medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . COVID-19 Healthcare Demand Projections: Arizona Esma S. Gel, Megan Jehn, Timothy Lant, Anna R. Muldoon, Trisalyn Nelson, Heather M. Ross Modeling Emerging Threats for Arizona (METAz) Workgroup Arizona State University, Tempe, AZ 85281 Last Update: May 7, 2020 Abstract DR AF T Beginning in March 2020, the United States emerged as the global epicenter for COVID-19 cases. In the ensuing weeks, American jurisdictions attempted to manage disease spread on a regional basis using non-pharmaceutical interventions (i.e. social distancing), as uneven disease burden across the expansive geography of the United States exerted different implications for policy management in different regions. While Arizona policymakers relied initially on stateby-state national modeling projections from different groups outside of the state, we sought to create a state-specific model using a mathematical framework that ties disease surveillance with the future burden on Arizona’s healthcare system. Our framework uses a compartmental system dynamics model using an SEIRD framework that accounts for multiple types of disease manifestations for the COVID-19 infection, as well as the observed time delay in epidemiological findings following public policy enactments. We use a bin initialization logic coupled with a fitting technique to construct projections for key metrics to guide public health policy. 1 Introduction Since its documented onset in December 2019 and formal identification in January 2020 in Wuhan, China, COVID-19 (SARS-CoV-2) has spread around the globe, infecting more than 3.5 million people globally by early May 2020 [4]. In an atmosphere of intense uncertainty around many of the epidemiological parameters for modeling including true case counts as a result of low testing availability, the Modeling Emerging Threats for Arizona (METAz) Workgroup of Arizona State University has developed and refined models for predicting the burden of disease in order to inform policy related to nonpharmaceutical interventions (i.e., social distancing). Because the burden of disease and transmission dynamics differ by location due to a variety of factors including geography, population, and environmental conditions, METAz chose to focus on state-level modeling to inform public health response efforts with greater precision. The modeling approaches we describe can be applied to any region or state where region-specific data are available. Here, we focus on the state of Arizona in the American Southwest (population of around 7.3 million, 113,990 sq. miles, majority population concentrated in centrally-located Maricopa County) as a proof of concept. At the time of the last update to the report, the following case counts have been reported in Arizona since March 4, 2020. As of May 5, Arizona’s healthcare system has not experienced an overwhelming surge of COVID-19 cases exceeding systemwide capacity to care for critically ill patients. Since Arizona has not yet exceeded existing hospital capacity for COVID-19 cases, a plateau in daily hospital admissions is a hopeful sign that social distancing measures may have 1 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . DR AF T helped Arizona to avoid overwhelming hospital systems as other states have experienced and allow time to prepare options for future management of the disease in Arizona. However, Arizona is still experiencing wide community spread of SARS-CoV-2. Due to a Cumulative COVID-19 Cases in Arizona relatively low rate of testing statewide, there is ongoing debate and uncertainty about whether © METAz, 2020; Not for release 8000 Arizona’s case prevalence data provides an accurate portrait of the true public health risk 6000 burden and whether we have passed an (initial) peak of infections and hospitalizations 4000 statewide and in individual counties. Current projections from a variety of modeling groups 2000 (i.e., IHME, UA, ASU) indicate that the peak number of cases will be reached in Arizona in mid-April - mid-May. However, it is important 3/9 3/16 3/23 3/30 4/6 4/13 4/20 4/27 5/4 to note that modeling projections are inherently uncertain, and accurate assessment of case Figure 1: Cumulative confirmed COVID-19 cases peaks will be possible only once the peak has in Arizona, between March 4 to May 5, 2020 passed. In light of the transmission dynamics and laboratory reporting delays for the SARSCoV-2 outbreak, peak determination will be possible approximately two to four weeks following peak occurrence. It is also important to note that there is still significant uncertainty about the transmission dynamics of the virus, including the degree of asymptomatic infection and transmission and the results do not capture the full range of uncertaintly. We demonstrate this observation through our modeling below. On April 16, the United States Government released Guidelines for Opening Up America Again, proposing a phased approach to re-opening the country. In order to progress into and through three sequential phases of opening businesses and other public and private services, states are expected to meet a set of gating criteria outcome metrics along with a set of capacity responsibilities for carrying out core public health and management functions. In order to move into Phase 1 with limited reopening of businesses and other services, states must demonstrate flattening the case rates, and in order to move into Phase 2 with expanded reopening of businesses and services states must demonstrate no rebound in case counts from the limited reopening in Phase 1. As a comparison, California has identified six controls required for “safe” re-opening: (i) expand testing to trace and track