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 23rd with the aim of controlling the pandemic, which has resulted into more than 81,000 reported cases until mid 2020 (WHO Team, 2020). The disease has spread in all parts of the globe by the end of 2020. 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, facemask use, 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 conventional mathematical modelling of disease spread has a long history of providing solid foundations for understanding disease dynamics, the models are sometimes aggregated, with usually detailed heterogeneities dismissed. These heterogeneities may 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 important impacts on epidemic dynamics and on the effectiveness of possible interventions (Grefenstette et al., 2013). Recently, the development of disaggregated agent-based models in infectious disease epidemiology has received considerable attention owing to their capability to capture the dynamics of disease spread combined with heterogeneous mixing and social networks of agents. Agent-based models are known to better reflect the behaviour of people and the system as a whole. Further, the diversity of policies and strategies that can be assessed using agent-based models is larger than their aggregate counterparts. Teleworking, for instance, may shift agents to participate in other activities or school closure may affect the activity patterns of all the household members. We use a large-scale agent-based model to consider the dynamics of COVID-19 transmission in the Sydney greater metropolitan area (Sydney GMA), Australia.

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, they typically show considerable variations from one study to another. Their methodologies also are only applicable to aggregated models such as susceptible–infected–resistant (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 of agent-based modelling of disease spread. Further, of the few prior attempts to calibrate such parameters (Chang et al., 2020; Rockett et al., 2020; Hoertel 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 observations’ replication, at the possible sacrifice of model system validity. As the first contribution of this paper, we use the response surface methodology (RSM) to efficiently transfer, adjust and 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, 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 agent-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 illustrate the benefits of an agent-based model in capturing the ground truth of how agents interact and their impact in shaping the system level response to several policies including the influences of easing social distancing restrictions, opening up businesses, timing of control strategies implementation, using facemask and quarantining family members of isolated cases to intervene the disease progression (as the second contribution). The intent is to provide guidance to the public health community worldwide to consider easing of restrictions using behavioural epidemiology models. It should be noted that we present marginal benefits of several containment strategies not the absolute magnitude of the benefits using our model which reflects, like all models, part of the ground truth. Also, we do not envision forecasting the future in this paper; instead, we introduce a tool or an approach to examine the effectiveness of hypothetical strategies which are impossible to be tested in the real world. All in all, while several agent-based models have been recently developed in the literature for disease spread simulations, i.e. Chang et al. (2020) and Rockett et al. (2020), the current paper is unique in 1) the use of a fully agent-based model which includes the real traffic network and activity scheduler for household agents (TASHA) and 2) the use of a structured method for model calibration.

Agent-based disease spread modelling

This section briefly explains the agent-based model used to model the pandemic spread and then, the methodology for model parameter calibration is introduced.

Related works

Deciding on appropriate control strategies among a wide range of possible alternatives is difficult; computer modelling is an invaluable tool for exploring the effects of various control strategies. Agent-based models are a class of computational models that provide a high-resolution—both temporal and spatial—representation of the epidemic at the individual level (Truszkowska et al., 2021; Kretzschmar et al., 2021). Agent-based models cover the sociodemographic attributes of people and attempt to reproduce the travel decisions and activity participations of people (Najmi et al., 2018). The use of the models has been recently surged to investigate the impact of non-pharmaceutical interventions for COVID-19.

Several agent-based models have been developed to simulate the spread of COVID-19 and evaluates the effectiveness of having various control strategies in place; the strategies include social distancing (Chang et al., 2020; Najmi et al., 2021), school closure (Chang et al., 2020; Truszkowska et al., 2021), facemask usage (Najmi et al., 2021; Müller et al., 2021), contact tracing (Aleta et al., 2020; Kerr et al., 2020), quarantining family members of isolated cases (Kerr et al., 2020; Chang et al., 2020), superspreading (Lau et al., 2020), and lockdown (Chang et al., 2020; Truszkowska et al., 2021). The agent-based models are developed for various locations including Australia (Chang et al., 2020), Singapore (Koo et al., 2020), the United States (Chao et al., 2020), and the United Kingdom (Ferguson et al., 2020). Features of these models include the simulation of in-home and out-of-home contacts (Chao et al., 2020; Kretzschmar et al., 2021; Kucharski et al., 2020), activity participation of agents (Chang et al., 2020; Müller et al., 2021), activity chains (Müller et al., 2021), and travel networks (Najmi et al., 2021). Our disease transmission model in this paper covers all the features and attempts to investigate effectiveness of the above-mentioned control strategies, except the school closure, in the Sydney GMA.

