Modeling COVID-19 for lifting non-pharmaceutical interventions

As a result of the COVID-19 worldwide pandemic, the United States instituted various non-pharmaceutical interventions (NPIs) in an effort to the slow the spread of the disease. Although necessary for public safety, these NPIs can also have deleterious effects on the economy of a nation. State and federal leaders need tools that provide insight into which combination of NPIs will have the greatest impact on slowing the disease and at what point in time it is reasonably safe to start lifting these restrictions to everyday life. In the present work, we outline a modeling process that incorporates the parameters of the disease, the effects of NPIs, and the characteristics of individual communities to offer insight into when and to what degree certain NPIs should be instituted or lifted based on the progression of a given outbreak of COVID-19.

In December of 2019, a cluster of pneumonia cases of unknown origin were identified in 2 Wuhan, China. An investigation into the cases commenced in early January 2020 that 3 led to the discovery of a novel coronavirus now designated SARS-CoV-2. The virus 4 causes an infectious disease now known as Coronavirus Disease 2019 or COVID-19. 5 Common symptoms of COVID-19 include shortness of breath, fever, dry cough, fatigue, 6 and respiratory distress. 7 On January 10 th , 2020 there were 41 confirmed cases of COVID-19 in China [1]. By 8 January 20 th , The Guardian reported that the Chinese National Health Commission 9 had confirmed human-to-human transmission of COVID-19 and the number of reported 10 cases had more than tripled to 139 [2]. That same day, Chinese authorities started In addition, a combination of testing and tracing anyone who came in contact with a 25 positive case -referred to as contact tracing -and requiring them to self-quarantine for 26 approximately 14 days is another tactic for limiting the spread. 27 The restrictions to daily life have driven the world into one of the largest recessions 28 in history [5]. Goldman Sachs has warned that the U.S. Gross Domestic Product (GDP) 29 could contract as much as 29% in the second quarter and the U.S. unemployment rate 30 rose from 3.6% in January 2020 to 14.7% in April 2020 [6]. The economic recession 31 creates an urgency to lift the NPIs and population restrictions that is in direct conflict 32 with the desire to stop the spread of disease and keep the population healthy. State and 33 federal leaders therefore need tools that can provide insight into the risk to populations 34 of lifting NPIs before the disease is completely wiped out or a vaccine is developed. 35 Empirical studies have shown that the same disease can exhibit heterogeneous 36 transmission characteristics as it spreads to different communities [7]. This fact has led 37 researchers to look for ways to more realistically model the contact structure of a given 38 population. In a separate paper we derived a mathematical framework that results in a 39 closed-form analytical solution using percolation theory and mean-field theory. The distribution. In the current work, we establish a procedure for inferring the degree 44 distribution of a given county in the U.S. from Census data [8]. This provides a 45 pre-pandemic community structure. We then constructed an agent-based model (ABM) 46 that incorporates the daily behavior of individuals in a given community, along with the 47 constraints to that behavior imposed by NPIs. The ABM ingests the pre-pandemic 48 community network inferred from Census data to drive social contact when no NPIs are 49 implemented. The post-pandemic contact structure emerges as a function of compliance 50 with NPIs and we are able to assess differences in the spread of disease as a function of 51 both contact network degree distribution and the impact that a given set of NPIs has 52 on the network structure. 53 To illustrate the utility of our approach we model the 24 county-equivalents of 54 Maryland in an experiment that asks what is the impact of a given percent of the 55 population being tested and a given level of participation in contact tracing if NPIs are 56 lifted 70 days after the onset of the pandemic? We show that different strategies can 57 have the same impact on disease progression depending on the contact structure of each 58 county. This underscores the importance of the modeling capability because it 59 facilitates a location-based phased approach for lifting NPIs and instituting test and 60 trace strategies. It also serves to underscore the importance of incorporating community 61 structure into the analysis. Seven of the 24 county-equivalents of Maryland show a • Transmissibility T is the average probability that an infectious individual will 73 transmit the disease to a susceptible individual with whom they have contact. 74 • Critical Transmissibility T c is the minimum transmissibility required for an 75 outbreak to become a pandemic. T c = k ( k 2 − k ) where k and k 2 are the mean 76 and variance of the degree distribution of the contact network.  Note that some studies refer to an effective reproductive number R e . In the definitions 83 above, R 0 depends on the degree distribution so there is no need to make this 84 distinction. R 0 and R e can be thought of as interchangeable terms. 85 Given the transmission rate r between vertex i and vertex j of a network graph and 86 the infection time τ and assuming that r and τ are independent random variables, the 87 average transmissibility is: where P r (r) and P τ (τ ) are the respective probability density functions (pdfs). For 89 simplicity, it is assumed that P r (r) = δ(r − r 0 ) and P τ (τ ) = δ(τ − τ 0 ) so that

