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Classifications: SOCIAL SCIENCES including Anthropology; Economic Sciences; Political Sciences; Social Sciences; and Sustainability Science.
Determination of COVID-19 parameters for an agent-based
model: Easing or tightening control strategies
Ali Najmi
a
, Farshid Safarighouzhdi
a
, Eric J. Miller
b
, Raina MacIntyre
c,d
and Taha H. Rashidi
a*
a
Research Centre for Integrated Transport Innovation, School of Civil and Environmental Engineering, The University of New Sou th Wales, Sydney, Australia
b
Department of Civil & Mineral Engineering, University of Toronto, 35 St. George Street, Room 305A, Toronto, ON M5S 1A4, Canada
c
Arizona State University College of Health Solutions, Phoenix, Arizona, USA
d
Kirby institute, Faculty of Medicine, the University of New South Wales, Sydney, New South Wales, Australia
(a.najmi@unsw.edu.au, f.safari@unsw.edu.au, miller@ecf.utoronto.ca, r.macintyre@unsw.edu.au, rashidi@unsw.edu.au)
Different agent-based models have been developed to estimate the spread progression of
coronavirus disease 2019 (COVID-19) and to evaluate different control strategies to control
outbreak of the infectious disease. While there are several estimation methods for the disease-specific
parameters of COVID-19, they have been used for aggregate level models such as SIR and not for
agent-based models. We propose a mathematical structure to determine parameter values of agent-
based models considering the mutual effects of parameters. Then, we assess the extent to which
different control strategies can intervene the transmission of COVID-19. Accordingly, we consider
scenarios of easing social distancing restrictions, opening businesses, speed of enforcing control
strategies and quarantining family members of isolated cases on the disease progression. We find the
social distancing compliance level in the Sydney greater metropolitan area to be around 85%. Then
we elaborate on consequences of easing the compliance level in the disease suppression. We also
show that tight social distancing levels should be considered when the restrictions on businesses and
activity participations are easing.
Keywords: Social distancing; Compliance level; Agent-based disease spread model; Control strategies
1. Introduction
Coronavirus disease 2019 (COVID-19) first emerged in Wuhan, China in December 2019 and is an ongoing
pandemic caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). China implemented
intense quarantine and social distancing and full lockdown of the cities in Hubei province on January 23
rd
with
the aim of controlling the pandemic, which has resulted into more than 81,000 reported cases so far (WHO
Team, 2020). The disease has already gone outside Hubei, reaching to at least 26 countries in all parts of the
globe by February. Control strategies of testing, tracing and lockdowns or other social distancing have been used
in many other countries successfully, whilst countries which have delayed on lockdowns have had more severe
epidemics. While the policies are effective and the pandemic has been largely controlled within China, the
intense quarantine and full lockdown come with huge human and economic cost, which may not be acceptable
in all countries. On the other hand, relaxing the restrictions can worsen the strain on the health care systems and
threaten societies by resurgence of infection.
Enhanced surveillance and testing, case isolation, contact tracing and quarantine, social distancing, case
isolation, household quarantine, teleworking, travel bans, closing businesses, and school closure are the most
common strategies implemented worldwide for slowing down infection spread. While many of the strategies are
currently in place in many countries, governments are looking for best policies for easing or lifting the control
strategies. Thus, the extent to which restrictions can be lifted so that the disease remains under control and the
economies do not suffer significant damage is a critical question.
While mathematical modelling of disease spread has a long history of providing solid foundations for
understanding disease dynamics, the models are sometimes aggregated, with population heterogeneities ignored.
These heterogeneities include zone population size and density, population age structure, age-specific mixing,
the size and composition of households, and, critically, travel and activity participation patterns which may have
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important impacts on epidemic dynamics and on the effectiveness of possible interventions (Grefenstette et al.,
2013). Recently, the development of disaggregated models in infectious disease epidemiology has received
considerable attention owing to their capability to capture the dynamics of disease spread combined with the
heterogeneous mixing and social networks of agents. While all the developed agent-based modes can capture
complex interactions between agents and to some extent their decisions, they cannot consider the interactions of
agents within a household and therefore, the interconnection between the travel decisions and activity
participation of different household members. For example, teleworking may shift agents to participate in other
activities or school closure may affect the activity patterns of all the household members. Building on the
preliminary version of the SydneyGMA model, which is an activity-based model developed for the Sydney
greater metropolitan area (GMA, see Figure A1), this paper focus on proposing a an agent-based disease
transmission model estimation that accounts for interactions between people.