Although the merits of agent-based models have shed light on technical complexities of their implementation as well as their scalability across scenarios (Keskinocak et al., 2020), their implementation is data hungry and costly. One of the complexities relates to the calibration of the models. The studies on agent-based disease spread models in the literature are either silent on how the calibration of the models have been performed (e.g. Perez and Dragicevic, 2009; Lau et al., 2020; Kretzschmar et al., 2020; Kucharski et al., 2020), or they have explicitly mentioned that the model parameters are calibrated in an ad-hoc and non-systematic ways, solely for the purpose of fitting the results to the observed data (e.g. Chang et al., 2020; Müller et al., 2021; Gaudou et al., 2020; Truszkowska et al., 2021). The agent-based models are large scale and highly non-convex, with many interactive parameters. Building COVID-19 spread simulators on top of the agent-based model further increases the complexity. The existence of non-linearities, the lack of closed form formulations for agent-based models and the existence of many interactive parameters make the system severely under-determined. Therefore, numerous sets of parameters can be found for the parameters such that the model reproduces the observed statistics. While there are many estimations for the parameters in observational epidemiologic studies in the literature, there is no study that systematically generates parameters for the agent-based models. Systematic calibration of an agent-based disease spread model is a key contribution of the current paper.

SydneyGMA model

The agent-based disease transmission model (ABDSM; Najmi, 2020) in this paper is coded in Python and built on an agent-based model developed for the Sydney GMA, called SydneyGMA, 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, 2009Travel Management Group, 2020). In addition to Sydney, TASHA has been applied in Toronto, Canada, where it is the operational model for Toronto transportation planning agencies (Miller et al., 2016), Finland (Birdsey et al., 2019), 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 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. Appendix 1explains more details on SydneyGMA. Note that the population size in SydneyGMA is about 5.8 million.

Disease spread parameter calibration

While SydneyGMA is originally developed to simulate the travel behavior of people, it is extended to model the transmission of the disease in the population while the people participate various activities including work and school and use different modes. We call the extension agent-based disease spread model which is built on SydneyGMA to simulate the spread of the disease over the social network (see Fig. 1). In the agent-based disease spread model, a disease spread simulator frequently runs SydneyGMA. Similar to the other agent-based models, the SydneyGMA is for daily travel scheduling while the agent-based disease spread model should cover the whole lifetime of pandemic which may be few months or years. The disease spread simulator, explained in Appendix 2, iteratively interacts with SydneyGMA model once per day and scrutinises the itinerary of each agent in the system. To illustrate more, the time-step is a day in which the disease state of each agent is updated. The changes in the states affect the travel behaviour and activity participation of each agent (and their family members itineraries) in subsequent days of the simulation.

Fig. 1
figure 1

The structure of agent-based disease spread models

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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 3, 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 2. The parameter calibration procedure is based on previously published work by Najmi et al. (2020).

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, facemask use; 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.

Control strategies

We evaluate several control strategies, namely: home quarantine of family members of the traced infected cases, social distancing, travel load reduction, facemask usage, 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.

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 2020. Following identification of a symptomatic case in a household, all household members remain at home for 14 days.

Social distancing (SD)

SD is a key parameter in disease transmission models and affects the rate at which sick people infect susceptible people; it refers to the extra care of people, to reserve extra distance from others, compared to the normal conditions (with zero SD). Thus, SD compliance of 0 does not mean that people are in full contact. 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). Thus, 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. Note that the SD compliance level is assumed to be the same, however, it is assumed to be variable and unknown everywhere in the system such as within the public transport system and in regarding the activities of participations.

Travel load (TL)

TL addresses trip cancellations and 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.