91
For a randomly chosen vertex, let p k denote the probability that this vertex has k 92 edges. Then G 0 (x) is the generating function for the degree distribution of this vertex: 93 An important result by Feld is that the degree distribution of the first neighbor of a 94 vertex is not the same as the degree distribution of vertices as a whole [11]. There is a 95 higher chance that an edge will be connected to a vertex of high degree, in fact, in 96 direct proportion to its degree. Let q k denote the degree distribution of a vertex at the 97 end of a randomly chosen edge. Then: excluding the randomly-chosen edge. The corresponding generating function for this 99 distribution is: The generating functions G 0 (x) and G 1 (x) are related. Let z = k kp k and using 101 Eq. (3): where G 0 (x) is the derivative of G 0 (x).
Using bond percolation and mean-field theory, Newman [12,13] showed that for 104 small outbreaks (clusters) when T < T c we can combine Eq. 1 with the generating 105 functions and then compute the average cluster size c as: where the angle brackets indicate the expected value. In the case of a pandemic where 107 T > T c we define H 1 (x; T ) as the generating function of the size of a cluster at the end 108 of a randomly chosen edge. We can then derive an iterative approach for calculating the 109 probability P of a pandemic. Let v = H 1 (1; T ), then the fixed point problem becomes: We expanded on this formulation to incorporate the NPIs of uniform and directed 111 social distancing. For social distancing, let b k denote the probability that a vertex of 112 degree k is present. Define the generating function F 0 (x) as: Similarly, F 1 (x) = F 0 (x)/z. This is a generalization of the generating functions G 0 (x) 114 and G 1 (x). Since F 0 (1) = 1 and F 1 (1) = 1, 1 − F 0 (1) is the probability that a randomly 115 chosen vertex has no active edges. In the case of uniform social distancing, vertices are 116 chosen to sequester at random so b k = b.

117
In the case of directed social distancing, it is assumed that: where all individuals are distanced with contact degree greater than K max . This implies 119 that: To compute the size c of small outbreaks (T < T c ) the generating functions G 0 (x) 121 and G 1 (x) are simply replaced with F 0 (x) and F 1 (x) respectively. For large pandemics, 122 the derivation is similar and the resulting fixed point problem is: Incorporating these generating functions into a time-dependent model is straight 124 forward. If we define v(t) as the average probability of a neighbor (connected via an 125 edge) being infected and w(t) as the average probability of recovery, then it can be 126 shown that the time-dependent spread of disease on a network with generating 127 distribution G 1 (x) and no NPIs is defined by: where u(t) = exp(−βw(t)/γ), β is the contact rate, γ is the recovery rate, and s 0 is the 129 proportion of initially susceptible individuals [14].
To model the time-dependent spread when NPIs are implemented and then lifted, we 131 can define different intervals of time where v(t) is modified to reflect the decrease in 132 potentially infected neighbors. In the case of uniform social distancing we replace v(t) 133 with: were b is the fraction of the population that is not sequestered. In the case of testing 135 and contact tracing, the model becomes more complicated, requiring another ordinary 136 differential equation v (t) to replace v(t) such that: The derivation of the full model is beyond the scope of the current work, so we refer the 138 interested reader to our companion paper.

139
Inferring Network Structure

140
The Analytical Model requires a priori knowledge of the social contact network and its 141 degree distribution in order to assess the risk of an outbreak. We are thus faced with the 142 need to infer the network from data collected on a given population.   The resulting progression from households to schools to work to public is illustrated 193 through the four stages of construction in Fig. 1. Disease propagation is a complex system [15]. The dynamics of a pandemic is a function 196 of the biological characteristics of the disease, the biologic response of those infected, 197 and the behaviors of those in the area affected by the disease. In this way a pandemic is 198 an emergent phenomena of the social systems within which it is embedded [16].