individual outbreaks and ensure the isolation and quarantine of those affected, (ii) protect vulnerable populations from infection and spread, most notably, seniors, people who are immunocompromised, and unhoused individuals, (iii) the ability of hospital and healthcare systems to meet the need of anticipated surges as stay at home orders are loosened, (iv) Work with academia and the pharmaceutical industry as they develop treatments and a vaccine for the virus, as well as protocols to distribute them, (v) develop strategies for schools and businesses to adhere to safe physical distancing guidelines, (vi) a plan to toggle back and forth between stricter and looser social distancing requirements depending on how the situation changes. Arizona has not yet developed a comprehensive plan that incorporates the full testing capabilities within the state (both molecular and serological) with a program linked to non-pharmaceutical interventions (NPI) including stay-at-home and other social distancing and infection mitigation policies and procedures. In order to re-open Arizona safely, a phased approach needs to be data-driven and focused on avoiding a rapid surge in cases through appropriate and effective policy for non-pharmaceutical interventions. 2 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . This paper proposes a mathematical framework that ties disease surveillance with future burden on Arizona’s hospital system and hospital resources. The mathematical model links together policy interventions with estimated outcomes for infections, hospitalizations, and deaths in an epidemiological analysis. One of the key features of such a model is the time-delay of new infections on confirmed case counts and the impact on the healthcare system. We propose methods to evaluate the likely outcomes for a range of policy decisions intended to keep Arizona safe while re-opening in a responsible and defensible sequence. 2 2.1 Methodology Structure of the Model 3 days DR 6 days 40% AF T We make use of a compartmental system dynamics model using an SEIRD framework that includes multiple compartments for infected individuals. This model structure allows us to estimate the number of patients in the hospital and assess model fit with respect to two sources of data: daily new cases and cumulative reported deaths over time. In essence, the population of interest, in this case, the population of the State of Arizona (assumed to be 7,278,717 in this study) is divided into states of Susceptible (S), Exposed but not yet infectious (E), Asymptomatic infected (Ia ), infectious and presymptomatic (Ip ), Symptomatic with a mild infection (Is ), symptomatic with a severe infection and hospitalized (H), symptomatic with a critical infection and in the ICU (C), undergoing additional recovery in ICU (B), Recovered and immune (R) and Dead (D), as shown in Figure 2. 81% 80% 60% 17.5% 2 days 6 days 4 days 7 days 1.5% 20% 50% 8 days Figure 2: Depiction of the compartmentalized system dynamics model used to represent transmission and disease progression for State of Arizona projections Our model defines separate bins for asymptomatic and presymptomatic individuals to explicitly account for transmissions by infected individuals who do not exhibit symptoms. Several results in the literature point to the fact that the viral shedding by these individuals are also different. In comparison, individuals who are exposed to the virus generally go through an incubation period (modeled by a rate of ζ) during which they are exposed but not yet infectious. This duration is modeled as 3 days in our study, to support an ensemble estimate of 5 days for time from exposure to symptoms and an estimate of 6 days serial time obtained from the literature [22, 9, 12, 1, 13, 5]. After the preinfectious period, individuals become infectious, either as an asymptomatic or a presymptomatic patient. The presymptomatic duration (modeled with rate δ) is assumed to be 2 days [19, 23]. Asymptomatic patients recover at a rate of γ = 1/6, corresponding to an average 3 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . DR AF T recovery duration of 6 days after the preinfectious period. We modeled a number of variations on how symptomatic individuals experience COVID-19. After the presymptomatic period of 2 days, a large fraction, 81% (denoted by ρ in the model) estimated by [21, 24], of individuals go through a 6-day period of relatively mild symptoms and recover similar to the asymptomatic patients [20]. The remaining 19% of symptomatic patients develop a severe or critical infection and seek care at a hospital. A large portion of the patients admitted to the hospital only have a severe infection and recover after an average duration of 7 days on a regular hospital bed. The clinicians we have been partnering with in Phoenix metropolitan area and Tucson hospitals have indicated that an average of 20% of these patients, however, progress to a critical infection, requiring ICU care and possibly intubation. In addition to patients that progress to the ICU from a regular hospital bed, our partnering clinicians informed us of a small fraction of patients that report to the hospital with a critical infection with breathing problems and are directly admitted to the ICU. Hence, in our model, there are two modes of admission to the ICU; one directly from the emergency room and the other one from a regular ward, after the patient’s infection progresses to a critical condition. The parameters for these splits are set to ensure that (i) fraction of symptomatic patients with mild infection is 81% [21, 24], (ii) the total fraction of symptomatic patients that develop a critical infection that requires ICU care is 5% [21] and (ii) 20% of