Facemask usage (FU)

Recently, FU is highly emphasised to reduce the chance of getting infected while participating in different outdoor activities. Different values of the facemask efficiency have been reported in the literature but almost all of them use odd ratio (e.g. Chu et al., 2020 and Schünemann et al., 2020). The model in the current paper needs the per contact efficiency of facemask as the paper uses an agent-based approach which simulates the interaction among agents. The per contact efficiency has not been reported in the literature and the possibility of using the OR estimations for the per contact efficiency is under debate. Therefore, we consider different values of 0.6, 0.7, 0.8, and 0.9 for the per contact facemask efficiency to address the ambiguity that exists for the per contact efficiency of facemask. We use these efficiencies in the infection rate of those agents that use mask while participating activities out of home. We assume that nobody wear mask at home. Similar to SD, we define different levels and investigate the influence of different levels of facemask usage while participating activities out of home. The FU level may vary between 0%—nobody wears mask- to 100%—everybody wear mask. In this paper we evaluate the disease spread at six FU levels of 0%, 20%, 40%, 60%, 80% and 100% for investigation.

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 assumed 50% reductions in the total number of trips for calibration purposes. However, according to Transport for NSW (2020), the PT usage reduced by 79% after lockdown. Thus, 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.

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 on 28 February 2020, this date is selected as the starting point of experiments. The calibrated agent-based disease spread model is used for policy analysis; the simulation results are presented and discussed in the following subsections. Each of the simulations is run three times to account for the randomness in the agent-based model where the averages of the evaluation measures are plotted.

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 2 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 observed in NSW. The SD compliance level and TL level strategies after lockdown are determined and considered at 85.9% (this value is determined by the calibration model), called the base SD compliance level, and 50%, called the base TL level, respectively (see Appendix 3). Figure 2(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 infection rate drops sharply, and the epidemic almost dies out. Figure 2(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. Thus, the model estimates that about half of the persons in quarantined state are the family members that are not actually infected. In reality, while family members of infected cases are quarantined, their infection to the disease has not yet been determined.

Fig. 2
figure 2

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

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Various SD compliances

In the model calibration, we found the base SD compliance level after the 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 3 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%, can increase 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.

Fig. 3
figure 3

A comparison of different SD compliance levels. The settings for other control strategies are the same as in the base scenario. a daily number of cases (linear), b cumulative cases (linear), c daily number of cases (logarithmic), and d cumulative cases (logarithmic). Note: Responding to the skewness of large values, (A) and (B) are plotted in logarithmic scale in (C) and (D)

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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.

Speed of implementation of lockdown

We evaluate the timing of the implementation of lockdown in Sydney GMA. Figure 4 explores the scenarios where all the control strategy settings are the same as in the base case scenario, but they are enforced either 3 or 7 days earlier or later than the actual introduction date. This figure reveals the impact of selecting an appropriate time to apply the control strategies. Left unchecked, the spread of the disease grows exponentially such that in the first three weeks the number of infected agents is small, and the situation does not seem dramatic. Then, the values change rapidly. Earlier enforcement could lead to 96% and 63% fewer cases for the scenarios with the lockdown implemented 7 and 3 days sooner, respectively. The delays of 3 and 7 days, on the other hand, could lead to, respectively, 130% and 570% increases in the number of cases. A week’s delay not only increases the pressure on the health system considerably but also requires an approximately 30-day longer suppression period.

Fig. 4
figure 4

A comparison between the influence of implementing the lockdown earlier (in greenish) and later (in reddish) while all the strategies are in place as in the base case scenario. a Daily number of cases, and b Cumulative number of cases

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Opening businesses

In the base scenario, we defined the base SD compliance and base TL levels. Furthermore, in Fig. 3, we showed that compliance levels over 60% can suppress the disease in a reasonable time (at the base TL level). Suppose that the generated trips increase by easing the restrictions on businesses to open again, but all other in-place strategies are still in effect. To examine this case, we run the model with different TL levels across both the base and 60% SD compliance levels to investigate the interaction effect of the SD and TL control strategies. The results of running the scenarios are presented in Fig. 5. The figure also explores the importance of the QF control strategy in controlling the disease spread.

Fig. 5
figure 5

A comparison of different travel load and its interaction with home quarantine strategy at two social distance compliance levels of 85.9% and 60%. a daily number of cases at the SD compliance level of 85.9%, b cumulative cases daily number of cases at the SD compliance level of 85.9%, c daily number of cases at the SD compliance level of 60%, and (D) cumulative cases daily number of cases at the SD compliance level of 60%. Note: Responding to the skewness of large values, (C) and (D) are plotted in logarithmic scale

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Having the QF strategy in place throughout the period, the base SD compliance is very successful in controlling the disease spread progression in a short period of time for all the TL levels. However, while the SD compliance level of 60% can be successful in suppressing the base travel load, the result is may not satisfactory for travel loads of 80% and over. This reveals that even slightly easing the social distance controls while the travel demand is close to the pre-COVID-19 travel demand level, may be ineffective.