199
Emergent phenomena are a characteristic of complex systems [17,18], systems made up 200 of many interacting, heterogeneous entities embedded in a relevant space. In these types 201 of systems the interactions among entities are as important to the overall dynamics as 202 the characteristics of the entities themselves. Therefore, a strict reductionist approach 203 July 2, 2020 6/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint will only provide partial insights into the system dynamics. For example, a detailed 204 biological analysis of a virus will only provide limited insights into how an eventual 205 pandemic may unfold. Regardless of the contagiousness of a virus, if all members of a 206 society maintain strict social distancing, the disease cannot spread. Given that this is a 207 complex system, an efficient way to discover its future state is to simulate it [19]. 208 Finally, the most natural way to express these systems as a simulation is to do so as an 209 agent-based model (ABM), [20,21].

210
Although our analysis is premised on inferred contact networks, we felt the 211 importance of exploring the dynamics associated with changes in behavior warranted 212 the inclusion of an ABM so one could more easily explore the impact of 213 non-pharmaceutical interventions (NPIs) and the rate of compliance. Furthermore, 214 creating this ABM allowed us to explore the basic reproduction number R 0 of the 215 pandemic as an emergent phenomena and one that is potentially unique to each infected 216 individual. In this way such things as super spreaders do not need to be explicitly 217 included as an exogenous "shock" but rather they emerge based upon the behavior of 218 the individual members of the society.

219
Overview of the ABM 220 The ABM is implemented in NetLogo [22]. The model is instantiated first with an input 221 file that defines the inferred contact network of a U.S. county scaled to be 222 approximately ten thousand individuals. These contact graphs are generated using U.S. 223 Census data and the algorithm described in the section Inferring Network Structure.

224
The environment size is scaled to approximate the population density of the county in 225 question. First, all members of the simulated society are created. Second, school, work, 226 home, and public contact networks are created. The physical space is created next.  The available NPIs include closing schools, closing work places, closing public venues, 241 imposing social distancing requirements (i.e., stay home orders), and isolating 242 individuals. Individual mitigation steps can also be modeled using the probabilities 243 associated with disease spread. Testing may also be performed within the simulated 244 society. Two different testing strategies can be employed. The first is random testing of 245 non-hospitalized individuals. The second distributes the tests across symptomatic and 246 asymptomatic individuals. Once tested or found to have a positive test, individuals can 247 be isolated for some period of time (e.g., three days while waiting for results or two 248 weeks if found to be positive). Last we incorporated contact tracing that is triggered by 249 either a positive test or a hospital visit. Agents who have opted-in to the contact 250 tracing are informed to self-isolate if they came in contact with an infected agent who 251 subsequently tested positive or went to the hospital.

252
The simulation ends when all individuals are no longer contagious (all individuals 253 are in the susceptible, deceased, or recovered states) or when a preset time step limit is 254 July 2, 2020 7/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. The disease progression model was designed to follow the dynamics of COVID-19 as 257 they were understood around March of 2020. Similar to a classic SEIR model, the 258 agents move through discrete states as the disease progresses within them. The disease 259 states include Susceptible, Exposed, Mild, Severe, Critical, Deceased, and Recovered.

260
All agents are instantiated in a state of Susceptible. Immediately prior to runtime a 261 user specified number of agents are set to the Exposed state.

262
In order to increase flexibility and respond to changes in the understood dynamics of 263 COVID-19 disease progression, the simulation uses default values that can be 264 overridden. The default dynamics are outlined in Tables 1 and 2. When agents are collocated, there is some chance that the disease will be transferred 280 from one agent to another. At each time step agents that are contagious (those in the 281 Mild, Severe, or Critical states) will look for another agent on the same patch (small 282 piece of the environment). If there is at least one other agent on the patch contagious 283 agents will attempt to pass the virus to one other agent. Successful passing of the virus 284 is a function of 1) a user specified probability of successfully getting the virus on the 285 July 2, 2020 8/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint other agent (e.g., is the infected agent wearing a mask or not), 2) a user specified 286 mitigation probability (e.g., did the potentially infected agent wash their hands a lot 287 and maintaining a distance of 6 feet from others), and 3) the health status of the target 288 agent (if they are already sick, they will not get sicker).

