy isto keep the vaccination plan as originally planned to 2 doses per individuals even though two cases of themore transmissible B1.1.7 have been detected in Hawai ‘ i . As of February 8, 2021 cases have been decreasingin all four counties.Not studied in this paper is hospital beds capacity, for the State of Hawai ‘ i . The county of Honoluluis home to most of the hospital facilities and healthcare workers. The primary reason we did not discussthis here is the lack of consistent and clear data regarding hospitalisations. Similarly, quantification of24OVID-19 related fatalities in the State of Hawai ‘ i is delicate, indeed for instance in January about 60 deathshave 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 futurepandemics. We are now working with the Hawai ‘ i government on scenarios to understand impact of liftingsome of the mitigation measures. Acknowledgments
This material is based upon work supported by the National Science Foundation under Grant No. 2030789.
References
1. Bertozzim A.L., Franco E., Mohler G., Short M.B., Sledge D. The challenges of modeling and forecastingthe spread of COVID-19 Proceedings of the National Academy of Sciences Jul 2020, 117 (29) 16732-16738; DOI: 10.1073/pnas.20065201172. Brauer F. Compartmental Models in Epidemiology. Mathematical Epidemiology. 2008;1945:19-79.doi:10.1007/978-3-540-78911- ‘ i COVID-19 Data Resources - Hawai ‘ i Data Collaborative. Hawai ‘ ‘ i (2020).https://hiema-hub.hawaii.gov/10. Data Creates Knowledge. Our Data - COVID Pau: Turning Data into Knowledge. Hawai ‘ i DataCollaborative (2021). https://covidpau.org/our-data/11. Economic Data Warehouse. Research & Economic Analysis | Economic Data Warehouse. State ofHawai ‘ i (2021). https://dbedt.hawaii.gov/economic/datawarehouse/12. Hawai ‘ i COVID-19 Data. Disease Outbreak Control Division | COVID-19 | Hawai ‘ i COVID-19Data. State of Hawai ‘ i (2021). https://health.hawaii.gov/coronavirusdisease2019/what-you-should-know/current-situation-in-hawaii/ Supporting information
S1 Fig. Counties Zip Codes.
Zip Code Tabulation areas for the four counties. From the State of Hawai ‘ iOffice of Planning 2010 Census Reference Maps. Fig 24. ZipCodes per County.
Zip Code Tabulation areas for the four counties. From the State ofHawai ‘ i Office of Planning 2010 Census Reference Maps. S1 Appendix. Model Dynamics.
The equations for the dynamics of the three population groups areessentially the same and are given below. Only the hazard rate and the parameters determining transition27ates into quarantine may be different between the three groups. S ( t + 1) = e − λ ( t ) S ( t ) (1) E ( t + 1) = (1 − e − λ ( t ) ) S ( t ) (2) E i ( t + 1) = (1 − p i − )(1 − q a,i − ) E i − ( t ) ,i = 1 , . . . , (3) E q,i ( t + 1) = (1 − p i − )( q a,i − E i − ( t )++ E q,i − ( t )) , i = 1 , . . . , (4) I ( t + 1) = (cid:88) i =0 p i (1 − q a,i ) E i ( t ) (5) I ( t + 1) = (1 − q s, ) I ( t ) (6) I ( t + 1) = (1 − q s, ) I ( t ) + (1 − r )(1 − q s, ) I ( t ) (7) I j ( t + 1) = r (1 − q s,j − ) I j − ( t )++ (1 − r )(1 − q s,j ) I j ( t ) , j = 3 , (8) I q, ( t + 1) = (cid:88) i =0 p i ( q a,i E i ( t ) + E q,i ( t )) (9) I q, ( t + 1) = I q, ( t ) + q s, I ( t ) (10) I q, ( t + 1) = I q, ( t ) + q s, I ( t )++ (1 − r )( q s, I ( t ) + I q, ( t )) (11) I q,j ( t + 1) = r ( q s,j − I j − ( t ) + I q,j − ( t ))++ (1 − r )( q s,j I j ( t ) + I q,j ( t )) , j = 3 , (12) R ( t + 1) = R ( t ) + rI ( t ) + rI q, ( t )++ (1 − p ) E ( t ) + (1 − p ) E q, ( t ) (13)Below is a detailed description of the variables, all of which depend on time, t , measured in days.• Variable S ( t ) . The number of susceptible individuals.•