The figure also shows that relaxing the QF control strategy significantly increases the disease suppressing period, even if a high compliance level of social distancing is in place. Further, relaxing the QF multiplies the number of patients. It also remarkably increases the magnitude of the daily infections, especially when coupled with a low SD compliance level. Thus, the QF strategy has significant interaction effects on both travel load and SD compliance level, such that ignoring the QF strategy multiplies the daily infection rate and infected cases. Note that few of the plots in Fig. 5 are for scenarios with high SD compliance level of 85.9% and high travel loads. It should be emphasised that the scenarios are model fictions, and improbable to be achieved in reality.

Wearing facemask

While many of the control strategies are currently in place in many countries, the continuation of enforcing some of these strategies (e.g. travel ban, school closure, and lockdown) for a long time is impractical. The continuation of these strategies may have detrimental effects on the economy, some irreversible and in the worst case, might result in an economic collapse. Thus, this section assumes TL is at the same level as before COVID-19 (almost 100%) when all the agents participate in their activities, including work, school attendance, recreational activities etc., freely (unless they are in quarantined); and analyses the influence of the facemask usage and its interaction with social distancing on controlling the disease transmission.

The starting point at which the FU and SD are imposed, including the daily number of infections and cumulative infections, may influence the performance of the control strategies. To address this issue and to better evaluate the performance of the facemask usage scenarios in controlling the disease transmission, we impose the use of facemask and complying the SD at different starting conditions provided in Table 1. In line with this, we allow agents in the system to progressively get infected without enforcing SD and FU control strategies. Given three different starting points, we impose the FU and SD control strategies. For example, at the starting point of 2 at which we apply the SD and FU control strategies, the daily and cumulative infections reach 108 and 699 cases. The average of the simulation results under the three starting points has been used to analyse the facemask efficiency.

Table 1 starting points of different random streams for facemask analysis
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The interactions of SD and FU control strategies are evaluated in terms of 1) reduction rate in the number of infections (Fig. 6a-d) and 2) the time it takes the disease spread getting under control (Fig. 6e-h) across different values of per contact facemask efficiencies. Note that to better understanding the development of infections, another representation of this figure is provided in Appendix 4. In Fig. 6, the estimated marginal means across different starting points are plotted. In analysing the figures, three matters should be considered. First, the SD compliance level of 70% is less likely to happen when the TL is almost 100%. Second, the percentages of reduction in Fig. 6 are obtained by comparing the number of infections obtained at different SD and FU levels with a scenario where no SD and FU control strategies (both the SD and FU levels are 0%) are in place. For better understanding of the meaning of one percent reduction in the number of infections, it is worth mentioning that the scenario with no SD and FU strategies generates about 3.75 million infections; this value is equivalent to 65% of population which lies within the range reported in Anderson et al. (2020a, b). Thus, one percent reduction corresponds to about 37.5 thousand infections. Third, the absolute values on y-axis of Fig. 6e-h should not be analysed as it is sensitive to the initial starting points; instead, the sensitivity of the results to the changes in the SD and FU levels are the key attributes that we seek for.

Fig. 6
figure 6

A comparison of different levels of wearing facemask, at different per contact efficiencies, and their interactions with social distancing levels when the TL is the same as pre-COVID. a-d The reduction rate in the number of infections at different per contact efficiencies, e–h The time it takes the disease spread getting under control at different per contact efficiencies