289
Contact Tracing and Testing Formulation 290 When citizens are initialized they 'decide' to participate in contact tracing (opt-in) or 291 not. This is done via a random draw against a user-specified parameter. A uniform 292 pseudo-random number is generated and if that number is less than the user-specified 293 threshold the citizen participates in contact tracing. Once set, this is held constant for 294 the duration of the run.

295
Contact tracing can be triggered in two basic ways. The first trigger for contact 296 tracing is when a symptomatic individual arrives at the hospital. The second is via 297 testing. If an individual tests positive and that tested individual has opted-in to the 298 contact tracing program, then contact tracing from that individual will commence. 299 At runtime (with the appropriate runtime settings) each citizen collects data on the 300 other citizens it comes into contact with. A time step is currently defined as one 301 12-hour period and a patch (the smallest unit of the landscape in the model) is a square 302 with each side 0.1 km in length. Given this scale, we assume citizens that are co-located 303 on a patch are likely enough to be in significant contact with each other as to warrant 304 being considered in the contract trace. NOTE: all agent IDs are collected whether or 305 not they have opted-in to the contact tracing program, this is done so we can produce a 306 contact network to analyze separately. This decision also improves runtime efficiency, as 307 it is far faster to query for the agents on a patch than to query for agents within a 308 certain distance.

309
At the beginning of each time step, agents update their health status and then 310 collect contact data in a first-in-first-out queue that is 28 elements long (14 days). For 311 this discussion we will assume the tracing is precipitated by testing a segment of the In broad terms, testing is accomplished in the simulation in one of two ways. Version 1 320 testing corresponds to random testing of all individuals outside of the hospital. In this 321 case a user-specified number of citizens are randomly chosen to be tested whenever 322 testing takes place. For version 2 of testing, at a given point in time a number of tests 323 are made available. This number is divided between symptomatic and asymptomatic 324 citizens. A set of citizens equal to or less than the number of allocated tests is then 325 randomly chosen and tested. Testing accuracy includes a user-defined false negative 326 rate, but false-positives are not modeled. This essentially means there is a 100% chance 327 that someone who received a positive test has COVID-19, but a citizen receiving a 328 negative test result is not guaranteed to be free of the disease.

329
Settings for testing can all be manipulated during runtime so there are no 330 initialization components. Users can choose which version of testing to use and set the 331 percent of the population to test. Alternatively, a user can specify an interval of testing 332 that starts and stops at specific time steps. The way the population is tested is random 333 with replacement. This means, for example, if the interval is set to 1 and 50% of the 334 July 2, 2020 9/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . population is to be tested, then on average half the population will be tested once a day, 335 but a specific citizen might be tested twice or not at all. 336 First, we calculate the number of tests available by multiplying the number of 337 citizens by percent to be tested parameter. This value is rounded to the nearest whole 338 number. Next we calculate how many of the total number are to be used on 339 symptomatic citizens. That number is created by multiplying the total number of tests 340 by the user-specified split value. Then we calculate the number of tests to be used on 341 asymptomatic citizens by subtracting the total symptomatic from total number of tests. 342 We then create two sets of citizens to test, one for symptomatic and one for 343 asymptomatic. Note there is no guarantee that there will be enough citizens to satisfy 344 the number of tests available. Symptomatic citizens are defined as those with "Mild," 345 "Severe," or "Critical" COVID-19 disease progression. Citizens with "Healthy," 346 "Exposed," or "Recovered" are considered asymptomatic. If there are extra tests those 347 tests are not used. The next step in testing is to determine the citizens who tested 348 positive. For the symptomatic group, since the only disease in the model is COVID-19, 349 that calculation is straightforward. We take the total number of individuals being tested 350 and multiply that by the accuracy of the test. That gives us the symptomatic citizens 351 with positive tests. The asymptomatic group is slightly different. That group contains 352 citizens who do not have the disease as well as those that do because we model false 353 negatives with test accuracy. To deal with this we need to grab only those individuals 354 who actually have COVID and then apply the test accuracy to that group to get the 355 number of citizens who are asymptomatic and will receive a positive test.

