Dynamics of COVID-19 under social distancing measures are driven by transmission network structure

In the absence of pharmaceutical interventions, social distancing is being used worldwide to curb the spread of COVID-19. The impact of these measures has been inconsistent, with some regions rapidly nearing disease elimination and others seeing delayed peaks or nearly flat epidemic curves. Here we build a stochastic epidemic model to examine the effects of COVID-19 clinical progression and transmission network structure on the outcomes of social distancing interventions. Our simulations show that long delays between the adoption of control measures and observed declines in cases, hospitalizations, and deaths occur in many scenarios. We find that the strength of within-household transmission is a critical determinant of success, governing the timing and size of the epidemic peak, the rate of decline, individual risks of infection, and the success of partial relaxation measures. The structure of residual external connections, driven by workforce participation and essential businesses, interacts to determine outcomes. We suggest limited conditions under which the formation of household “bubbles” can be safe. These findings can improve future predictions of the timescale and efficacy of interventions needed to control second waves of COVID-19 as well as other similar outbreaks, and highlight the need for better quantification and control of household transmission.

oxygen to fraction of inspired oxygen ratio <300, and/or lung infiltrates >50% within 24 to 48 hours.Hospitalization and supplemental oxygen are generally required.
• Critical infection -These individuals experience respiratory failure, septic shock, and/or multiple organ dysfunction or failure.Treatment in an ICU, often with mechanical ventilation, is required.
A summary of the variable definitions: The basic reproductive ratio R 0 of this model is: Our model makes several assumptions with regards to the clinical and epidemiological dynamics of COVID-19.We do not explicitly track asymptomatic infections, which have been estimated to be around 20% of infections [2] (but estimates range from 1% to 50%, reviewed in [3]).However, in our model asymptomatic infections can be considered to be part of the "mild infections" compartment.There is significant evidence that asymptomatic individuals are infectious, and with this assumption their infectiousness would be equal to those with mild infection.For simplicity we assume that critical infection always occurs after passing through a stage of severe infection, while in reality there appears to be some individuals who progress directly from mild to critical infection.Similarly, we assume that only individuals who have progressed to critical infection die, though there is now some evidence that death can occur unexpectedly in individuals who are not already hospitalized.We do not think that any of these assumptions affect the main conclusions of our paper, which does not focus on hospital resource use or morbidity/mortality estimates.In general our model allows for individuals at all stages of infection to transmit to others.However, for this paper we have assumed that only individuals with mild infection can transmit.We think it's likely that an individual is most infectious during this stage, when they would still be in the community and feeling well enough to interact with others.We thus ignore transmission from hospitalized patients to their healthcare providers ( β 2 = β 3 =0).We make the standard SEIR model assumption that the time until an infected individual experiences symptoms is the same as the time until they become infectious, whereas it has now been shown for COVID-19 that there is significant transmission risk starting ~1 day before symptom onset.While this disease feature is important for studies that examine symptom based case detection/isolation, for simplicity we have ignored this feature in our model, which doesn't focus on these issues.The serial interval produced by our model parameters agrees with observed values, and so we believe our timescales for infections spread are realistic.We do not explicitly consider age-dependent rates of infection or progression to more serious stages.
The differential equation version of our model is available as an online simulation tool in which users can explore the effects of these assumptions of model structure as well as parameter values on model outputs : https://alhill.shinyapps.io/COVID19seir/

Stochastic network implementation
To avoid the assumptions inherent in formulating an epidemiological model using standard differential equations (e.g.assuming a randomly-mixing population, deterministic dynamics, and exponentially-distributed durations of each infection stage), we implement the model as a stochastic process simulated on a transmission network.
We believe that this implementation is important for our research questions, for a few main reasons.Firstly, respiratory infections are spread by close physical contact that occurs in highly structured contact networks, which impact the growth rate of outbreaks, the relationship between an individual's inherent infectiousness and the basic reproductive ratio R 0 , the variability in secondary infections between individuals, and the effects of control measures on spread.Secondly, typical differential equation models implicitly assume that the durations of infection stages are extremely long-tailed, which can lead to unrealistic conclusions about the timescale of the epidemic response to control measures as well as to the relationship between the early growth rate, serial interval or generation time, and R 0 .Finally, we believe it is important to model the uncertainty in epidemic trajectories that arises from the inherent stochasticity of transmission.
In our stochastic formulation, we assumed that the duration of each stage of infection was gamma-distributed, with both the mean and variance taken from the literature.Individuals were connected with a fixed, weighted contact network that determined the potential paths of transmission.The network is represented as a sparse matrix to save memory (a list of the index of each node in an edge, along with the edge weight).The model was implemented with a discrete time stochastic process that tracked the state of each individual and the time since they first entered that state.The model was implemented in Python using JAX, a framework for generating high-performance code optimized to run on GPUs.Our code was entirely run in the cloud on Google Colab.The code is available at : https://github.com/alsnhll/COVID19NetworkSimulations

