key: cord-0659790-scx1hios
authors: Chang, Sheryl L.; Harding, Nathan; Zachreson, Cameron; Cliff, Oliver M.; Prokopenko, Mikhail
title: Modelling transmission and control of the COVID-19 pandemic in Australia
date: 2020-03-23
journal: nan
DOI: nan
sha: a3ec2c34f77f54f03fdc1e60db040ede8a93a03a
doc_id: 659790
cord_uid: scx1hios

In this paper we develop an agent-based model for a fine-grained computational simulation of the ongoing COVID-19 pandemic in Australia. This model is calibrated to reproduce several characteristics of COVID-19 transmission, accounting for its reproductive number, the length of incubation and generation periods, age-dependent attack rates, and the growth rate of cumulative incidence during a sustained and unmitigated local transmission. An important calibration outcome is the age-dependent fraction of symptomatic cases, with this fraction for children found to be one-fifth of such fraction for adults. We then apply the model to compare several intervention strategies, including restrictions on international air travel, case isolation, social distancing with varying levels of compliance, and school closures. School closures are not found to bring decisive benefits. We report an important transition across the levels of social distancing compliance, in the range between 70% and 80% levels. This suggests that a compliance of below 70% is unlikely to succeed for any duration of social distancing, while a compliance at the 90% level is likely to control the disease within 13-14 weeks, when coupled with effective case isolation and international travel restrictions.

The 2019-2020 coronavirus pandemic is an ongoing pandemic of coronavirus disease 2019 (COVID- 19) , caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). The first outbreak, which originated in December 2019 in Wuhan, the capital of Hubei province, and rapidly spread to the rest of Hubei and all other provinces in China, has been largely eradicated within mainland China by mid-to late March 2020, having generated more than 81,000 cases (cumulative incidence on 20 March 2020 [1] ). This was largely due to intense quarantine and social distancing measures, including isolation of detected cases, tracing and management of their close contacts, closures of potential zoonotic sources of SARS-CoV-2, strict traffic restrictions and quarantine on the level of entire provinces (including suspension of public transportation, closures of airports, railway stations, and highways within cities), cancellation of mass gathering activities, and other measures aimed to reduce transmission of the infection [2, 3, 4] .

Despite the unprecedented and robust prevention and control measures, the spread of COVID-19 was not contained to China, and the disease spread to other countries. The epidemic has been recognised by the World Health Organization (WHO) as a public health emergency of international concern on 31 January 2020, and on 11 March 2020 the WHO declared the outbreak a pandemic [5] . As of 21 March 2020, over 285,000 cases have been confirmed worldwide, causing more than 11,500 deaths [6, 7] . The disease established a sustained local transmission in many countries around the globe, with the number of confirmed cases exceeding or approaching 10,000 in several nations. More than 180 countries and territories have been affected, including Italy (47,021 cases), Spain (24, 926) , Iran (20, 610) , the USA (20, 227) , Germany (20,099), France (12, 612) , South Korea (8, 799) as the top eight affected nations [8] . The cumulative incidence, incidence, and the growth rate of cumulative incidence are traced for these countries, as well as Australia, in Appendix A, see Fig. 8, 9 and 10 respectively.

The scale of the COVID-19 pandemic has grown several orders of magnitude in a matter of weeks, from hundreds to thousands to tens of thousands, with the rate of these transitions varying across countries.

Of particular interest to our study is the time periods when the epidemics are sustained locally in these countries, but before the effects of adopted intervention strategies are fully felt. One immediate observation is that during this period, the growth rate of cumulative incidence in many of the traced national epidemics is averaging within the range between 0.2 and 0.3, that is, there are 20% to 30% daily increases in new cases on average. This is particularly evident for Spain, France, and Germany ( Fig. 9) , as well as China, Iran and Italy (Fig. 8) . Average estimates like this may help to reduce uncertainty around key epidemiological parameters which are required to calibrate disease transmission models, before investigating possible effects of various intervention policies.

While worldwide public health emergencies have been declared and mitigated in the past-e.g., the "swine flu" pandemic in 2009 [9, 10, 11, 12] -the scale of socio-economic disruptions caused by the unfolding COVID-19 pandemic is unparalleled in recent history. Effects of the COVID-19 pandemic have quickly spilled over from the healthcare sector into international trade, tourism, travel, energy and finance sectors, causing a panic in the equity markets worldwide [13] . Australia is beginning to feel most of these effects, with the number of confirmed COVID-19 cases crossing 1,000 on 21 March 2020 and a cumulative incidence growth rate consistently above 20%. If the pandemic continues to follow these trends in Australia, the population is likely to experience the same devastating growth as previously seen in other COVID-19 affected nations.

In an effort to mitigate this damage, there is an ongoing debate on the utility of specific interventions (e.g., school closures), the low compliance with social distancing measures (e.g., reduction of mass gatherings), and the optimal combination of particular health intervention options balanced against social and economic ramifications, and restrictions on civil liberties. A rigorous and unbiased evaluation of available options is urgently required, and this study aims to provide a timely input to the pandemic response planning in Australia. We quantitatively evaluate and compare several mitigation and suppression measure, using a highresolution individual-based computational model calibrated to key characteristics of COVID-19 pandemics. In particular, this comparative analysis identifies minimal levels of social distancing compliance required for controlling COVID-19 spread in Australia in the near future, as well as a trade-off between these levels and duration of the interventions. More precisely, our simulations suggest that, without a 80-90% compliance with social distancing strategies, the epidemic will not be effectively controlled.