patients in a regular bed progress to a critical infection [15]. Studies in the literature cite a diverse range of outcomes for patients in the ICU, but most agree that the ICU duration for patients that eventually recover is generally longer. For example, [18] cites point estimates for the duration of onset-of-symptoms to death to be 17.8 days and from onset-of-symptoms to hospital discharge to be 22.6 days. This additional time is also due to various steps that caregivers have to take to arrange for care after the ICU period since generally patients that underwent intubation and other invasive procedures require subsequent care in other postacute facilities. This additional “recovery” time is represented as another bin, with a duration of 4 days (modeled with rate α). The reported average ICU stays in the literature are generally very diverse; we adopted a conservative point estimate of 8 days to align with the symptom onset to recovery/death estimates [18] as well as other more detailed studies that tracked patients’ progress through the hospital [24]. One of the important parameters in the model is ω, which represents the fraction of asymptomatic patients. Several studies point to the importance of modeling transmissions by asymptomatic individuals, who may never be aware that they were transmitting the virus during a period of infectiousness. However, point estimates on the fraction of individuals that experience asymptomatic infection vary greatly from context to context. In our models we adopted a relatively high asymptomatic rate of 40% based on point estimates observed by (author?) [16] because this assumption allows us to obtain worst-case estimates on the prevalence of infections in the general population given that in the absence of widespread testing of asymptomatic individuals, the asymptomatic patients are generally undetected. In our modeling and analysis, we explicitly consider the possibility that only a small fraction of the true incidence of infections are detected as COVID-19 cases and reflected in the reported case counts and deaths. One such example that points to a large undetected fraction of cases is [10], indicating that 86% of the early infections in China were undocumented, implying that the “actual” cases in a population may be more than 7 times the detected cases. The same study also offers a rate of transmissions by asymptomatic individuals at 55% of the transmission rate by symptomatic individuals, which we reflect in the force of infection, λ(t) shown in Figure 2. Subsequently several other papers have offered additional understanding on the role of asymptomatic infections in transmission and its prevalence in different contexts [14, 8, 16, 7, 2]. We use these papers along with the actual data on new cases and deaths in Arizona to obtain point 4 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . estimates for model parameters. We also devise an initialization algorithm to identify initial values of the compartments in the model. The ordinary differential equations (ODE) that define the system dynamics are given by Equations (1) thru (10). S 0 (t) = −βt λ(t) S(t) (1) 0 E (t) = βt λ(t) S(t) − ζ E(t) (2) Ia0 (t) Ip0 (t) Is0 (t) 0 = ζ ω E(t) − γ Ia (t) (3) = ζ (1 − ω) E(t) − δ Ip (t) (4) = δ Ip (t) − γ Is (t) (5) H (t) = γ ψ Is (t) − µ H(t) (6) 0 (7) 0 (8) 0 (9) 0 (10) C (t) = γ (1 − ρ − ψ) Is (t) − ν C(t) + µ φ H(t) B (t) = ν (1 − υ) C(t) − α B(t) R (t) = γ Ia (t) + γ ρ Is (t) + µ (1 − φ) H(t) + α B(t) D (t) = ν υ C(t) The time dependent force of infection, λ(t) is modeled as 0.55Ia (t) + Ip (t) + Is (t) + 0.05[H(t) + C(t) + B(t)] . N − D(t) T λ(t) = (11) DR AF This expression is motivated by the fact that asymptomatic individuals transmit the disease at a reduced rate as discussed above, and patients under care in the hospital are relatively well isolated via institutional infection control measures so they only transmit at a rate that is equal to 5% of the presymptomatic or symptomatic patients. Studies that point to the high-infectiousness of presymptomatic patients [3] implies that infections are mostly driven by patients in these compartments. We model a time dependent transmission rate, βt , denoted by the subscript t to represent the time dependency. Together with the force of infection and the current pool of susceptible individuals, the transmission rate βt yields the rate at which susceptible individuals get exposed to the infection. The force of infection term can be thought of as the probability that an arbitrary individual is infectious at a rate equivalent to that of a symptomatic patient. The transmission rate, βt represents the average rate of contact between susceptible and (symptomaticequivalent) infectious people multiplied by the probability of transmission given contact. Hence, given the above force of infection and the number of individuals in the susceptible compartment, the rate at which individuals become exposed to the virus at time t is strongly driven by the term, βt . A good way of thinking about the impact of non-pharmaceutical interventions such as social distancing, stay-at-home orders, school closures, wearing masks, etc. is through the term βt , and how the different interventions impact either (i) the average number of infectious individuals that susceptible individuals contact, or (ii) the probability of transmission given contact. Note that an increase in either of these two values would lead to an increase in the effective transmission rate at a given time, which will then increase the rate at which susceptible individuals get exposed to the virus. We find Figure 3 to be informative to understand the effect of these two variables to understand the impact of social distancing and other