356
Finally, we need to isolate these citizens. All citizens who are tested are placed in  Currently, given a population of ten thousand agents, the simulation creates densities of 367 44 agents per square km, 10 agents per square km, and 1 agent per square km. Next, 368 the agents are instantiated. After all agents are created, undirected links are created 369 between pairs of agents. After all links are created, all connected components are 370 assigned to another agent that represents the location of their interaction. For example, 371 if there are 5 agents connected together by school-type links, they will all be assigned to 372 a single schoolhouse agent. The same is done for all other types of links. The final step 373 is to take all agents not assigned to a home (those that live alone) and assign them to 374 one.

375
Once all agents are assigned to a location agent, the location agents are then placed 376 within the environment. This can be done in one of two ways. The first is to randomly 377 place all location agents about the environment. The other way is to place all home 378 agents on the right half of the environment and all non-home agents on the left side of 379 the environment. This allows us to simulate counties that have segregated land use or 380 integrated land use. Once that locations are placed, all links are removed to reduce the 381 memory footprint of the simulation and a random selection of a user specified number 382 of agents are exposed to the disease.

383
The initialization process can be time consuming when importing the inferred 384 contact network. Therefore, once a population is created via the inferred network, the 385 July 2, 2020 10/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020.   . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . currently ingests the graphical structure, we noted that runs performed with the same 433 pseudo-random number seed are not exactly the same, i.e., reproducibility is not 434 guaranteed. As a result, we base all our results on mean behavior rather than a specific 435 replication of the simulation. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint reported in Maryland. This is a good exercise for ensuring model results are realistic, 438 but it should be noted that precise statistical matches are not expected. There is 439 uncertainty due to testing, the timing of NPIs, the actual adherence to NPIs, and 440 relative scale of our 10,000 person simulations and the actual populations of a given 441 county. Nevertheless the results shown in Fig. 5 and 6 indicate that our model results 442 reasonably represent the counties they are intended to model. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint off). Finally, there are a number of parameters directly associated with the spread of 449 the disease: transmission probability, mitigation probability, compliance with social 450 distancing orders, compliance with isolation orders, and structure and extent of testing. 451 In our validation exercise the simulation demonstrated sensitivities one would expect 452 to find in a model of this type. Disease spread was highly correlated to transmission 453 probability and mitigation probability. Furthermore, testing made a significant 454 difference when it was coupled with a population that complied with isolation orders.

455
No unexpected sensitivities were uncovered, but it is important to note that  The NPIs included in the agent-based model are social distancing, isolation of 478 infected individuals and individuals waiting for test results, and the closing of schools, 479 workplaces, or public venues (e.g., grocery stores, shops, parks). In the ABM, all agents 480 have a home location and spend at least half their time at that location (i.e., nights).

481
Most agents also have a non-home location such as a workplace, a school, or public 482 venue. Agents with non-home locations spend daytime hours at these locations. When 483 social distancing is turned on, agents perform a random draw (compared against a user 484 definable threshold) before leaving their home location. If the random number does not 485 exceed the threshold, the agent stays home. This allows the user to vary the likely 486 compliance to social distancing orders and to allow for agents to occasionally leave their 487 home for necessities such as food and non-COVID healthcare. This is equivalent, in the 488 limit, to uniform social distancing in the analytical model.

489
To implement isolation of infected individuals, those who test positive for COVID-19 490 in the ABM and those waiting for their test results (assumed to take three days in the 491 simulation), are placed in isolation. When an agent is in isolation, they either stay at 492 their home location or the hospital. These individuals will remain in isolation for two 493 weeks when tested positive or three days when waiting for test results that come back 494 negative. There is a user defined probability that an individual will comply with the 495 isolation order.

496
July 2, 2020 14/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . Finally, homes, schools, workplaces, and public venues all have a specific location in 497 the ABM and agents move from one of these locations to another depending upon time 498 of day and their inferred contact network and demographic characteristics. With the 499 exception of homes, these locations have a variable that allows them to be closed or 500 opened. When closed agents will not go to them when they attempt to leave home. If 501 the agent has no locations outside their home that are open, they will stay home. Any 502 combination of venues can be closed, allowing for partial or phased re-openings to be 503 simulated.