In this paper, we present results of the high-resolution (individual-based) pandemic modelling in Australia, using a modified and extended agent-based model, AceMod, previously developed and validated for simulations of pandemic influenza in Australia [14, 15, 16, 17] . AceMod, the Australian Census-based Epidemic Model, employs a discrete-time and stochastic agent-based model to investigate complex outbreak scenarios across the nation over time. Stochastic agent-based discrete-time simulation models such as these have been established as useful tools for tracing fine-grained effects of heterogeneous intervention policies in diverse epidemic and pandemic settings [18, 19, 10, 20, 9, 21, 22, 23, 24, 25] , including for policy advice currently in place in the USA and the UK [26] .

The AceMod simulator comprises over 24 million software agents, each with attributes of an anonymous individual (e.g., age, gender, occupation, susceptibility and immunity to diseases), as well as contact rates within different social contexts (households, household clusters, local neighbourhoods, schools, classrooms, workplaces). The set of generated agents captures average characteristics of the real population, e.g., AceMod is calibrated to the Australian Census data (2016) with respect to key demographic statistics. Potential interactions between spatially distributed agents are represented using data on mobility in terms of commuting patterns (work, study and other activities), adjusted to increase precision and fidelity of commute networks [27] . Each simulation scenario runs in 12-hour cycles ("day" and "night") over the 196 days (28 weeks) of an epidemic, and agents interact across distinct social mixing groups depending on the cycle, for example, in working groups and/or classrooms during a "day" cycle, and their households, household 2 clusters, and local communities during the "night" cycle. The interactions result in transmission of the disease from infectious to susceptible individuals: given the contact and transmission rates, the simulation computes and updates agents' states over time, starting from initial infections, seeded in international airports around Australia [14, 15] . Simulating disease transmission in AceMod requires both (i) specifics of local transmission dynamics, dependent on individual health characteristics of the agents, such as susceptibility and immunity to disease, driven by their transmission and contact rates across different social contexts; and (ii) a natural disease history model for COVID-19, i.e., the infectivity profile from the onset of infection, over an incubation period, to the peak of infectivity, to recovery, for a single symptomatic or asymptomatic individual. It is precisely this part of the model which demands a careful study and calibration to available estimates of key transmission characteristics of COVID-19 spread.

Despite several similarities with influenza, COVID-19 has a number of notable differences, specifically in relation to transmissions across children, its reproductive number R 0 , incubation and generation periods, proportion of symptomatic to asymptomatic cases [28, 29, 30] , the infectivity of the asymptomatic and presymptomatic individuals, etc. (see Appendix B). While uncertainty around the reproductive number R 0 , the incubation and generation periods, as well as the age-dependent attack rates of the disease, have been somewhat reduced [3, 4, 31] , there is still an ongoing effort in estimating the extent to which people without symptoms, or exhibiting only mild symptoms, might contribute to the spread of the coronavirus [32] . Furthermore, the question whether the ratio of symptomatic to total cases is constant across age groups, especially children, has not been explored in studies to date, remaining another critical unknown.

Thus, our first technical objective was to calibrate the AceMod model for specifics of COVID-19 pandemic, in order to determine key disease transmission parameters of AceMod, so that the resultant dynamics concur with known estimates. In particular, we aimed to stay within a range of the reproductive number (the number of secondary cases arising from a typical primary case early in the epidemic) R 0 = [2.0, 2.5], which has been reported by the WHO-China Joint Mission on Coronavirus Disease 2019 [3] . Several recent studies estimated that before travel restrictions were introduced in Wuhan on 23 January 2020, the median daily reproduction number R 0 in Wuhan was 2.35, with 95% confidence interval of (1.15 − 4.77) [33] . An agent-based model of the Imperial College COVID-19 Response Team used a baseline assumption that R 0 = 2.4, while examining values between 2.0 and 2.6 [26] .

In our model, R 0 was investigated in the range between 1.6 and 2.8, by varying a scaling factor κ responsible for setting the contagiousness of the simulated epidemic, as explained in Appendix C [14, 16] . The value of R 0 = 2.27 (κ = 2.75) was found to produce the closest match to our target calibration variables, as shown in Figure 1 .

We maintained the incubation period (the interval from the infection to the onset of disease in an individual) around the mean value of 5.0 days, as reported in several studies, e.g., the mean incubation period was reported as 5.2 days, 95% confidence interval (CI), 4.1 to 7.0 [34] , while being distributed around a mean of approximately 5 days within the range of 2-14 days with 95% CI [35] .

Importantly, we aimed to keep the resultant growth rate of cumulative incidenceĊ around 0.2, in order to be consistent with the disease dynamics reported internationally. Another key constraint was a low attack rate in children, reported to be in single digits. For example, only 2.4% of all reported cases in China were children, while a study in Japan observed that "it is remarkable that there are very few child cases aged from 0-19 years", with only 3.4% of all cases in this age group [36] . In doing the calibration, we varied several "free" variables, such as transmission and contact rates, the fraction of symptomatic cases (making it age-dependent ), the probability of transmission for both symptomatic and asymptomatic agents, and the infectivity profile from the onset of infection.