NPI interventions. Staying on the same β curve of 0.20 while increasing the average number of contacts for a susceptible individual from 10 to, say, 20 requires that the probability of transmission given contact be reduced from 0.02 to 0.013 through measures that reduce the probability of transmission given contact with an infectious individual. Such measures may involve hand washing practices, wearing masks, keeping 5 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Description Time to infectiousness Presymptomatic duration Asymptomatic infectious period Mild infection recovery time Severe infection recovery time Critical infection to death Additional days to recover after ICU Fraction of asymptomatic infections Fraction of mild symptomatic infections Fraction hospitalized on regular bed Fraction of hospitalized progressing to ICU Mortality among ICU patients Parameter ζ −1 δ −1 γ −1 γ −1 µ−1 ν −1 α−1 ω ρ ψ φ υ Value 3 days 2 days 6 days 6 days 7 days 8 days 4 days 40% 81% 17.5% 20% 50-60% Sources [22, 9, 12, 1, 6, 17, 11] [23, 19] [21, 20] [21] [21, 5] [18, 24] [18] [16] [21] [21] [15] data fit Table 1: Point estimates used for model parameters and sources 2.2 probability of transmission given contact DR AF T 6+ ft apart, etc. As the interactions between individuals are expected to increase after the stay-athome orders are lifted, the importance of such measures should be more rigorously emphasized. It is also useful to note that a modest 15% increase in both values would result in a 32.25% increase in β, which would have dire consequences for the transmission dynamics. The model parameters and point estimates for them obtained from the literature are given in Table 1. We next 0.10 explain our approach of initializing the compartments and β=0.15 β=0.20 fitting the transmission rate β for the month of April (durβ=0.25 ing which Arizona has enacted a stay-at-home order) and 0.08 mortality rate at the ICU, υ, using publicly available data on case counts and COVID-19 related deaths in Arizona. Initialization of Compartments 0.06 0.04 We first present a methodology to initialize the model in a manner that is independent of the transmission rate, β. 0.02 In particular, we consider the data on cumulative number of confirmed cases in Arizona, where the first reported 0.00 cases were on March 4, 2020, as shown in Figure 1. We 0 5 10 15 20 25 30 use these data to obtain the number of new cases on each average number of contacts day. The average reporting delay on COVID-19 tests is about 6 days in Arizona. Given that our model indiFigure 3: Transmission rate, β reprecates an incubation period of 5 days and average time sented as a product of the average numto seek testing (when it is available) is about 3 days after ber of contacts and the probability of symptom-onset, we obtain “presumed” exposure dates for transmission given contact with an inthe reported new cases on each day. A visual that shows fectious individual this logic is shown with the blue bars (reported new cases over time) and the orange bars (numbers eventually detected, shown on the presumed exposure dates) in Figure 4. Note that the orange bars show the number of individuals exposed to the virus on the given day, who are then eventually detected by testing. 6 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Initialization Scheme Arizona COVID-19 Confirmed Cases, 3/4/2020 thru 4/28/2020 1400 Detected New Cases 1200 Detected Exposures Total Exposures, 4X 1000 800 600 400 200 4/13 4/9 4/11 4/7 4/5 4/3 4/1 3/30 3/28 3/26 3/24 3/22 3/20 3/18 3/16 3/14 3/12 3/8 3/10 3/6 3/4 3/2 2/29 2/27 2/25 2/23 2/21 2/19 0 2 weeks Figure 4: Reported new cases and presumed exposure dates DR AF T As discussed above, a large portion of the individuals exposed to the virus on a given day are never detected due to the fact that (i) a significant portion of these individuals never develop symptoms; and (ii) some symptomatic individuals are never tested, their infections are attributed to another influenza-like illness, or their case is missed due to false negative results in COVID-19 tests. To account for the large rate of undetected infections, we have devised a novel approach using an “X-factor” initialization scheme where we multiply the number of eventually detected-exposed individuals by the X-factor to obtain the “underlying overall exposures” on a given presumed exposure day. In Figure 4, the grey points depict exposures in an “X-factor of 4 scenario.” The X-factored exposures on presumed exposure days are then fed into our SEIRD model, keeping the transmission rate to zero. We obtain an approximate continuous time function by interpolating over these presumed exposures, called W (s). Figure 5a shows the approximated rate of exposures over time in X-factor of 4 scenario between 3/4 and 3/29 in Arizona; the black dots are the daily presumed exposures also shown in Figure 4. We then numerically evaluate the convolution Z t E[Ni (t) W (s), 0 ≤ s ≤ t] = W (s)fi (t − s)ds (12) 0 to obtain the expected number of individuals in compartment i, i ∈ {Ia , Ip , Is , H, C, B, R, D} at the time t, where fi (τ ) denotes the probability that an individual would be in Bin i τ time units after exposure to the virus. The fi (·) functions for each bin in the model can be obtained by simulating the above stated model with one exposed individual and transmission rate of zero. As an example, Figure 5b shows the fraction at the hospital, fH+C+B (·) versus time. The solution to the ODEs is unique given a set of initial values for the number in each bin at time “zero.” Using the above initialization logic, we calculate the number that we expect to see in each bin on a chosen presumed exposure day, using all of the data on new cases reported on the presumed exposure days prior to this point, and using the number of presumed exposures on that day to initialize the E compartment. We are then -almost- ready to simulate the model starting from that day and observe the number in each compartment to obtain projections. 