Model parameters
We estimated the distribution of the duration of each stage of infection from the literature (Table 1) .For the incubation period, we used an estimate of 5 4 days from [2,4], which is consistent ± with most other estimates.The duration of mild infection, which we assume is roughly equal to the infectious period, can be estimated from a few different sources: a) the duration of mild symptoms, b) the time from symptom onset to hospitalization (e.g.time to progress to severe stage), or c) the duration of viral shedding via sputum or throat swabs, d) inferred from both the incubation period and the "serial interval" between symptom onset in an index case and a secondary case they infect.Considering (d), we took an estimate of the serial interval from Bi et al [2] , who used a large cohort of transmission pairs and reported values separately for situations where the index case was not rapidly isolated or hospitalized during mild infection.Similar values were found in [5][6][7][8].Some other studies have estimated smaller values (e.g.[9]), likely due to rapid isolation of symptomatic cases in Asia [6].This value implies an infectious period of 6 2 days.This is ± relatively consistent with estimates of the time from symptom onset to hospitalization [10][11][12][13], and is roughly equivalent to the time at which average viral loads drop 4-5 orders of magnitude from peak values [14].
The duration of severe infection in our model is equivalent to the time from hospital admission to recovery for individuals who did not progress to the critical stage, or the time from hospital admission to ICU admission (since critical cases require ICU-level care).Since it is hard to find direct estimates of this duration, we instead used estimates of the total time from symptom onset to ICU-admission (e.g.combined length of mild + severe infection) [12,13], and subtracted the inferred duration of mild infection.This led to an estimate of 6 4.5 days.We estimated the ± duration of critical infection (the length of ICU stay) directly from cohort studies to be 8 +/-6 days [12,15].With these estimates, we verified that the total time from symptom onset to death/recovery agreed with data (~20 10 days) [5,12,16].Note that we assumed that the ± duration of each stage of infection was independent of the previous stage and was also independent of the eventual outcome.
In each stage of infection, an individual can either progress to the next stage or recover, and the probability of each was also estimated from the literature [1,17,18] (Table 2) .These large clinical cohort studies estimated that ~ 20% of infections required hospitalization (i.e.progress to severe stage), ~5% require ICU care (i.e.progress to critical stage), and an overall case fatality risk of 2%.This leads to probabilities of progression of 0.2 from I 1 → I 2 , 0.25 from I 2 → I 3 , and 0.4 from I 3 → D. However, there is significant uncertainty in these values.More recent estimates suggest the rates of progression to more serious stages of infection might be lower after correcting for asymptomatic/undiagnosed cases in China [16], but in contrast, recent studies from the US suggest higher rates of ICU admission and death among hospitalized patients compared to in Asia [19,20].Since the results of our paper focus on the timing of the peaks of different infection stages but not on the prevalence at these peaks, they are not sensitive to these assumptions.
We chose a value of the transmission rate β such that the early epidemic doubling time was ~ 4 days (growth rate r = 0.17/day) and the basic reproductive rate R 0 = 3.While some studies have estimated R 0 values as low as 2, these have generally used estimates based only on the serial interval which are mathematically problematic, used short estimates of the serial interval that are influenced by rapid case isolation in Asia as opposed to longer values found in other studies that correct for this, and fit to longer doubling times that what was observed early in the outbreak in the US and Europe.For a simple unweighted network, we estimate β using the formula R 0 = β T 1 ( n -1) where, n is the mean degree of the network and T 1 is the average duration of mild infections.This relationship is modified for the weighted two-layer network, ).As this equation suggests, the rate of w HH w EX n HH n EX infection is constant per time per contact for a given contact type, and hence would be described as "density-dependent" transmission.
The time at which we implemented interventions in our simulations was chosen to occur at a realistic time in the epidemic relative to real responses to COVID-19.To estimate this time for a typical US metro area, we downloaded case and death counts for each US county and aggregated them into the top 50 largest metro areas.Then we collected the time that stay-at-home orders were implemented in each of these regions, and looked at the median cumulative case and death counts by that day, and chose our intervention time to match those values.We found that there were on average around 200 cases per million inhabitants at time of stay at home intervention (range [30,1000]), and ~5 [0-20] deaths per million.We assumed that reported "cases" are hospitalized individuals only (I 2 ).These values were recreated in our simulation in well-mixed populations on Day 40, which we used as the intervention time.At this time, ~0.5% of the population had ever been infected (including E, I 1 , I 2 , I 3 , R, and D).Since the median day shelter-in-place orders were implemented across these metros was April 1, Day 0 in our simulation corresponds to ~ Feb 20.For simulations in other networks, we kept R 0 constant but due to the population structure, the exponential growth rate of the epidemic varied between different values of the household and external contact structure.Thus for each structure we chose slightly different intervention start times to keep the infection prevalence consistent across comparisons.The start times varied from Day 43 (when w EX / w HH = 3, 1), Day 45 (when w EX / w HH = 1/3) to Day 55 (when w EX / w HH = 1/9).[1,17,18] Severe infection I 2 f 2 0.25 [1,17,18] Critical infection I 3 f 3 0.4 [1,17,18] Well-mixed network structure