In calibrating these variables, we minimised changes in order to represent acceptable epidemiological characteristics. For example, we aimed for the generation period (the interval, in days, between successive onsets of symptoms along a transmission chain) to stay in the range [6.0, 10.0] [34, 37, 26] . This is in line with the reported mean serial interval of 7.5 days (with 95% CI of 5.3 to 19) [34] and the 6.5-day mean generation time reported by the Imperial College COVID-19 Response Team [26] . We set the symptoms' duration after the peak of infectivity around the mean value of 12.0 days, on a linearly decreasing profile from the peak. The best match in our calibration, corresponding to R 0 = 2.27, was found to produce the 3 generation period of 6.4 days.

The contact and transmission rates across various mixing contexts have been mostly set as in pandemic influenza [14] , with the following notable exceptions, as detailed in Appendix C and D. The probability of transmission for asymptomatic/presymptomatic agents was set as 0.3 of that of symptomatic individuals (lower than in the AceMod influenza model). Both symptomatic and asymptomatic profiles were changed to increase exponentially after a latent period of two days, to the infectivity peak, set at the end of the incubation period, see Appendix C.

The fraction of symptomatic cases was set to two-thirds of the total cases (σ = 0.669), which concurs with the modelling study of Ferguson et al. [26] . However, we found that the best calibration is achieved when this fraction is age-dependent, with the fraction of symptomatic cases among children calibrated to one-fifth of the one for adults, that is, σ c = 0.134 for children, and σ a = 0.669 for adults. This calibration outcome per se is in agreement with the reported low attack rates in children worldwide, and the observation that "children are at similar risk of infection as the general population, though less likely to have severe symptoms" [38] . Another study of epidemiological characteristics of 2,143 pediatric patients in China noted that over 90% of patients were asymptomatic, mild, or moderate cases [39] . In our study, the attack rates in children have converged to 6%, as shown in Figure 2 , that is, only 6% of infections are detected in children, even with a relatively high reproductive number R 0 = 2.27 and a relatively long generation period of 6.4 days (in comparison, the generation period for influenza varies in AceMod in the range from 3.35 to 3.39 days).

In summary, this combination of parameters resulted in the dynamics that matched several COVID-19 pandemic characteristics, producing the rateĊ of cumulative incidence during a period of sustained local transmission (i.e., days 40 to 80 since the onset) in the range [0.15, 0.2], as shown in Figure 1 . This was achieved while keeping the attack rate in children just over 5%, and agreeing with established range of R 0 , and the incubation and generation periods.

Once the model was calibrated, we focused on our primary objective: evaluating potential effects of several intervention strategies that have been currently deployed in Australia, or have been considered for a deployment.

It is well known that, without efficient and timely interventions, long-distance travel typically carries a virus around the globe within weeks to months of the onset of the outbreak, often causing a worldwide public health emergency [9, 10, 11, 12] . In an attempt to prevent, slow down and eradicate the spread of COVID-19, several pandemic intervention strategies, including various approaches to containment, mitigation and suppression, have been investigated, deployed, and adjusted across the world in the last months. While these strategies inevitably vary across nations, they share fundamental approaches which are adapted by national healthcare systems, aiming at a broad adoption within societies. In the absence of a COVID-19 vaccine, as pointed out by Ferguson et al. [26] , mitigation policies may include case isolation of patients and home quarantine of their household members, social distancing of the individuals within specific age groups (e.g., the elderly, defined as older than 75 years), as well as people with compromised immune systems or other vulnerable groups. In addition, suppression policies may require an extension of case isolation and home quarantine with social distancing of the entire population. Often, such social distancing is supplemented by school and/or university closures.

Some of these intervention strategies and their combinations have shown early promise, while some have been less effective, being delayed by logistical constraints, as well as low adoption level, due to diverse factors often unique to the affected countries. For example, the model developed by the Imperial College COVID-19 Response Team have demonstrated that a combination of mitigation and suppression strategies deployed over three to five months may "reduce peak healthcare demand by 2/3 and deaths by half" [26] .

In Australia, an accurate investigation and evaluation of the COVID-19 spread and possible interventions, needs to carefully include demographic specifics, since the population is concentrated mainly along the coast (around urban areas). For instance, it has been previously established that an epidemic of a respiratory disease, such as influenza, typically develops in two waves, initially affecting the more densely populated urban areas, and then spreading to regional and rural areas [15, 16, 17] . In particular, as argued by Cauchemez et al. [40] , "back-and-forth waves of transmission between the school, the community, and the household" demand an explicit account of distribution and structuring of schools, grades, and classes in epidemiological models of respiratory diseases. The AceMod simulator has integrated layered school attendance data from the Australian Curriculum, Assessment and Reporting Authority (ACARA), within a realistic and dynamic interaction model, comprising both mobility and human contacts. These social mixing layers represent the demographics of Australia as close as possible to the Australian Bureau of Statistics (ABS) 2016 Census and other datasets, as described in Appendix E. We considered several intervention strategies: case isolation; restriction on international arrivals ("travel ban"); social distancing with the population compliance levels, defined below, varying from 0.0 (no social distancing, i.e., the baseline mode) to 1.0 (full lockdown mode), in increments of 0.1 (10% compliance); and school closures -independently of social distancing. Each of these scenarios were traced over time and compared to the baseline model, in an attempt to quantify their potential for the curtailing the epidemic in Australia, identify minimal levels of the social distancing compliance, and determine the contribution of school closures to the mitigation effort.