7 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . 1 Exposed at time 0, Fraction in the hospital t days after W(s) for 4X Scenario 1200 © METAz, 2020; Not for release © METAz, 2020; Not for release 0.04 800 0.03 avg. fraction number exposed on day 1000 600 400 0.02 0.01 200 0.00 0 5 10 15 20 25 30 0 35 10 20 30 40 50 day index day index (a) The W (s) function for the X-factor of 4 scenario, obtained by inflating the daily new cases (b) fH+C+B (t) under assumed parameters Figure 5: Building blocks for backcasting procedure used for initialization 2.3 Fitting Transmission Rate and Mortality DR AF T In our study, we initialize the bins on 3/30 (i.e., this calendar day is our t = 0) and use the actual data on presumed exposures (under any assumed X-factor scenario) starting from 3/31 until 4/15 to fit the transmission rate, βt . We tried a number of different initialization dates, but the results on the β fit were comparable, and furthermore, since the stay-at-home order was issued in Arizona on March 31, we expect that the transmission rate starting from 3/31 to stay relatively consistent during the period 3/31 to 4/15 with respect to the exposures that happened during this time period. This is why we selected to initialize on this date. We use a least-squares method to identify the best value of β to describe the transmission rate under the stay-at-home order in Arizona. As an example, Figure 6a shows the model fit along with the 95% prediction intervals for the number of exposures under a 4X scenario. The grey points in the graph show the raw values (without the 4X correction) of the presumed exposures (or, 1X scenario). In addition to fitting the transmission rate, β, we use the cumulative number of COVID-19 related deaths in Arizona to fit the mortality rate among the ICU patients. Note that in our model, we assume that all patients who die will do so in the ICU, which ignores the deaths that occur outside the hospital. At the time of the writing of this manuscript, Arizona’s healthcare capacity, beds, ICU have been sufficient to care for COVID-19 patients. Therefore, to our knowledge, Arizona has not experienced significant reported deaths outside the hospitals due to an inability for patients to access critical care services. There is, however, ongoing debate about whether COVID-19 related deaths are under-reported in Arizona and nationwide. Given our assumption for this modeling exercise that deaths are primarily occurring in the ICU, for this analysis we assumed that the information on the reported deaths is relatively accurate. Figure 6b shows the cumulative number of deaths that the model predicts under a 4X loading scenario, with death rate υ = 0.5408 and β fixed at the fitted value of 0.2226. We see that the model produces relatively tight prediction intervals and generally does a good job of predicting the deaths between 3/31 and 5/5 when we compare it to actually reported data. Note that under the 1X loading scenario, the ICU death rate produced by the model fit procedure was on the order of 2.5; that is, the assumption of 100% detection rate was not aligned with the point estimates we used in the model to predict the reported death rates. Given that there is widespread belief that COVID-19 deaths are underreported, we understand this finding to be in support of the idea that only a small fraction of the infections are detected that thus reported in the official case counts. In 8 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . the next section, we present projections for 1X (as an overly optimistic case), 4X, and 6X loading scenarios to provide a range of scenarios. Presumed Exposures for 4X Scenario, β=0.2226 Deaths for 4X Scenario, with υ=0.5408 2000 © METAz, 2020; Not for release 400 1500 © METAz, 2020; Not for release 300 1000 200 500 100 3/31 4/7 4/14 4/14 4/21 (a) Model predicted 4X exposures between 3/31 and 5/5 with 95% prediction intervals; best fit for β = 0.2226. Red dots are 4X presumed exposures obtained from real data, gray dots are 1X presumed exposures, obtained through backcasting of daily new cases 4/28 (b) Model predicted cumulative number of deaths between 3/31 and 5/5 with 95% prediction intervals; best fit for υ = 0.5408 under 4X loading scenario. Red dots are the reported COVID-19 deaths for the period in Arizona. Model Projections DR 3 AF T Figure 6: Fitting values for β and υ using case counts and deaths We provide projections on the number of deaths, number hospitalized and total infections for a number of cases that differ in X-factor and the transmission rate over time. We first start with the benchmark cases of 1X, 4X and 6X loading scenarios simulated under the assumption of constant transmission rates obtained by fitting the model to data during the stay-at-home period. While the transmission rate that is indicated by the model fitting exercise outlined above is relatively low, indicating a Reffective value of approximately 1, it is useful to observe the dynamics in a relatively long horizon of 500 days, as given in Figure 7. Day 0 in this simulation is 3/31, where we initialize our model and run it with the beta and υ values that we fitted using the new remaining data on new cases and deaths after this point (i.e., 16 points of backcasted presumed exposures and 30 days of data on deaths). Given the large initial susceptible population that we use for the model (i.e., 7,278,717) it takes around 200 days to reach