504
Maryland includes a mix of rural and urban counties. Baltimore and the suburbs of 505 Washington, D.C. are the most populated areas with over 3 Million people, while Kent 506 County has only around 19,434 inhabitants [8]. Table 3 lists the population, area, and 507 density of each county according to the U.S. Census estimate in 2018. Using the U.S. Census ACS data and the algorithm described earlier, we constructed 509 the 24 contact structure graphs to represent the pre-NPIs state for initializing each 510 simulation. The parameters used in constructing the graphs are shown in Table 4.

511
These graphs were ingested into the ABM as the initial contact structure. The degree 512 distributions of each county graph are characterized by the means and standard 513 deviations listed in Table 5.

514
The full experiment consisted of three sets of simulation runs. The first was a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. .  start of each run. The NPIs were the closing of school and workplace venues, but not 520 public venues. Social distancing was also enforced starting on day 10 at 95% and then 521 reduced to 50% after 70 days. When the NPIs were lifted a regime of testing and 522 contact tracing was instituted. For this particular set experiment we employed one-step 523 contact tracing. That is, agents who came in direct contact with an infectious agent and 524 opted-in to the program were traced. But agents who came in contact with an agent 525 who was traced were not in turn traced. In this scenario only symptomatic people were 526 tested and contact tracing commenced for those cases that tested positive and had . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . random testing regime. This includes agents that are in the Susceptible, Exposed, Mild, 533 or Recovered states. The same five levels of optInRate were used, but the percent 534 tested was varied across a set of higher testing levels. In our exploratory 535 experimentation we found that higher percentages of random testing are required to 536 achieve similar impact because the same quantity of tests uncovers fewer true-positives. 537 Tables 6, 7, and 8 outline the parameter settings for each of the three scenarios. Note 538 that by setting social distancing to a high percentage but leaving venues open, we 539 simulate minimal interaction that occurs at essential businesses such as grocery stores. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. .  The key insight is that any 554 strategy the state of Maryland adopts will need to treat 7 of the 24 counties differently. 555 Referring to Table 3, it is interesting to note that Harford County has roughly 75% fewer 556 people than Montgomery County and Montgomery County is roughly 70% less dense 557 than Baltimore City. Yet all three of these locations have an average maximum infected 558 that is approximately four times larger than 17 of the counties in rest of the state.

559
July 2, 2020 18/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint Next we analyzed the impact of a 50-day NPI strategy followed by a regime of 560 symptomatic testing and contact tracing. From a broad perspective we can see in Fig. 8 561 and Fig. 9 that the NPIs and testing and tracing combine to reduce the total 562 cumulative cases considerably. Here we can see that if each county has the ability to 563 test 1% of its population daily then the overall number of cases can be drastically 564 reduced. Also note that, for this level of testing and contact tracing, the dynamics in 565 Baltimore City separate from the other counties, most likely due to its extremely high 566 density. There is still a difference from one county to the next due to the differences in 567 density and contact structure. We selected three of the counties to look at in greater 568 detail that are notionally representative of high, medium, and low density locations.  Baltimore City has the highest population density out of the 24 locations. Harford is 570 seventh out of 24 in terms of density and Worcester is near the bottom. Fig. 10, 11, and 571 12 show the mean peak infections for each of the 25 design points of the symptomatic 572 testing scenario, along with the baseline mean peak infections for each of these counties. 573 The combined impact of the NPIs, testing, and tracing is evident, but the variation in 574 If we focus on any one county, we can analyze the interaction effects of different 592 levels of testing and contact tracing, as well as if symptomatic or random testing 593 produce different results. Recall that five of our design points between symptomatic 594 testing and random testing overlap. Specifically, for all five levels of optInRate, the 595 1.0% testing level is included in both experiments. Holding the optInRate constant at 596 0.75, we can see in Fig. 16 that more than 5.0% random testing is required to achieve 597 the same results at 1.0% symptomatic testing. This result may seem misleading at first 598 because healthcare professionals agree that more testing and random testing of 599 asymptomatic people is highly recommended. It is important to note that all 600 symptomatic agents in the model are indeed infected with COVID-19. So 1.0% testing 601 of symptomatic individuals is testing a large percentage of the infectious population.