The case isolation mitigation strategy was modelled along the lines considered in the study of the Imperial College COVID-19 Response Team [26] : 70% of symptomatic cases stay at home, reduce their non-household contacts by 75% (so that their transmission rates decrease to 25% of the standard rate), and maintain their household contacts (i.e., their transmission rates within household remain unchanged). No home quarantine strategy for the members of the affected households has been considered in this study, unlike the model of Ferguson et al. [26] which considered that 50% of the affected households limit their non-household contacts as well. We opted to exclude this policy at this stage, in order to identify the effects of case isolation more clearly. The case isolation is assumed to be in force from the onset of the epidemic, as has been the case in Australia.

Restriction on international arrivals is set to be enforced from the moment when the number of confirmed infections exceeds the threshold of 1,000 cases. This concurs with the actual epidemic timeline in Australia, which imposed a ban on all arrivals of non-residents, non-Australian citizens, from 9pm of 20 March 2020, with a requirement for strict self-isolation of returning citizens. The number of COVID-19 cases crossed 1,000 cases on 21 March 2020, so the threshold chosen on our model is realistic. The restriction on international arrivals is included in modelling of all other strategies, and is not traced independently, as this mitigation approach is not under debate.

Social distancing (SD) has been implemented in our model by removing all working group contacts, and setting all non-household contacts to 10% of the standard rate (or 50% in Appendix F), while keeping the contacts within households unaltered. As mentioned above, the SD compliance levels vary from the zero-SD mode to the full lockdown mode, with a fraction of agents (the SD compliance level) following these constraints. Similar to the restriction on international arrivals, SD strategy is triggered by crossing the threshold of 1,000 cases. An alternative threshold of 2,000 cases, matching the actual numbers reported on 24 March 2020, is considered for comparison (Appendix F), in order to evaluate a delayed introduction of strong social distancing measures.

Finally, school closures (SC) are considered to remove both students and their teachers from school interactions (their corresponding transmission rates are set to zero), but somewhat increase their interactions within households. Such adjustments may be modelled with a varying degree of the increased household contacts, but in this study we simplified the approach by setting only one level (50% increase), with the intention to consider a more fine-grained approach in the near future. School closures are assumed to be followed with 100% compliance, and may be concurrent with all other strategies described above. For example, they may account for scenarios when, under a partial SD compliance, some household members may choose to leave their households during daytime and interact at work, while their children and/or teacher partners (i.e., other adults) stay at home. SC strategy is also evaluated as triggered by crossing the threshold of 1,000 cases -this is not a current practice in Australia, and so we investigate the SC intervention separately from SD strategy (by setting SD compliance as zero). Hence, the evaluation of school closures is meant to provide an input to policy setting, rather than forecast changes to possible epidemic dynamics 7 at this stage. We note that, at the moment (21 March 2020), Australian Federal Government does not recommend schools closures. While the case isolation strategy is assumed to last during the full course of the epidemic, the duration of SD and/or SC strategies varies, across a range of time periods, e.g., 28, 49, 70, 91 days, that is, across 4, 7, 10, 13 weeks.

The comparative analysis is carried out by AceMod, across all intervention strategies, for the calibrated set of parameters, including R 0 = 2.27 (i.e., scaling with κ = 2.75), and the transmission and contact rates as detailed in Appendix D. The infectivity of infected agents is set to exponentially rise and peak at 5 days, after an incubation period which includes two days of zero infectivity (latent period). The symptoms are set to last up to 12 days post the infectivity peak, while linearly decreasing -this results in the generation period around 6.4 days. The probability of transmission for asymptomatic/presymptomatic agents is set as 0.3 of that of symptomatic individuals; and the age-dependent fractions of symptomatic cases are set as σ c = 0.134 for children, and σ a = 0.669 for adults.

All figures below show typical runs, not the averages over multiple runs, in order to illustrate a realistic epidemic development over time, without smoothing. The typical runs are chosen within the range observed over multiple simulations carried out by AceMod, and use identical random number seeds to control for stochastic initial conditions.

A trace of the baseline model-no interventions whatsoever-is shown in Fig. 3 , with clear epidemic peaks in both incidence and prevalence evident after 105-110 days from the onset of the disease in Australia, i.e., occurring around mid-May 2020 in the absence of any interventions. The scale of the impact is very high, infecting nearly 50% of the Australian population. This baseline scenario is provided only for comparison, in order to evaluate the impact of interventions, some of which are already in place in Australia. To re-iterate, we aim to consider timely intervention scenarios applicable to current situation in Australia, where the number of confirmed COVID-19 cases crossed 1,000 on 21 March 2020, and the growth rate of cumulative incidenceĊ stayed above 20% for longer than a week. We observe that the simulated baseline generates the 20% cumulative incidence increase, in an agreement with actual dynamics.