herd immunity as long as the transmission rate is maintained at this current constant level. The number of hospitalizations reaches 26,650 on day 175, which corresponds to mid-September 2020. This figure demonstrates that policies that were initially put in place to limit contacts have been effective in reducing transmission, but also preserve a high pool of susceptibles that can be returned into mixing with the general public and can ignite future outbreaks. While visualization of the epi curves is useful to gain insights into the long-term behavior and other concerns such as peaks and herd immunity, it is more informative to focus on shorter-term predictions since it is hard to imagine a real-life scenario under which β stays constant over a very long period of time due to measures taken by individuals and public health officials. The “baseline” plots given in Figure 8 show the total infected deaths and hospitalizations as well as exposures and deaths under the 1X, 4X and 6X loading scenarios with fitted transmission and mortality rates at the ICU. The best fit β values were 0.2221, 0.2226 and 0.2229 for 1X, 4X and 6X scenarios. The 9 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . 4X Loading Scenario, β=0.2226, υ=0.5408 4X Loading Scenario, β=0.2226, υ=0.5408 80 000 © METAz, 2020; Not for release © METAz, 2020; Not for release 6 × 106 60 000 Total Infected Susceptible 4 × 10 6 Infected Hospitalized 40 000 ICU Recovered Dead 2 × 106 20 000 100 200 300 400 500 0 (a) Susceptible, infected and recovered 100 200 300 400 500 (b) Infected, hospitalized, ICU and dead Figure 7: Baseline case of 4X loading with constant β = 0.2157 υ values used for 1X, 4X and 6X scenarios were, 0.95, 0.5408 and 0.3386. To fit the mortality rate in the 6X scenario, we kept the data on reported deaths in tact and fitted the value of υ to the data in a 6X loaded model. An alternative approach would have been to inflate the death numbers to account for the observation that COVID-19 related deaths may be underreported. Our approach yields a mortality a rate of about 34% which we decided to adopt for our projections under 6X loading scenario. Assuming a 30% underreporting of deaths, for example, results in a fitted mortality rate of 46% in the ICU but we do not use that number in our projections to keep to a evidence-based conservative set of estimates on the death toll of the epidemic. Actual vs. Projected Deaths, Baseline Actual vs. Projected New Exposures, Baseline T 3000 12 000 AF © METAz, 2020; Not for release © METAz, 2020; Not for release 2500 DR 10 000 8000 1X 4X 6000 2000 1X 4X 1500 6X 6X 4000 1000 2000 500 0 3/31 4/14 4/28 5/12 5/26 6/9 0 3/31 6/23 (a) 4X exposures inferred from actual data 4/14 5/12 5/26 6/9 6/23 (b) Cumulative number of deaths Projected Hospitalizations, Baseline Total Infected, Baseline 120 000 4/28 12 000 © METAz, 2020; Not for release © METAz, 2020; Not for release 10 000 100 000 80 000 1X 4X 60 000 8000 1X 4X 6000 6X 6X 40 000 4000 20 000 2000 4/14 4/28 5/12 5/26 6/9 6/23 4/14 (c) Total infected 4/28 5/12 5/26 6/9 6/23 (d) Hospitalized patients Figure 8: Fitted model predictions with 1X, 4X and 6X loading scenarios, with transmission rate β of 0.2221, 0.2226, 0.2229 and ICU death rate υ of 0.95, 0.54 and 0.34, respectively. The red dots in plots correspond to data used for fitting 4X scenario parameters. We see that both 4X and 6X provide plausible fits to the data on cumulative deaths (by adjusting 10 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . the mortality rate υ). While we don’t directly use hospitalization numbers in our analysis, the current hospitalization numbers appear to be close to the number predicted by the 4X loading (1065 patients). In these graphs, the light orange shading indicates the two-week period after 5/5 (last data point used). The projections show that it is reasonable to expect a slowly increasing number of patients in the hospital due to the above stated fact that there is still a large number of susceptible individuals in the population. Better data on the numbers in the hospital through testing and rigorous reporting practices would be invaluable to track the progress and fit improved models. 3.1 Summer Effect There is currently debate on the impact of higher summer temperatures of Arizona on the transmission rate of COVID-19, both with regard to a potentially suppressive effect on virus survivability in elevated temperatures, as well as the behavioral effect of extremely hot temperatures changing patterns of indoor and outdoor activity in Arizona’s desert environment. While we are not certain about a potential summer effect, particularly on virus survivability, we have found it to be a useful context to demonstrate the sensitivity of outbreak dynamics to the transmission rate β. Total Infected @4X, initial β=0.2226, υ=0.5408 , Summer Effect Hospitalized @4X, initial β=0.2226, υ=0.5408 , Summer Effect © METAz, 2020; Not for release © METAz, 2020; Not for release 150 000 15 000 4X No summer effect 100 000 β ↓ 25% on 5/29 10 000 T β ↓ 50% on 5/29 5/12 5/26 6/9 6/23 7/7 7/21 DR 5000 β ↓ 25% on 5/15 AF 50 000 5/12 (a) 4X Total Infected 5/26 6/9 6/23 7/7 7/21 (b) 4X Hospitalized Figure 9: Fitted model predictions with 4X loading with transmission rate β of 0.2226 and ICU death rate υ of 0.54 under five possible summer effect cases In Figure 9, we plotted the total infected and the hospitalizations under four different scenarios with respect to the summer effect. The plot shows the tradeoff between an early summer effect versus a later but more significant summer effect. The figure also demonstrates the impact of a 25% to 50% reduction in the transmission rate as well as the impact of the timing of the summer effect in flattening the curve further. 