Table 1: Model parameters for duration of each stage of infection
We approximated a well-mixed population by randomly connecting each individual to 100 other individuals in the population.While a truly "well-mixed" network would connect every one to everyone else, with the large population sizes we use (10 6 ), this would require huge amounts of memory and negate the computational efficiency of using sparse matrices to represent the networks.Since in reality each individual will only transmit to a few others before recovering, any uniform random network with a large degree is a good approximation to a fully-connected network.

Two-layer household network structure
Construction: We constructed a weighted two-layer network, consisting of a layer for within-household connections and another for external connections.Individuals were first assigned households using the distribution of household sizes in the United States (data obtained from the 2010 census, mean household size n HH ).All individuals in a household .5 ~2 were connected to each other.Each individual was then assigned random external contacts.The degree distribution for external connections was obtained from contact survey data that recorded daily interactions of individuals [22,23].This data was originally collected for a subset of countries and then projected to other countries using a wide range of demographic data.The contacts are age structured and include the type, duration, location and frequency of the contact.These surveys were designed to capture interactions relevant to the spread of respiratory diseases, and include interactions consisting of either physical contact or close face-to-face conversations.From this data, we obtained daily non-household contacts by summing 'work', 'school' and 'other' contacts.For the United States there were on average n EX (mean standard deviation) daily non-household contacts, equivalent to 3x 7.5 2 ~ ± ± household contacts.The variance was obtained by the variance in the mean across all age groups.We assigned external degrees to individuals following a binomial distribution with this mean and standard deviation.This assignment was done randomly and did not depend upon the size of the person's household.The network layer was created by giving 'stubs' to individuals equal to their external degrees.These stubs were then randomly paired between individuals in the population to create connections.In addition to the number of contacts, the probability of infection also depends upon the duration and intensity of the contact.We assigned weights ( w HH , w EX ) to the two layers of the network to account for this.We considered different scenarios (keeping R 0 fixed) where, w HH and varied w EX to reflect the 1 = 3, 1, 1/3, 1/9 = relative importance between household and external contacts.
In order to investigate the robustness of our results with respect to details in the large-scale clustering of the network, we also constructed a hierarchically structured external layer using ideas from nested metapopulation models [24,25].Individuals were assigned to 'neighborhoods' of size 10,000 (there are 100 such neighborhoods for the population size of 1 million) and as an extreme case 90% of their external connections were forced to be within the same neighborhood with n EX as before.

