Traveler data
We stratified each population into 9 age groups by a 10-year band, with the last age group set as those 80 years and older. We simulated both natural population dynamics (birth and death rates) and population movement due to inbound and outbound travelers in each city. In this study, we collected inbound international inbound and outbound traveler statistical data from multiple global and local statistical sources 29–33. For the domestic inbound and outbound travelers statistical data, we retrieved from local news and travel department websites 32–37. The average daily inbound and outbound travelers from international and domestic sources before the outbreak of COVID-19 are listed in Table 1. The daily change of international travelers in Daegu and Nairobi were adjusted according to the daily global mobility data, and the daily change of international travelers in New York and Los Angeles were adjusted according to the monthly change of I-94 arrivals data 38. We adjusted the daily domestic travelers according to the daily change of mobility data from Google mobility reports 25.
Table 1
Daily import and export travelers in the four cities before the outbreak of COVID-19
Travelers
|
New York
|
Los Angeles
|
Daegu
|
Nairobi
|
Domestic import
|
154637
|
75249
|
31085
|
1117
|
International import
|
13658
|
11578
|
2289
|
2773
|
Domestic export
|
162450
|
77173
|
31176
|
931
|
International export
|
13231
|
11340
|
3752
|
361
|
The domestic and international incidences of COVID-19 were estimated using daily infected cases divided by the total number of travelers:
$${\text{i}.{\theta }}_{t}= \frac{{i.I}_{t}}{i.T}$$
$${\text{d}.{\theta }}_{t}= \frac{d.{I}_{t}}{d.T}$$
where i.θt and d.θt are global and domestic incidence of COVID-19 infection in day t, and i.It is global daily infected cases in day t, and d.It is domestic daily infected cases in day t. Both global and domestic infected cases were adjusted with a 7-day moving average. The estimated incidence rates were adjusted to age-specific incidence rates according to the global tourism age structure and country age structures.
Population mobility
We retrieved population mobility data from Google Covid-19 community mobility reports 25. Figure 6 shows the change of mobility in each city since the outbreak of COVID-19. The mobility in working, other activities and school substantially dropped between march and mid-April in New York, Los Angeles and Nairobi. By contrast, Daegu did not show much reduction in terms of any category of mobility. The average mobility increased after mid-April due to the opening up policy in the US. From the mobility data, we can also tell that Nairobi started loosening their social distancing and working-at-home policies since April. The mobility of home increased since the intervention strategies were implemented, which might indicate growing contact rates at home. The time-series of contact matrices were adjusted by the change of daily change of mobility.
SEIR-HQD model framework
In this study, we adapted an SEIR model to an age-specific SEIR-HQD model for a period of 365 days. SEIR-HQD model considers 7 states of infection including susceptible (S), exposed (E), infectious (I) and recovered (R), hospitalized (H), quarantined (Q) and dead (D). The SEIR-HQD model incorporates the age structure, birth rates and death rates dynamics of the affected population in Daegu, New York, Los Angeles and Nairobi.
Figure 7 Schematic framework of SEIR-HQD epidemic model “S = Susceptible, refers to the full city population”, “E = Exposed, refers to infected but not infectious yet”, “I = Infected, refers to population who are infected and infectious”, “R = Recovered, refers to the population who are recovered”, “Q = Quarantined, refers to the population who are quarantined”, “H = Hospitalized, refers to people who are hospitalized, “D = Dead, refers to the population who are dead infected”. ITs and ETs refer to the imported and exported travelers who are susceptible, respectively. ITe and ETe refer to the imported and exported travelers who are exposed, respectively. ITi and ETi refer to the imported and exported travelers who are infected, respectively. \(\nu\) is the birth rate per thousand population, \(\mu\) is the death rate of population, \({\beta }\text{S}\text{I}\) refers to the infection force, \({\sigma }\) is incubation rate, \({\gamma }\) is recover rate, \({\omega }\) is the death rate of infected population, \({\phi }\) is the hospitalization rate, \({\rho }\) is quarantine rate.
Mathematical model and parameters setting
When the susceptible populations are exposed to infectious individuals, a percentage then transition into infected status at a given probability defined by an age-specific transmission rate. After the incubation period, the exposed population then become infectious, but if they are quarantined, we assume that they do not impact susceptible individuals in the next generation. For those who are infectious, given the hospitalization rate of infectious cases, we further calculate the number of people who are in need of further medical care in the hospital. Our model also simulates the quarantine of individuals and hospitalized cases are sub-states of infected cases that will not cause a secondary infection. The quarantine individuals might also become hospitalized. The epidemic evolution model is described as follows:
![](https://myfiles.space/user_files/44073_bbc9ffc5e562ebe7/44073_custom_files/img1598297257.png)
The parameters involved in the model are obtained from literature and are presented in Table 2.