3.2 Opening Scenarios A more likely scenario awaiting Arizona is an increase in the transmission rate due to the lifting of the Governor’s stay-at-home orders and re-opening of businesses that were deemed to be nonessential. While it is not possible to know how β will change as a result, it is useful to understand the way in which increases in transmission rates will influence the overall dynamics of the epidemic. We start by demonstrating the impact of a very modest, mere 30% increase in transmission rate from its current estimated value. We are not arguing that there will be a 30% increase in β since we do not have the data to support such an argument, but a 30% increase in β may, for example, be a result of 15% increase in the average number of contacts and a 15% increase in the probability of transmission given contact as demonstrated in Figure 3. One can easily imagine such 11 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . increases in the average number of contacts as well as probability of transmission given contact with an infectious individual after the NPIs are relaxed. Hence, these scenarios are presented as relatively moderate levels of increase; the increase in transmission rate β can certainly be much higher. Figure 10 shows the hospitalizations over a period of about five months for three different ways that this increase may happen: an “early” 30% increase on 5/15 upon the lifting of the current stay-at-home orders in place on 5/1, a “late” 30% increase on 6/15 and a gradual 10% increase on 5/15, 6/1 and 6/15, as well as keeping the transmission rate the same at β = 0.2226 for the 4X loading scenario. The qualitative insights will remain the same for the other scenarios. Total Infected @4X, initial β=0.2226, υ=0.57 700 000 Hospitalizations @4X, initial β=0.2226, υ=0.54 © METAz, 2020; Not for release 80 000 © METAz, 2020; Not for release 600 000 500 000 β=0.2226 60 000 β ↑30% on 6/15 400 000 β ↑ 10% gradually 40 000 300 000 β ↑ 30% on 5/15 200 000 20 000 100 000 5/12 5/26 6/9 6/23 7/7 7/21 8/4 8/18 9/1 9/15 9/29 5/12 5/26 6/9 (a) 4X Total Infected 6/23 7/7 7/21 8/4 8/18 9/1 9/15 9/29 (b) 4X Hospitalized AF T Figure 10: Total infections and hospitalizations for the early, late and gradual increase in transmission rate DR Even for a relatively modest estimate of the opening on the transmission rate, we see that the transmission dynamics changing drastically, even for very gradual increases of 10%. The hospitalizations predicted as a result of these transmission rate changes show the impact on the healthcare resources. Even though the results in the above figure are alarming, it is hard to imagine that we will not be reacting to such increases in hospitalizations, etc. so it represents a worst-case in how the epidemic will unfold. The more realistic scenario is that we will be tracking the behavior of the epidemic and will be triggering NPI actions to manage the impact on healthcare resources and public health. Hence, it is useful to view the short-term behavior of the curve to gain some insight into the signals that one can look for in the data as we relax the stay-at-home orders. Figure 11 plots the presumed exposures inferred from data (for 4X loading) as well as the reported COVID-19 deaths in Arizona (the blue curve in these plots is the same as the orange curves in Figure 8). The figure clearly shows that we will be observing an increase in transmission rate, but unfortunately with a significant time lag. The increase in presumed exposures starting from 5/15 shown in Figure 11a will be observed in the case counts data starting from 6/1. This fact is also clearly shown in Figure 11b; we expect to start seeing increases in death counts starting from the beginning of June. If the transmission rate increases more gradually, then it will be even harder to conclusively say that the transmission rate has increased. Depending on the case, the detection of a rate increase and its likely magnitude can take a lag of about a month, or may be more, depending on the quality of data. Suppose that we detect an increase in the transmission rate in the very optimistic case of two weeks or relatively pessimistic case of four weeks after the actual increase in β, and react with a stay-at-home order that returns the transmission rate to its baseline value. To keep the discussion simpler, let’s consider the case of gradual increase in β under which the transmission rate was set to increase in increments of 10% every two weeks starting from 5/15. Let’s assume that after the 12 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Actual vs. Predicted New Exposures Actual vs. Predicted Deaths 25 000 10 000 © METAz, 2020; Not for release © METAz, 2020; Not for release 20 000 8000 4X 15 000 6000 10 000 4000 5000 2000 0 3/31 4X early β↑ 4X gradual β↑ 4/14 4/28 5/12 5/26 6/9 6/23 7/7 7/21 4X slow β↑ 0 3/31 4/14 4/28 (a) 4X new exposures 5/12 5/26 6/9 6/23 7/7 7/21 (b) 4X deaths Figure 11: Presumed exposures and deaths for 4X loading under different β increase scenarios; gradual increases of 10% on 5/15, 20% on 6/1, 30% on 6/15 and slow increases 5% on 5/15, 15% on 6/1 and 30% on 6/15 (each from baseline β) DR AF T detection of rate increase, the rate goes back to the low baseline value after the reactive shutdown. Figure 12c and 12d clearly demonstrate the impact of the reactive shutdown in comparison to the curve with constant β = 0.2226 for 4X loading. While there is a difference in the height of the peaks between the curves, the figure also indicates that reactive shutdowns can be very effective to mitigate the consequences of increases in transmission rate, particularly if the detection time lag is kept to the minimum