Furthermore, the virologic and epidemiologic characteristics of SARS-CoV-2, including transmissibility
and mortality, are not yet fully known. Despite a surge of efforts to estimate the disease spread parameters, these
parameter estimates typically show considerable variation from one study to another. They also are only
applicable for aggregated models such as SIR-based models. To the best of our knowledge, there are no
guidelines or research on the parameter estimation of pandemic diseases modelling in agent-based models,
mainly due to the complexity of agent-based models and the existence of many interactive parameters. This
paper contributes to the determination of COVID-19-specific parameters useful for agent-based modelling of
disease spread. Further, of the few prior attempts to calibrate parameters (Chang et al., 2020), these efforts have
been unstructured in that the interconnections among the parameters on the pandemic effects are not considered.
Unstructured calibration refers to the sequential adjustments of parameters in a relatively ad hoc and non-
systematic way. Although an unstructured calibration approach may reproduce observed statistics, the approach
can be problematic for many reasons, including the failure to consider interactions among parameters, and
excessive focus on reproducing observed statistics, at the possible sacrifice of model system validity. In this
paper we use response surface methodology (RSM) to efficiently calibrate the model while considering the interactions
of their constituent parameters. By optimally calibrating parameters, their unbiased impacts on disease spread
can be captured. Given the observed statistics of the Sydney GMA, including the number of cases and public
transport (PT) usage after lockdown, we calibrate the parameters for an agent-based model for the Sydney
GMA. It is noteworthy to say that the transport activity-based model of Sydney includes the actual transport
network with models reflecting the overall travelling behaviour of people in an urban metropolitan area.
After calibration of the transmission model parameters, we use the model to explore several scenarios
examining the influences of easing social distancing restrictions, opening up businesses, timing of control
strategies implementation, and quarantining family members of isolated cases to intervene the disease
progression. The intent is to provide guidance to public health agencies worldwide as they consider easing of
restrictions.
2. Model description and calibration
This section briefly explains the activity-based model used to model the pandemic spread and then, the
methodology for model parameter calibration is introduced.
2.1 SydneyGMA model
The agent-based disease transmission model in this paper is built on an activity-based model developed for the
Sydney GMA, called SydneyGMA model, which has several properties that are valuable for analysing the
effectiveness of COVID-19 control strategies. Firstly, SydneyGMA uses the Travel/Activity Scheduler for
Household Agents (TASHA), an operational, state-of-the-art model of daily travel and out-of-home activity
participation that considers both individual activities as well as joint household activities, along with a full range
of within-household interactions (Miller and Roorda, 2003; Miller et al., 2005; Roorda and Miller, 2006; Roorda
et al., 2008, 2009; TMG, 2015). In addition to Sydney, TASHA has been applied in Toronto, Canada (where it is
the operational model for Toronto transportation planning agencies), Helsinki, Finland, and Temuco, Chile. All
parameters of the Toronto model are transferred to the Sydney model. Consequently, in the case of school
closures or widespread working from home, the activities of households will be realistically rescheduled,
factoring in the extra time derived from removing school- and work-related activities from the household's
regular schedule. Secondly, mode choice is computed for each household individually, and interactions between
household members using their vehicle on individual or joint trips are captured, as well their usage of other
modes of travel, notably transit. Thirdly, the model “assigns” transit (PT) trips to explicit paths through the
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transit network, enabling different components of transit trips (including in-vehicle, walking to/from transit, and
waiting and transferring) to be estimated and considered as potential situations for disease spread. Therefore,
utilising the SydneyGMA augments the disease spread modelling by accounting for potential locations of disease
spread and more accurately modelling interactions among household members as a result of adjustments to their
daily activities. The limitation of SydneyGMA is brought in Appendix B)
2.2 Disease spread parameter determination
The disease spread model, explained in Appendix C, iteratively interacts with SydneyGMA model once par day
and scrutinises the itinerary of each agent in the system. Accordingly, it updates the disease state of each agent.