Table 2
Parameters in the age-specific SEIR-HQD model
Parameters
|
Value
|
Reference
|
Basic reproduction number R0
|
Varies by city, see Appendix 1.
|
Estimated in this study
|
Transmission rate
|
Varies by age, see Appendix 1.
|
Estimated in this study
|
Average incubation period, dinc
|
5.8 days (4.8–6.8)
|
Backer et al (2020)
|
Average duration of infection, dinf
|
7–11 days (assume growing by age)
|
Cao et al (2020) and Bi et al (2020)
|
Initial number of infected, I0
|
2 cases per million in four cities
|
Assumed in the study
|
Hospitalization rate, φit
|
Varies by age, see Appendix 1
|
Ferguson et al (2020) and Verity et al (2020)
|
Quarantine rate, ρ
|
0%-50%
|
Assumed in scenarios
|
Fatality rate, ωi,t
|
Varies by age, see Appendix 1.
|
Verity et al (2020)
|
Rt estimation
To simulate the spread of COVID-19 in different policy packages, we estimated the location-specific reproduction number, Rt, with serial interval data and incidence rates over time in the four cities. Rt is the average number of secondary cases over the total infected individuals at certain time 42. The serial interval data was retrieved from Du et al (2020). We assume a gamma prior distribution for serial interval using Bayesian statistical inference based on the above transmission estimation framework. After a 1000 burn-in, we run 15,000 iterations and sampled every 100th step via Markov Chain Monte Carlo simulation over a 7-days evaluation window and generated serial interval from the beginning of the outbreak to July 1, 2020. Rt is estimated using Wallinga and Teunis approach 44. R0 in each city is estimated using the average value of Rt over the first 30 days since the outbreak time.
Age-specific transmission rates
The transmission rate differs from the location, population mobility and contact probability. Therefore, we calculate the transmission rate matrix based on contact matrices in different location settings at country level. We first adjusted the contact matrices by age-specific population, the more population in certain age group, the higher probability of this group population gets in contact with one in other age groups. The contact matrices that were developed in Prem et al (2017) depend on the national population density. At city-level contact matrices, we further adjusted the contact matrix data by weights of population density in each city over the national average.
![](https://myfiles.space/user_files/44073_bbc9ffc5e562ebe7/44073_custom_files/img1598297769.png)
where
and
represent age groups,
is contact matrix in each city,
is the proportion of population in age group
to the total population in a city,
is transmissibility, which is defined as the transmission probability of a contact between an infectious individual with a susceptible one,
is the basic reproduction rate, and
is the transmission rate matrix among individuals in different age groups. Transmission rate indicates the rate of infectious cases infect secondary cases in certain age-group population, which is the product of transmissibility and contacts.
Scenario design for interventions and the timing of policy action
Applying the SEIR-HQD model, we designed two sets of scenarios to explore: 1) the age-specific effects of policy interventions, 2) the effects of age-targeting policy intervention, and 2) the effectiveness of policy action at different time points since the diagnosis of the first case.
For the age-specific effects, we designed 8 scenarios that tested school distancing, reduction in other mobility, increasing quarantine rates, city lockdown and a mixture policy package (Table 3). The city lockdown intervention refers to both inbound and outbound international travelers and domestic travelers are prohibited to travel during the lockdown period.
Table 3
Scenario design for age-specific effects analysis.
Intervention
Scenario
|
School closure
|
Working from home
|
Reduction in other mobility
|
Quarantine rate
|
City lockdown
|
Scenario A
|
100%
|
0%
|
0%
|
0%
|
0%
|
Scenario B
|
0%
|
50%
|
0%
|
0%
|
0%
|
Scenario C
|
0%
|
80%
|
0%
|
0%
|
0%
|
Scenario D
|
0%
|
0%
|
50%
|
0%
|
0%
|
Scenario E
|
0%
|
0%
|
80%
|
0%
|
0%
|
Scenario F
|
0%
|
0%
|
0%
|
10%
|
0%
|
Scenario G
|
0%
|
0%
|
0%
|
0%
|
100%
|
Scenario H
|
100%
|
50%
|
50%
|
10%
|
100%
|
We also reviewed the policy actions in four cities from the first case detected to July 1, 2020 (SuFigure 2). We followed the real policy actions to simulate the business-as-usual scenarios in the four cities. Then we move each strategy 1 week earlier to see the effects of early actions.