2 ~ ±
Intervention: Intervention, corresponding to social distancing measures, was modeled by reducing the weight of the external layer, w' EX w EX where, is the 1 ) = ( − ε (0 ) ε ≤ ε ≤ 1 'intervention efficacy'.When we are in the parameter regime where the probability an individual infects any given external contact over the duration of their infectious period is significantly less than one (i.e.R 0 EX < n EX ), reducing the weight of external contacts is equivalent to randomly removing external contacts (i.e.n' EX n EX ).Only in the regime where the transmission rate 1 ) = ( − ε per contact is so high that R 0 EX is limited only by the number of contacts would these two alternative methods of implementing social distancing lead to different results.Household contacts were either unaffected ( w' HH w HH ) or doubled ( w' HH w HH ) during intervention, to = = 2 represent the increased time spent with household members.Partial relaxation of intervention : We modeled a scenario of partial relaxation of social distancing measures in which every household could "merge" with another household.This relaxation altered the household layer so that all households in the network were paired with another random household and the two were merged to create a fully-connected joint household ( n' HH ).We considered two scenarios for how the external layer changed during partial relaxation 5 ~ of intervention.In the baseline scenario, the external layer was the same as during intervention.In a second scenario, the number of external contacts per individual was reduced so that the average number of total contacts was the same before and after merging ( n' EX n EX -n HH ).This = partial relaxation was only conducted for the scenario where household and external connections had the same weight ( w HH and w EX ).
Individual probability of infection as a function of household size: We computed the individual probability of infection retrospectively, after the epidemic had died out, for the case of a 100% effective intervention.We counted the number of individuals who were ever infected by the end of the epidemic and calculated the corresponding distribution of their household sizes.This is a conditional probability that gives the probability of household size, given that an individual was infected P(HH size|inf).The probability of infection given household size was then calculated using Bayes' rule, P(inf|HH size) = P(HH size|inf) * P(inf)/P(HH size) where, P(inf) is the fraction of the total population that was infected during the epidemic and P(HH size) is the distribution of the household sizes in the population.The probability was averaged over 10 iterations of the simulation.

Five-layer network structure
We constructed a non-weighted 5-layer (1 household and 4 external) network for an age-structured population with realistically structured external layers.The population was divided into four age groups: preschool aged (ages 0-5), school-aged (ages 5-19), working-aged (ages 19-64) and elderly (ages 65+).The distribution of ages in the United States was obtained from the 2018 World Bank Age Structure data which consists of the population divided into 5-year age groups.In addition to the broad age groups, we also kept track of the 5-year age group that an individual belonged to.The contact survey data [23] used to construct the 2-layer network was also predominantly used here to determine the statistical properties of the layers.
Household layer : The household layer was constructed in the same manner as in the 2-layer network.Individuals were assigned to fully-connected households using the distribution of household sizes in the United States from the 2010 census (mean household size, n HH ).