In particular, the changes each day between agents’ disease states affect their travel behaviour and activity
participation (and their family members itineraries) in subsequent days of the simulation.
There are several factors that affect the movement rates (probabilities) among the different disease
states. The factors can be categorised into 1) travel behaviour-specific parameters, 2) disease-specific parameters,
and 3) policy-specific parameters. The travel behaviour-specific parameters affect out-of-home activity
participation rates, destination choices, travel mode choices, the start time, location and duration of out-of-home
activity episodes, and contact number for activity type. Except for the contact number, the other parameters are
transferred from the original TASHA model and adjusted for the Sydney context and integrated to the transport
network of Sydney.
The disease-specific parameters include incubation period, average time required for an infected agent to
recover, and the probabilities of: becoming infected (per contacted person), transitioning from infectious to
quarantined (per day), infected agents dying (per day), and transitioning from quarantined to recovered (per day).
In Appendix D, we describe the parameter calibration procedure used to determine the parameters for the
agent-based disease spread models and present the resulting calibrated parameters in Table C1. The parameter
calibration procedure is based on previously published work by Najmi et al. (2019b).
The strategy-specific parameters determine the policies that might be applied by policymakers and
authorities to slow down disease spread. These include, but are not limited to, the enforcement of business
closings, teleworking, and, if applicable, easing the restrictions on businesses; school closures and re-openings;
infected case isolation; quarantining of family members; social distancing; and the dates when the restrictions are
in place. Of these, variations in school closure strategy have not been considered in this paper due to the huge
uncertainty that exists with respect to the impact of the virus on children. Another strategy-specific parameter is
the change of trip generation rates, which is usually ignored in conventional disease spreading models.
3. Control strategies
We evaluate several different control strategies, namely: home quarantine of family members of the traced
infected cases, social distancing, travel load reduction, and the date when the control strategies are imposed.
Different scenarios are run to explore these control strategies and the dates when they are implemented.
However, we do not explore the impact of case isolation (CI) and school closure (SC) in this paper. CI and SC
strategies are set to our best estimate of current values for the Sydney GMA and are held constant across all
experiments. We assume that CI is implemented from the start day of the epidemic, as has been the case in
Australia and most other countries. The SC strategy comes into effect in the analysis in the week starting 23
March 2020. Early in this week, the schools were still open, but it was up to parents to decide whether to send
their children to school or not. Thus, SC is considered to remove schools and universities from the list of
activities for a majority of students. We assume that universities are partially open and 10% of university
students continue to travel to universities in this scenario. Obviously, the SC affects the daily travel itinerary of
the students and their family members. Studies have estimated that SC requires around 15% of the workforce to
take time off work to care for children, which is associated with considerable costs (Scott, 2020). This changes in
the activity participation is captured by SydneyGMA.
Scenario assumptions for each of the control strategies examined are briefly described in each of the
following sub-sections.
3.1 Quarantined family members (QF)
QF is a common strategy to control pandemics. While different levels of quarantine strategies are implemented
worldwide, we only investigate the existence or the lack of this strategy. In the case of existence, we assume that
the strategy is implemented from the day of finding the first case in New South Wales (NSW), on 22 January
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2020. Following identification of a symptomatic case in a household, all household members remain at home for
14 days.
3.2 Social distancing (SD)
SD is a key parameter in disease transmission models and affects the rate at which sick people infect susceptible
people. We impose SD in our model by the adjustment of all non-household contacts (referred to as compliance
level) while the intra-household contacts are kept unchanged which is in line with the pandemic studies of
Chang et al. (2020) and Ferguson et al. (2020). So, the SD compliance levels may vary from zero-SD – no
compliance- to full lockdown-full compliance, with a rate at which the contact rates are affected following the
SD control strategy. This strategy came into effect in NSW on 31 March 2020.
3.3 Travel load (TL)
TL is used to reduce non-essential trips, including leisure, sport, and religious activities. Also, it includes the
reduction in trips due to teleworking, layoffs, and quitting a job. Similar to SD, we define different levels and
investigate the influence of enforcement to eliminate unnecessary trips. We consider the TL level in Sydney
GMA in April 2020 as the extreme level in our investigations and explore the influences of easing the
restrictions. Despite some rare cases, as in Wuhan, where the TL levels have approached 0%, in many other
countries, the enforcement of the severe TL restrictions is impossible. The TL strategy comes into effect within
the analysis starting from 23 March 2020.