All the following interventions include restrictions on international arrivals, triggered by the threshold of 1,000 cases. Two mitigation strategies are of immediate interest: (i) case isolation, and (ii) school closures, combined with case isolation. Both of these strategies are shown in Fig. 3 , with the duration of the combined strategy (SC and case isolation) set as 49 days (7 weeks), starting after the threshold of 1,000 cases is reached on day 42 since the onset. The case isolation approach, applied without SC, delays the epidemic peak by just over a week, while reducing the severity at the peak time by around 24% (incidence peak), and 22% (prevalence peak). The overall attack rate, however, is reduced insignificantly, showing that case isolation alone will not be effective for epidemic suppression.

Adding school closures to the case isolation approach also does not achieve a significant reduction in the overall attack rate (Fig. 3) . While the peaks of both incidence and prevalence are delayed by about two weeks (15 days for both incidence and prevalence), due to a slower growth rate of cumulative incidence, their magnitudes remain practically the same. We also traced the dynamics resulting from SC strategy for two specific age groups: children and individuals over 65 years old, shown by Fig. 4 and 5 . The two-week delays in occurrence of the peaks are observed across both age groups, suggesting that there is a strong concurrence in the disease spread across these age groups. We also observe that, under this strategy, there is no difference in the magnitude of the incidence peak for the older age group. Interestingly, for children, the 8 magnitude of the incidence peak increases by about 8% under the SC strategy coupled with case isolation, shown by Fig. 4 . This may be explained by increased interactions of children during various household and community social mixing, when schools are closed.

In short, the only tangible benefit of school closures, coupled with case isolation, is in delaying the epidemic peak by two weeks, at the expense of a slight increase in the contribution of children to the incidence peak. Given other societal costs of school closures (e.g., drawing their parents employed in healthcare and other critical infrastructure away from work), this strategy may be less effective than previously suggested (e.g., school closures are considered an important part of pandemic influenza response). There is, nevertheless, one more possible benefit of school closures, discussed in the context of the overall social distancing, as described below.

Our next step is to compare social distancing strategies, coupled with case isolation, across different compliance levels. Low compliance levels, set at less than 70%, did not show any potential to suppress the disease in the considered time horizon (28 weeks), while the total lockdown, that is, complete social distancing at 100%, managed to reduce the incidence and prevalence to zero, after 49 days of the mitigation. However, since the total lockdown is never perfect, we need to focus on the practically achievable compliance levels: 70%, 80% and 90%. For example, Fig. 3 includes a comparison with the SD level 70% for the entire population, and Figures 4 and 5 trace this strategy for two specific age groups (children and older adults).

Duration of all SD strategies is set to 91 days (13 weeks), and not surprisingly, there is a significant delay of about 12 weeks before the epidemic peak, occurring when the SD strategy (70% compliance) ends. Importantly, during the time period that the SD level is maintained at 70%, the disease is not controlled entirely, with the numbers of new infected cases (incidence) remaining in hundreds, and the number of active cases (prevalence) remaining in thousands. Thus, once social distancing is removed, the epidemic resumes, suggesting that 70% compliance is inadequate. The two higher levels of SD, 80% and 90%, are more effective at suppressing prevalence and incidence during the 13-week social distancing period. Figure 6 contrasts these three levels of SD compliance, "zooming in" into the key time period, immediately following the introduction of social distancing. Crucially, there is a qualitative difference between the lower levels of SD compliance (70%, or less), and the higher levels (80%, or more). For the SD compliance set at 80% and 90%, we observe a reduction in both incidence and prevalence, lasting for the duration of the strategy (91 days). The 80% SD compliance does not completely eradicate the disease, but reduces the new cases to less than 100, with prevalence below 1,000 (during the suppression period, before the resurgence). It is evident that this level of compliance would succeed if the strategy was implemented for longer period, e.g., another 5-6 weeks.

The 90% SD compliance practically controls the disease, bringing both incidence and prevalence to very low numbers of isolated cases. It is possible for the epidemic to spring back to significant levels even under this level of compliance, as the remaining sporadic cases indicate a potential for endemic conditions. We do not quantify these subsequent waves, as they develop beyond the immediately relevant time horizon. Nevertheless, we do share the concerns expressed by the Imperial College COVID-19 Response Team: "The more successful a strategy is at temporary suppression, the larger the later epidemic is predicted to be in the absence of vaccination, due to lesser build-up of herd immunity" [26] .

The cumulative incidence for the best achievable scenario (90% SD compliance coupled with case isolation and restrictions on international arrivals) settles around 2,500 cases during the suppression period, before a possible resurgence, at some point after intervention measures are relaxed. This is an outcome several orders of magnitude better than the worst case scenario, developing in the absence of the combined mitigation and suppression strategies.

In order to compare the scenarios in which social distancing measures are triggered by 1,000 confirmed cases, with the actual epidemic curve in Australia, we investigate an alternative threshold of 2,000 cases (Appendix F). The best agreement between the actual and simulation timelines is found to match a delayed but high, 90%, SD compliance, appearing to be followed from 24 March 2020, after a three-day period with a weaker compliance.

Differences between 70% and 90% SD compliance levels are also visualised in choropleth maps of four largest Australian Capital Cities: Sydney, Melbourne, Brisbane and Perth, shown in G, at day 60, that is, at a time when these two compliance levels result in a tangible divergence.