.5 ~2
School layer : The school layer contained connections between the school-aged age group in the population.This external layer was constructed using the technique described by Ball et al [26], where a network layer with a given degree distribution and correlations among connections (i.e."clustering" or "transitivity") can be constructed.The degree distribution in this layer was obtained from school contact survey data [23], which estimated that the school-going population in the United States, on average, had n SCHOOL school-related contacts daily.The 7.3 1.8 ~ ± variance was obtained by the variance in the mean across the school-aged (5-19) age groups.Individuals were assigned degrees randomly from a binomial distribution with this mean and standard deviation.The age-structure of contacts at school suggests a significant level of clustering by age group.To create correlated connections, the method of Ball et al requires two additional parameters: The number of groups to divide the population into, and , which is n r roughly the extent to which individuals within the same group are connected.corresponds r = 1 to individuals being connected only within their group whereas implies completely random r = 0 connections without any correlation with members of their own group.Averaged over the school age groups (5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19), we found that of school contacts for an individual belonged to their 7% ~5 own age group.Since there are three 5-year age groups in our school-aged population, we divided our population into those three groups ( ) and chose .3 n = 0.57 r = Work layer : The work layer consisted of connections between the working-aged group in the population.This layer was constructed similarly to the school layer.We obtained the mean and standard deviation in number of daily work contacts from the contact survey data ( ). .0 2.3 5 ± The variance was obtained by the variance in the mean across working-aged (20-64) age groups.Individuals were randomly assigned a work-place degree from a binomial distribution with the mean and standard deviation.Then we used a separate study by Potter et al that mapped real work-place networks to estimate the level of clustering (transitivity), at ~0.1 [15].Note that Potter et estimated a higher degree, since their network contained total contacts in a work network and not just the daily contacts as given by the contact survey data, but the coefficient of variation is similar.We again used the Ball et al technique [26] to create clustering in the network.High transitivity can be achieved by choosing appropriate correlation parameters and .We assumed this clustering arose from the fact that people belonging to the same n r work-place have a higher chance of being connected to each other.According to NAICS (North American Industry Classification System), of businesses in the United States have 0% ~8 10 ≤ employees and so for the sake of simplicity, we assigned each individual to a 'work-place' of size ten ( ).We picked in order to have a high level of transitivity ( n = 10 # of working individuals 0.8 r = ) while also ensuring inter work-place connections..12~0 Friend (social contacts) layer : The friend layer represents social contacts of people, their 'friend circles'.Individuals were assigned to fully-connected friend groups, where friend groups consisted of people belonging to the same age group (preschool, school, working, elderly).The distribution of sizes of these friend groups were obtained from Wrzus et al [27], which is a meta-analysis of the effects of age on social networks.From their data, we estimated that the mean sizes of friend groups for individuals less than 20 years of age is , that for the 0 ~1 working age population and for the elderly.These constitute total social contacts for ~7 ~5 the individuals and not just their daily interactions as given by the contact survey data.The 'other' category in the contact survey data [23] gives the number of daily interactions that an individual has that are not within the household, at school or at the work-place.In our network, the friend layer and the community layer together constitute this 'other' category.According to the data, averaged over the age groups, there are such interactions for an 4.3 1.9 ~ ± individual in the United States.The variance was obtained by the variance in the mean across all age groups.Since the total social contacts are much higher than this daily value, we scaled the sizes of the friend groups ( n FRIEND n FRIEND ) to reflect daily social contacts.The scaling → 4 / factor was chosen to ensure that the community layer didn't end up being too sparse.We chose to do this instead of creating a weighted network for the sake of simplicity.The friend group sizes were drawn using the negative binomial distribution to account for the large variance (estimated variance post scaling: 6.25, 2.5, 1.75 for the three age-groups) seen in the data.
Community layer : This layer constitutes the additional random contacts an individual has during the course of their day.As mentioned previously, together with the social layer this constitutes the 'other' category in the contact survey data.We chose the average degree for this layer, n COMM such that the combined degree for the two layers matches what is seen in .72 0.76 ~1 ± the data.We used a binomial distribution and assigned degrees randomly to the individuals.This layer was constructed in the same manner as the external layer in the 2-layer network.It amounts to using the Ball et al [26] technique with and n = 1 .r = 0 Sensitivity analysis: We introduced the idea of "neighborhood" clustering to check the robustness of the results to clustering of contacts at an intermediate-scale between households and the city as a whole.As in the 2 layer network, individuals were assigned to neighborhoods of size 10,000.School and community layer contacts for individuals were predominantly within their neighborhood.The community layer was created by enforcing 90% ( ) of the .9r = 0 connections to be within the same neighborhood ( ) with n COMM .00 n = 1 .720.76 ~1 ± School-aged individuals from each neighborhood, belonging to the same 5 year age group, were assigned to schools of size 500 (~ average size of public schools in the US according to the 2017 data from the National Center for Education Statistics).The degree distribution of the school contacts was the same as before, n SCHOOL but all school contacts for an 7. Intervention : The social distancing intervention was modeled by deleting a certain percentage of external connections.School connections were always completely deleted during intervention, whereas social and community connections were deleted depending upon what we termed as the 'efficacy' of intervention.For example, efficacy corresponds to deleting 5% 8 5% 8 of contacts in these layers.We considered two scenarios for the effect of intervention on the work-layer.In one case, similar to the social and community layer, a percentage of work contacts was deleted depending upon the intervention efficacy.Random deletion of connections leads to a large reduction in the transitivity of the work layer, from to .In the .12~0 .02 ~0 second case, the effect of intervention was modeled as a clustered deletion of workplaces instead.For example, intervention efficacy corresponds to of workplaces being 5% 8 5% 8 dissolved.Clustered deletion still maintains a high level of transitivity in the work layer..10~0 Note as all school connections were completely deleted during intervention, the total effective efficacy of intervention was a bit higher than that for the social, community and work layers.For example, efficacy in these external layers corresponds to a total efficacy of .5% 8 8% 8 Probability of infection for an individual working during intervention : We calculated the probability of infection for two intervention efficacies (85%, 70%) at day 300 after the start of the outbreak.We first obtained the fraction of the infected people (at day 300) who were still working during the intervention.This gives the conditional probability that an individual was working during intervention given that they were infected, P(working|inf).We calculated the probability of infection given that an individual was working during intervention using Bayes' rule, P(inf|working) = P(working|inf) * P(inf)/P(working) where, P(inf) is the fraction of the total population that was infected by day 300 of the epidemic and P(working) is the fraction of the total population that was working during intervention.The probability was averaged over 10 iterations of the simulation.
Probability of infection for an individual living with working household members during intervention : This was also calculated at day 300 of the epidemic for the two intervention efficacies and, averaged over 10 iterations of the simulation.We obtained the fraction of the infected people (at day 300) who had at least 1 household member who was working during intervention.This corresponds to the probability that an infected individual had at least one working household member during intervention, P(HH working|inf).As before, the probability of infection given that an individual was living with working household members during intervention was then calculated using Bayes' rule, P(inf| HH working) = P(HH working|inf) * P(inf)/P(HH working) where, P(inf) is the fraction of the total population that was infected by day 300 of the epidemic and P(HH working) is the fraction of the total population that had at least one working household member during the intervention.
Probability of infection for a non-working individual with no working household members during intervention : This was calculated in the same way as the other probabilities.We obtained the fraction of the infected people (at day 300) who were not working and had no working household member, P(HH not working|inf).As before, the required probability was then calculated using Bayes' rule, P(inf| HH not working) = P(HH not working|inf) * P(inf)/P(HH not working) where, P(inf) is the fraction of the total population that was infected by day 300 of the epidemic and P(HH not working) is the fraction of the total population that was not working and had no working household members during the epidemic.