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Figure 6a–d reveal several intuitive results. First, the SD and FU strategies are fully complementary in reducing the number of infections so that the negligence in undertaking one of them can be compensated by using the other one. Second, higher facemask efficiency plays a more effective role in high compliance levels of FU compared to the lower levels of FU. For example, while the facemask efficiency of 90% is 28% more efficient than the facemask efficiency of 60%, in increasing the reduction rate in the number of infections, at the FU compliance level of 60%. However, this value is only 8% at the FU compliance level of 20%. Third, across all the per contact facemask efficiencies, the 0% and 20% of facemask usage rates are not sufficient to keep the number of cases low, unless the SD compliance level is high, at the 70%, which is less likely to happen. At the SD compliance level of 50%, the FU level of 20% does also reduce the number of cases significantly but it may still put pressure on the health system. The FU levels of 40% and higher have promising performances at the SD levels of at least 50% across different facemask efficiencies. Fourth, the number of infections shows a significant sensitivity to the lower values of SD and FU control strategies. In contrast, the sensitivity reduces by increasing the SD and FU levels. The figure also shows that wearing masks by over 80% of people can be a conservative solution for opening up the economy. At these levels, the number of infections shows the lowest sensitivity to the facemask efficiency and SD compliance level. This is a plausible strategy for opening the economy owing to the fact that making the facemask usage a mandatory rule and controlling people’s compliance to the rule is much easier than enforcing social distancing. Social distancing is a fuzzy concept, and its compliance is at most a behavioral requirement which is not to a large extent controllable by local authorities. In contrast, the facemask usage is a binary concept of yes/no; thus, controlling and penalising people who avoid using facemask should be a convenient solution controlled by enforcement aiming at full implementation.

Figure 6e-h reveal that the times to control the disease transmission has the highest interactive effect at the FU levels 20% and 40% where the time it takes to control the disease highly depends on the SD level. The FU levels of 20% and 40% show a non-monotonic behaviour. At these levels, the society reaches the herd immunisation and supresses the virus at the low and high SD compliance levels, respectively. In both the cases, the virus is eliminated earlier than the situations where the FU level is about 20% or 40% with a moderate SD compliance level. The FU levels of 0% has an increasing trend meaning that increasing the SD compliance level postpones the herd immunisation achievement. In contrast, the FU levels of 80% and 100% have a decreasing trend meaning that the higher SD compliance levels supress the virus earlier. FU level of 60% shows a high sensitivity to the facemask efficiency and SD compliance level. At the SD level of 0% and the facemask efficiencies of less than 80%, FU level of 60% takes a long time to control the disease; the reason is that the infection rate that the society experiences is neither high enough to reach the early herd immunisation nor low enough to supress the virus. At a higher level of any of the facemask efficiency or SD compliance levels, 60% can be a sufficient FU level to control the disease.

Conclusion

NSW had the largest number of cases, and the greatest challenges in disease control. This paper presented a behavioural agent-based model for modelling the actual mobility of Sydney residents where interactions of agents, their travel trajectory and system level attributes such as traffic condition on different modes of transport are captured. Using the extremely high resolution of activities in the system, we were able to measure marginal costs and benefits of hypothetical conditions of the system and people. We could simulate situations with different levels such as the compliance profile of people in response to different containment policies which is impossible otherwise if not having a simulation tool like ours. To establish a reliable foundation for the sensitivity analysis, we calibrated our agent-based model to match what was observed in NSW during the lockdown. Then we assessed numerous combinations of levels of various well-known policies such as social distancing, travelling limitations, facemask usage, and full lockdown. Our proposed bottom-up modelling framework unleashes the power of high computing capacity for policy appraisal without requiring any discounts or limits on modelling how people behave in the system.

We showed that to open up again, on a backdrop of low disease incidence, mitigating resurgence of COVID-19 and maintaining the hard-won gains was critical. We estimated that the likely compliance with social distancing was 85.9% during the period of lockdown in Sydney GMA, and that reduction in compliance could result in disease resurgence. As society re-opens, enhanced surveillance and testing for COVID-19 is essential, and at the first signal of resurgence, lockdown should be implemented without delay. We also showed that a delay of even 1 week can be costly. A return to normal travel and use of public transport in Sydney GMA will result in a risk of resurgence but can be mitigated. We also discussed that the use of facemasks can be key to safer resumption of travel within Sydney.

We admit that the agent-based models like ours are data hungry to be calibrated, however we position ourselves in the literature alongside others argued that huge assumptions about the performance of aggregate models are not less harmful than data and computational requirements of disaggregate agent-based models. Nonetheless, each of these modelling paradigms have huge advantages to offer, so we aimed at presenting the benefits of the agent-based modelling scheme which is relatively overlooked for modelling pandemic situations. Also, this paper attempted to calibrate disease spread parameters specific to agent-based models. Other research studies can use the calibrated parameters while developing their agent-based disease spread models and then adjust the parameters if required.