It is clear that there is a trade-off between the level of SD compliance and the duration of the SD strategy: the higher the compliance, the shorter period it needs to be implemented for. Both 80% and 90% compliance levels are practically achievable within reasonable time periods: 18-19 and 13-14 weeks respectively. We point out, however, that lower levels of compliance (at 70% or less) do not succeed for any duration of the imposed social distancing limits. This qualitative difference is of major policy setting importance, indicating a sharp transition in the performance of these strategies in the region between 70% and 80%. We do not attempt to establish a more precise level of required compliance, e.g., 75%. Such a precision would be of lesser practical relevance than the identification of 80% level as the minimal acceptable level of social distancing, with 90% providing a shorter timeframe. Importantly, a three-day delay in introducing strong social distancing measures is projected to require an approximately three-week longer suppression period, beyond 91 days considered in the primary scenario (Appendix F).

At this stage we revisit school closures. As shown in Fig. 7 , an addition of SC strategy to the SD set at 70% also generates a reduction in incidence, albeit progressing at a higher level than such reductions observed at 80% and 90% SD levels, coupled with school closures. This suggests that another potential benefit of school closures is that it may "compensate" for about 10% lack of SD compliance. This combination, however, would require a much longer duration of the coupled strategy (70% SD and SC), and may be impractical.

In short, the best intervention approach identified by AceMod is to combine restrictions on international arrivals (already implemented in Australia), case isolation (also already implemented to a reasonable extent, but demanding increasing testing and monitoring resources), and social distancing with at least 80%-90% compliance and a duration of 91 days (13 weeks). Any compromise on the recommended compliance levels is likely to lengthen the duration of the required suppression measures. We point out that our results are relevant only for the duration of the mitigation and suppression, and a resurgence of the disease is possible once these interventions cease, as shown in Fig. 6 1 . Hence, we do not quantify the precise impact of control measures beyond the selected time horizon (28 weeks), and focus on the time period in the near future, aiming to provide immediately relevant insights. Furthermore, our results should not be seen as policies optimised over all possible parameter combinations, but rather as a clear demonstration of the extent of social distancing required to reduce incidence and prevalence in the next six months.

In this study we simulated several possible scenarios of COVID-19 pandemic's spread in Australia. The model, AceMod, was calibrated to known pandemic dynamics, and accounted for age-dependent attack rates, a range of reproductive numbers, age-stratified and social context dependent transmission rates, household clusters and other social mixing contexts, symptomatic-asymptomatic distinction, long and varying incubation periods, and other relevant epidemiological parameters.

An important calibration result was the need for age-dependent fractions of symptomatic agents, with the fraction of symptomatic children found to be one-fifth of that of the adults. While other combinations of parameters may also succeed in calibration, setting the age-dependent fractions of symptomatic cases may be important for other modelling studies across the world.

An analysis of spatiotemporal characteristics of COVID-19 pandemic in Australia was carried across a range of intervention strategies, some of which are already in place, while some are under discussion. By Case isolation + SD compliance =0.7 Case isolation + SD compliance =0.8 Case isolation + SD compliance =0.9 Figure 6 : Strong compliance with social distancing (at 80% and above) effectively controls the disease during the suppression period, while lower levels of compliance (at 70% or less) do not succeed for any duration of the suppression. A comparison of social distancing strategies, coupled with case isolation, across different compliance levels (70%, 80% and 90%). Duration of each social distancing (SD) strategy is set to 91 days (13 weeks), shown as a shaded area. Case isolation and restrictions on international arrivals are set to last until the end of each scenario. Traces show incidence (a), prevalence (b), cumulative incidence (c), and the growth rate of cumulative incidenceĊ (d). running multiple computer simulations, while varying details of the micro-simulation, we estimates epidemic dynamics, in terms of the infection's prevalence and incidence, its peaks and waves, and other indicators, including age-dependent attack rates. We reported several findings relevant to COVID-19 mitigation and suppression policy setting. The first implication is that the effectiveness of school closures is limited, producing a two-week delay in epidemic peak, without a significant impact on the magnitude of the peak, in terms of incidence or prevalence. The temporal benefit of the two-week delay may be offset not only by logistical complications, but also by some increases in the fractions of both children and older adults during the period around the incidence peak.

The second implication is related to social distancing (SD) strategy, which showed no benefit for lower levels of compliance (at 70% or less) -these levels do not contribute to epidemic control for any duration of the social distancing restrictions. Only when the SD compliance levels exceed 80%, there is a reduction in incidence and prevalence. Our modelling results indicate existence of an actionable transition across these strategies in the range between 70% and 80%. In other words, increasing a compliance level just by 10%, from 70% to 80%, may effectively control the spread of COVID-19 in Australia (during the suppression period). We also reported a trade-off between the compliance levels and the duration of SD mitigation, with 90% compliance significantly reducing incidence and prevalence after a shorter period of 91 days (13 weeks). Although a resurgence of the disease is possible once these interventions cease, we believe that this study could facilitate a timely planning of effective intervention strategies.

Future research will address several limitations of our study, including a more fine-grained implementation of natural history of the disease, incorporation of more recent ABS data from 2020, inclusion of home quarantine strategy for the affected households, as well as a more refined school closures strategy. We also hope to trace specific spatial pathways and patterns of epidemics, in order to enable a detailed understanding of how the infection spreads in diverse circumstances and localities, with the aim to identify the best ways to locate and curtail the pandemic spread in Australia 2 . Other avenues lead to analysis of precursors and critical thresholds for possible emergence of new strains [41, 42, 43] , given genomic surveillance data interpreted as complex networks [44, 45, 46, 47, 48] , dynamic models of social behaviour in times of health crises [49, 16, 50, 51] , and analysis of global socioeconomic effects of the COVID-19 pandemic [52, 53] .