3.4 Date of lockdown (DL)
The date when the control strategies are implemented is a controversial decision for authorities. This is a
difficult decision for governments, as it has detrimental effects on economies and, in the worst case, might result
in economic collapse.
It should be noted that an important effect of lockdowns is on travel behaviour, and, as a result, on
urban travel demand. There is no current data that provide information about the changes in travel decisions of
agents after lockdown. Thus, we need to make some assumptions, the most important of which is the travel
volume after lockdown. As there is no reliable data on the generated trips after lockdown in Sydney GMA (in
April 2020) compared to before, we assume 50% reductions in the total number of trips. However, according to
Transport for NSW (Transport for NSW, 2020), the PT usage reduced by 79% after lockdown. So, the change
in the PT usage is a piece of reliable information we used and adjusted the utility of PT mode in SydneyGMA to
fit the simulated ratio to the observed statistic.
The next section explores the effects of implementing and relaxing each of these control strategies.
4. Runs and results
As the system is probabilistic, starting with very small number of infected cases (e.g. one or two cases) may
substantially affect the simulation results, depending on whether the model quarantine them sooner or later.
Thus, we use an initial set of four infected cases in the population. Because there have been four active cases in
Sydney GMA in 28 February 2020, this date is selected as the starting point of experiments. Numerous
simulation runs of the combined SydneyGMA and calibrated agent-based disease spread model were run and
the simulation results are presented and discussed in the following subsections.
4.1 Base case
The base case scenario is equivalent to the settings that reproduce the observed statistics; thus, it is the output of
the calibration model. Figure 1 shows the base case scenario obtained from the simulation of the ongoing spread
of COVID-19 and reproduces the disease spread progression in SydneyGMA. In the scenario, all the control
strategies are in place as in reality in NSW. The SD compliance level and TL level strategies after lockdown are
determined and considered at 85.9%, called the base SD compliance level, and 50%, called the base TL level,
respectively (see Appendix D). Figure 1 (A) and (B) reveal the high performance of our calibrated disease
transmission model in reproducing the observed infected cases. As a result of the restrictions implemented by
the Australian government in the last week of March 2020, the reinfection rate drops sharply, and the epidemic
almost dies out. Figure 1(C) shows the simulation result of running the model in the base scenario. This figure
distinguishes between the isolated (but not necessarily infectious) and non-isolated cases. So, the model
estimates that about half of the persons in quarantined state are the family members that are not actually
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infected. In reality, while the family members of infected cases are quarantined, their infection to the disease has
not yet been determined.
Figure 1: Power of the calibrated SydneyGMA -based disease spreading model in reproducing the daily number of cases (A), the cumulative
number of cases (B) and the number of cases at each state of the pandemic modelling (C) in the base-case scenario.
4.2 Various SD Compliances
In model calibration, we found the base SD compliance level after shutdown in the Sydney GMA. However, the
exploration of easing the compliance level on the disease distribution allows policymakers to identify the
minimum compliance levels for which the disease might be controlled. Figure 2 shows the simulation results of
the social distancing strategies, coupled with QF and base TL level, across different compliance levels. We do
not consider the SD compliance level of 100% as it is almost impossible to achieve. The figure reveals that
compliance levels of less than 70% do not show enough strength to suppress the disease within 3 months. At
these compliance levels, the number of emerging new cases is higher than the potential of the health system to
find and isolate the infected cases. While the SD base compliance level could eliminate the disease, or hold it
close to zero cases, in about 2 months, the lower SD compliance levels of 80% and 70% could control the
disease with a delay of 14 and 28 days respectively. Reducing the SD compliance by 15.9%, from 85.9% to 70%,
increases the cumulative number of cases by 59%. Still, this is much better than the scenario in which there is
50% or less SD compliance level in place.
The compliance levels between 50% and 60% are still effective in reducing the infected cases (at base TL
level), but they do not suppress the disease in a short period of time. Thus, control of the disease with these SD
levels required a longer time period. In these cases, the resurgence of disease spreading is probable. The SD
compliances levels of less than 50% are not strong enough, for any duration, to suppress the disease.
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