602
Conversely, the random testing regime is forced to distribute the tests across a mix of 603 infectious and non-infectious people. Since the non-infectious population is larger when 604 NPIs are employed, the diluted number of true-positive tests makes the random regime 605 appear less effective at higher levels of testing. In actuality, this reinforces the message 606 of increased random testing. We know that many COVID-19 cases often exhibit few 607 symptoms even though the individuals are infectious. These individuals are less likely to 608 submit for testing because they might not even know they are sick. Increased levels of 609 random testing provides greater opportunity of finding and isolating those cases -as 610 illustrated by the model results -but that also means a greater level of testing is 611 required to actually find those who are infected. It is also important to note that 612 random testing is required to estimate the prevalence of the disease.  This generally holds true for the other counties, but again the influence of contact 619 structure and density can lead to a less monotonically decreasing relationship as 620 illustrated in Fig. 19. In the county heatmaps we see that testing and contact tracing 621 have less well defined results for rural counties. This is largely due to the structure of 622 these communities and the fact that the number of infected individuals is small (per 623 10,000 people). As such the probability of random testing finding an infected individual 624 is also small. This leads to fewer infected agents across all design points.

625
July 2, 2020 25/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. .  . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. . . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted July 5, 2020. .   . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted July 5, 2020.  Initial conclusions suggest that the analytical models can provide a complementary 667 approach for the coarse-grain prediction of disease spread in social contact networks 668 when rapid turnaround is required with low computational overhead. A more fine-grain 669 analysis is afforded by the ABM model when detailed predictions are required.

671
In the present work, we illustrated an ensemble modeling approach (shown graphically 672 in Fig. 26) for assessing alternate strategies of implementing and subsequently lifting 673 non-pharmaceutical interventions in response to the COVID-19 pandemic. We 674 underscored the previously-known result that social contact structure is a key factor in 675 the size of an outbreak or pandemic and we illustrated how closed-form analytical 676 models, network diffusion models, and agent-based models can be used in concert to 677 provide insight to decision-makers in the face of uncertainty. We summarized our 678 findings in a limited design of experiments that focused on the 24 counties and 679 county-equivalents of the state of Maryland. We showed that the different counties of 680 July 2, 2020 29/32 . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted July 5, 2020. . https://doi.org/10.1101/2020.07.02.20145052 doi: medRxiv preprint Maryland fall into at least two distinct categories in terms of risk of large outbreaks and 681 illustrated how different levels of testing can be employed to the same effect if the social 682 contact structure is taken into account. Finally, we showed that our analytical model 683 produces a coarse-grain assessment that is in line with the ABM results. This approach 684 is faster and less computationally expensive when rapid decision-making is necessary. It is important to note that no model or suite of models is a panacea. Ultimately 686 decision-makers are forced to make a choice under uncertainty to protect both the health 687 and the economic well-being of the citizenry. The approach outlined here is designed to 688 provide insight into the marginal impact of one NPI and testing strategy versus another. 689 This approach should be utilized by the decision-makers in conjunction with empirical 690 analysis of the current state of their county or region of interest. The model parameters 691 or logic should be constantly updated and the models re-run with new information as it 692 comes available. That is, this modeling approach is designed for use in real-time 693 alongside decision-makers at the time decisions are being formulated and implemented. 694 To that end, the analysis presented here should be taken as notional rather than 695 indicative of what might or might not happen in Maryland over the coming months.

696
During the writing of this report, unforeseen events extraneous to COVID-19 led to 697 social unrest, protests, and riots in many major cities across the United States. Most of 698 these locations were still operating under some level of restrictions to control the 699 pandemic. Clearly, protests and riots bring people into close proximity and may 700 ultimately prove to be super-spreading events. This sort of unpredictable event is not 701 included in our model nor have we seen them included in the models we reviewed. This 702 serves to underscore the difficulty and challenges of forecasting the progression of 703 complex systems. Models and the insights they provide can help, but they are 704 ultimately limited by assumptions. Decision-makers therefore require a combination of 705 reliable data from their region of interest, rigorously designed models that make as few 706 simplifying assumptions as possible, and ultimately the fortitude to make a decision in 707 the face of uncertainty.