The Authors are grateful to Kristopher Fair, Philippa Pattison, Mahendra Piraveenan, Manoj Gambhir, Joseph Lizier, Peter Wang, Vitali Sintchenko, Tania Sorrell, and Stephen Leeder, for discussions of various intricacies involved in agent-based modelling of infectious diseases, and computational epidemiology in general. The Authors were supported through the Australian Research Council grants DP160102742 (SC, NH, OC, CZ, MP) and DP200103005 (MP). AceMod is registered under The University of Sydney's invention disclosure CDIP Ref. 2019-123. We are thankful for a support provided by High Performance Computing (HPC) service (Artemis) at the University of Sydney. Figures 8 and 9 trace cumulative incidence C, incidence, and growth rate of cumulative incidenceĊ = [C(n + 1) − C(n)]/C(n), for time step n, for the top eight affected countries: China, Iran, Italy, South Korea 8, Spain, Germany, France, USA 9. The time series begin from the day when the total number of confirmed cases exceeds five. Figure 10 traces these time series for Australia. 

The natural history of disease is a description of the disease from pathological onset to recovery from the perspective of a single individual, profiling their infectiousness over time [54] . In the past, the AceMod simulator has been used to model pandemic influenza within Australia, and here we detail modifications of the natural history aimed to account for COVID-19 specifics. The natural history model considers three distinct phases of infection. The first phase is the latent period during which individuals are infected but unable to infect others, set in the COVID-19 model as two days. The second phase is the incubation period, characterised by the onset of symptoms and an increasing infectivity, set in the COVID-19 model to lasts for five days. We model this increase in infectiousness as an exponential increase which varies from 0% to 100% over three days (see figure 11 ). Following the incubation phase, the infectious reaches its peak, and then decreases linearly over 12 more days, until the recovery, with immunity, occurs after 17 days. Finally, we assume that asymptomatic cases are 30% as infectious as symptomatic cases. Unlike influenza, where we assume that the asymptomatic fraction is the same for adults as for children, for the SARS-COV-2 coronavirus we assume that while 67% of adult cases are symptomatic, a significantly lower fraction (13.4%) is symptomatic in children. Figure 11 : Profile of the infectivity used as the natural history of COVID-19, for both symptomatic and asymptomatic cases. After two days, individuals become infectious, with the infectivity rising exponentially until its peak at five days. After this peak, the infectivity linearly decreases, with full recovery occurring at 17 days. At comparable points within the natural history of disease, asymptomatic individuals are 30% as infectious as symptomatic individuals.

The primary dynamics of AceMod are the infection transmissions. At each time-step the simulator determines the probability of infection for an individual, based on the infection levels in each of their mixing contexts. At each time step we consider all daytime or all nighttime contexts. Let X i (n) be a random variable describing the state of individual i at time step n. At each time step we calculate p i (n) = P (X i (n) = latent|X − i(n − 1) = susceptible), the probability that a susceptible individual is infected at n. Each individual belongs to a number of mixing groups with which an agent interacts, denoted g ∈ G i (n), as well as an associated static set of agents A g . Within each of these contexts, we define a probability p g j→i that individual j infects individual i in context g in a single time step. The probability that a susceptible agent i is infected at a given time step n is thus calculated as:

where p g j→i is the context-dependent probability that infected individual j infects susceptible agent i in mixing group g. We also define a scaling factor κ (proportional to the reproductive number R 0 ), as a free Table 1 : Daily contact probabilities c g j→i for different contact groups g, reported by [24] , reproduced from [14] , except for the rates in household clusters. parameter which allows us to vary the contagiousness of simulated epidemic scenarios:

where n j denotes the time when agent j becomes infected, and q g j→i is the probability of transmission from agent j to i at the infectivity peak, derived from the transmission or contact rates. This model assumes that for all contexts, the probabilities of infection over a given time period are known. In cases where this information is unavailable, we instead utilise contact rates reported and calibrated in previous studies. Thus, a majority of the transmission and contact probabilities follow our previous work on pandemic influenza [55, 56, 24, 40, 14, 15] , see Tables 1 and 2 in section D. Full details regarding their application can be found in [14] .

In this study we used "the attack rate pattern weighted index case" to calculate R 0 [21, 17] . The method is based on age-specific attack rates, computed as averages over many simulation instances, in order to reduce the bias in determining a typical index case, present due to population heterogeneity. As argued in [57, 17] , given the correlation between age group and population structure, the age-stratified weights, assigned to secondary cases produced by a sample of index cases, improve the estimation of the reproductive number R 0 .

Following [14] , with some minor adjustments, the transmission and contact probabilities are given in Tab. 1 and Tab. 2, respectively.

At the beginning of AceMod simulation, a surrogate population is generated. This surrogate population is matched to coarse-grained distributions arising from the 2016 Australian census published by the Australian Bureau of Statistics (ABS). In particular we use Statistical Areas (SA1 and SA2) level statistics [58] regarding age, household composition and workplaces in generating this surrogate population. Individuals in the population are separated into 5 different age groups preschool aged children (0-4), children (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) , young adults (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29) , adults (30-65) and older adults (65+). Along with these assigned characteristics, individuals are assigned a number of mixing contexts based on the census data. The AceMod simulator is a discrete-time simulation, where each simulated day is separated into two distinct portions: 'daytime' and 21 'nighttime'. In the daytime, workplace and school-based mixing are considered, whereas nighttime mixing considers household spread, and other local spread at the neighborhood (SA1) and community (SA2) levels.