COVID-19 Data
Wuhan, China : Data from Wuhan, China was obtained from the two daily situation reports published each day: http://wjw.wuhan.gov.cn/ztzl_28/fk/yqtb/index_11.shtml .We extracted new cases, new deaths, the number of individuals currently hospitalized with severe infection (which we took as a proxy for "hospitalized") and the number of individuals currently hospitalized with "critical" infection (which we took as a proxy for individuals in the ICU).Data was already digitized by Li et al [28] for January and February ( https://github.com/c2-d2/COVID-19-wuhan-guangzhou-data); we added data into March.For some dates the numbers of severe and critical cases were only reported for the entire province of Hubei, and in those instances, following Li et al, we assumed the proportion of those attributable to the city of Wuhan was equal to the proportion of currently active cases occurring in Wuhan.The vast majority of the Hubei outbreak took place in Wuhan.
Lombardy, Italy : Data on daily new cases and deaths as well as current patients hospitalized or in ICU for the Lombardy region of Italy was downloaded from Github repository maintained by the Department of Civil Protection in Italy : https://github.com/pcm-dpc/COVID-19` Madrid, Spain : Data for daily new cases, daily deaths, daily new hospital admissions, and daily new ICU admissions were obtained from an online application maintained by the National Center for Epidemiology, using data from the Ministry of Health: https://cnecovid.isciii.es/covid19/ .In the "documentation and data" section of the application there is a link to a .csvfile with all the data used in the web app.
• S: Susceptible individuals • E: Exposed individuals -infected but not yet infectious or symptomatic • I i : Infected individuals in severity class i .Severity increases with i and we assume individuals must pass through all previous classes ○ I 1 : Mild infection ○ I 2 : Severe infection ○ I 3 : Critical infection • R: Individuals who have recovered from disease and are now immune • D: Dead individuals • N=S+E+I 1 +I 2 +I 3 +R+D Total population size (constant) To describe the average time course in a large, well-mixed population, the model can be represented by the following set of differential equations: where, and with the weight and mean degree of the household f HH =

Table 2 : Model parameters for probability of progressing from each stage of infection 6
New York City, New York, USA : Daily new cases and deaths were downloaded from the Github repository of the New York City Department of Health and Mental Hygiene: https://github.com/nychealth/coronavirus-data .Number of currently individuals hospitalized or in ICU by date was obtained from the Github repository for digital news platform The City, who obtains this data directly from the New York state governor's office: https://github.com/thecityny/covid-19-nyc-dataLos Angeles County, California, USA: Daily new cases and deaths were obtained from the Github repository maintained by the Los Angeles Times newspaper: https://github.com/datadesk/california-coronavirus-data .The number of individuals currently in the hospital or ICU was obtained from the California Health & Human Services Open Data Portal: https://data.chhs.ca.gov/dataset/california-covid-19-hospital-data-and-case-statistics/resource/6 cd8d424-dfaa-4bdd-9410-a3d656e1176e?view_id=b23b0158-a85d-4bf2-95b1-96f7556f7342