of two weeks. As the detection time lag increases, however, the effectiveness of the reactive shutdown to mitigate the impact of the peak decreases. It is also worthwhile to note that in the scenario presented, the reactive shutdown is issued on 5/29 and 6/15 in the 2-week lag case and 4-week lag case, respectively. Even after the reactive shutdowns, we expect to continue seeing increased numbers of total infections and hospitalizations, which will likely raise public questions about the rationale for the shutdowns if they failed to mitigate infections and deaths, making the public policy management aspects of the intervention more challenging. In our framework, it is possible to calculate the expected excess number of exposures or deaths (or any other epidemiological measure) as a function of increased β values over time. Figure 13 depicts the excess observations that we would “expect” to see in the data, over time. Note that both plots start from the date of 5/15, which is the date for which Arizona is going to be lifting the stay-at-home orders, as of 5/1. We can observe from the plots that the excess new cases and deaths start getting reported about 2 weeks after the first 10% increase in β. We assumed that the assumption on detecting 1/4 of the actual cases (i.e., 4X scenario) and plotted the excess that you would expect to be detected in this scenario in Figure 13a. Note that these are expected increases in the case counts and deaths assuming a homogeneous increase in the transmission rate across the entire susceptible population in the State. Hence, typically the numbers we expect to pick up from the data will be smaller. This also points to the importance of rigorous testing and monitoring of new cases since this framework, supported with good quality data, can yield an ability to develop reactive shut-down strategies like the one depicted in Figure 12. Figure 13 omits the prediction intervals to keep the demonstration of excess new cases and deaths simple but the prediction intervals on the number of new cases and deaths, allows us to construct “control limits” that would signal an “out-of-control” situation with respect to the transmission rate, β. Our current work involves development of these trigger control limits under explicit consideration of the various sources of model uncertainty. The success of such approaches, however, depend on the quality and consistency of the data that we get on the case counts and 13 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . Actual vs. Predicted Deaths Actual vs. Predicted New Exposures 60 000 60 000 © METAz, 2020; Not for release © METAz, 2020; Not for release 50 000 50 000 40 000 40 000 30 000 30 000 20 000 20 000 10 000 10 000 4X 4X gradual β↑ 0 3/31 4/28 5/26 6/23 7/21 8/18 9/15 0 3/31 4X gradual β↑, 2-wk 4X gradual β↑, 4-wk 4/28 (a) 4X new exposures with reactive shutdown 5/26 6/23 7/21 8/18 9/15 (b) 4X deaths with reactive shutdown Hospitalizations Total Infections 700 000 80 000 © METAz, 2020; Not for release © METAz, 2020; Not for release 600 000 60 000 500 000 4X 4X gradual β↑ 400 000 4X gradual β↑, 2-wk 40 000 300 000 4X gradual β↑, 4-wk 200 000 20 000 100 000 5/26 6/23 7/21 8/18 9/15 5/26 6/23 7/21 8/18 9/15 (d) 4X hospitalizations with adaptive shutdown AF (c) 4X total infections with adaptive shutdown 4/28 T 4/28 DR Figure 12 deaths, which in turn depends on the testing policies and rigorous reporting of COVID-19 related deaths. 4 Discussion In future work, we look forward to refining the model, applying it to other areas, creating additional tools. We note that this model iteration was constructed based on the stated Arizona stay-at-home model remaining in place until 5/15. After this model was constructed based on the 5/15 reopening expectation, the Arizona governor announced on 5/4 that businesses, including salons and dine-in restaurants, would begin reopening between 5/8 and 5/11. We anticipate that our projections will shift in future iterations based on these policy changes. In future work, we further look forward to testing this model against data from other states beyond Arizona in an effort to validate this approach for other public health policy making jurisdictions. Acknowledgements: We would like to acknowledge the contributions of the Arizona Department of Health Services Modeling Working Group: Amber Asburry, Steven Robert Bailey, Timothy Flood, Joe Gerald, Heidi Gracie, Katherine Hiller, Ken Komatsu, Josh Labaer, Mark Manfredo, Anita Murcko, Vern Pilling, Timothy Richards, George Runger, Marguerite Sagna, Lisa Villarroel, Patrick Wightman, and Neal Woodbury. 14 medRxiv preprint doi: https://doi.org/10.1101/2020.05.13.20099838.this version posted May 16, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license . 2500 Excess new cases, gradual 10% β↑ on 5/15, 6/1 and 6/15 @4X 1000 2000 800 1500 600 1000 400 500 200 0 5/16 5/30 6/13 6/27 Excess deaths, gradual 10% β↑ on 5/15, 6/1 and 6/15, @4X 0 5/16 (a) Expected excess new cases 5/30 6/13 6/27 (b) Expected excess deaths Figure 13: Expected excess new cases and excess COVID-19 deaths (in comparison to the baseline β = 0.2226 case, assuming a 10% gradual increase on 5/15, 6/1, 6/15 in baseline β) References [1] Q. Bi, Y. Wu, S. Mei, C. Ye, X. Zou, Z. Zhang, X. Liu, L. Wei, S. A. Truelove, T. Zhang, et al. Epidemiology and transmission of covid-19 in shenzhen china: Analysis of 391 cases and 1,286 of their close contacts. MedRxiv, 2020. DR AF T [2] D. C. Buitrago-Garcia, D. Egli-Gany, M. J. Counotte, S. Hossmann, H. Imeri, G. Salanti, and N. Low. The role of asymptomatic sars-cov-2 infections: rapid living systematic review and meta-analysis. medRxiv, 2020. [3] H.-Y. 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