The population generation begins with the contexts needed for nighttime mixing, which can be thought of as "home regions". The simulation iterates through each SA1, creating a cumulative density function (CDF) describing the size and type of households expected based on two dependent probability distributions defined by the ABS. Given this CDF, the procedure begins to randomly generate households, with the generation of agents occurring during this process. Once a household is generated for an SA1, agents are generated to match the size and type of the household (e.g., a single parent family of size four will generate one adult and three children). In order to generate attributes for this surrogate population, the simulation then reads in CDFs describing the population statistics of the given SA, with each of these agents being assigned some attributes based on these population distributions.

Following the population of the home regions, the AceMod simulator assigns work and school regions to individuals within the population. This process is based on the "Travel to work" data published by the ABS, which defines a number of individuals N living in home region i and working in region j. In order to satisfy each of these "worker flows", a number of unassigned working-age individuals (19-64 years old) in region i are selected at random and assigned to work in location j. School allocation, on the other hand, is somewhat more complicated as detailed data about student home locations is not available from the ABS. Instead, we use the available data from the Australian Curriculum, Assessment and Reporting Authority (ACARA), detailing the locations of schools, along with a proximity based model which biases children allocation towards closer schools. More detail about student allocation can be found in previous studies [15] .

We trace scenarios of COVID-19 pandemic spread in Australia, initiated by passenger arrivals via air traffic from overseas. This process maintains a stream of new infections at each time step, set in proportion to the average daily number of incoming passengers at that airport [15, 16] . These infections occur probabilistically, generated by binomial distribution B(P, N ), where P and N are selected to generate one new infection within a 50 km radius of the airport, per 0.04% of incoming arrivals on average.

On 21 March 2020, the number of confirmed COVID-19 cases in Australia crossed 1,000, following the ban on all international arrivals of non-residents, non-Australian citizens, put in place the night before. The primary scenario considered in this study introduces a social distancing policy, at varying degrees of compliance, triggered by crossing the same threshold: 1,000 confirmed cases. To compare this scenario with the actual epidemic timeline in Australia, where even stronger measures (e.g., closures of non-essential 22 services and places of social gathering) have been introduced a few days later, by 23 March 2020, we also investigate a threshold of 2,000 cases. This number was exceeded in Australia three days later, on 24 March 2020, and provides an alternative threshold, allowing us to evaluate a delayed introduction of strong social distancing measures. For this comparison of social distancing (SD), we set all non-household contacts to 50% of the standard rate (for both scenarios), while still removing all working group contacts, and keeping the households contacts unchanged.

As expected, a delayed response results in higher epidemic peaks, doubling the prevalence in comparison with the primary scenario -across different levels of compliance, as shown in Fig. 12 . The cumulative incidence for 90% SD doubles as well, from around 5,000 total cases, to just under 10,000. In the simulation timeline, the alternative threshold is crossed on day 50, and if this is aligned with 24 March 2020 on the actual timeline, one may see that the incidence along the 90% SD curve starts to reduce from day 59 (aligned with early April 2020), and the prevalence peak is reached around days 62-65 (aligned with early to mid-April 2020). At the time of reporting (2 April 2020), the timing of actual incidence and prevalence peaks, as well as the estimation of the cumulative incidence in Australia to be in the range of 8,000-10,000 total cases, are interim projections, and not actual observations. Nevertheless, the agreement between the actual and simulation timelines appears to be the strongest for 90% SD compliance, applied from 24 March 2020, following a period of weaker compliance between 21 and 24 of March 2020.

We also observe that a three-day delay in introducing strong social distancing measures results in an approximately three-week lengthening of the required suppression period, confirmed by separate runs with a longer suppression duration (not shown).

Differences between 70% and 90% SD compliance levels are visualised in choropleth maps of four largest Australian Capital Cities: Sydney, Melbourne, Brisbane and Perth (Fig. 13 ). These snapshots depict the incidence in these cities at day 60, illustrating how these two compliance levels diverge at that time. Growth rate in cumulative incidence (d) 70% compliance (threshold=1000) 80% compliance (threshold=1000) 90% compliance (threshold=1000) 70% compliance (threshold=2000) 80% compliance (threshold=2000) 90% compliance (threshold=2000) Figure 12 : A three-day delay in introducing strict social distancing doubles the disease prevalence. A comparison of social distancing strategies, coupled with case isolation, across different compliance levels (70%, 80% and 90%). Two scenarios are contrasted: the threshold of 1,000 (matching actual numbers on 21 March 2020), and a delayed alternative with 2,000 cases (matching actual numbers on 24 March 2020). Duration of each social distancing (SD) strategy is set to 91 days (13 weeks), shown as a shaded area for the primary threshold (1,000 cases). Case isolation and restrictions on international arrivals are set to last until the end of each scenario. Traces show incidence (a), prevalence (b), cumulative incidence (c), and the growth rate of cumulative incidenceĊ (d). 

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