COVID-19: to reduce the spread of the virus – social distancing must be adopted by at least 80% of the population

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A University of Sydney data study from the Faculty of Engineering has revealed that social distancing must be adopted by at least 80 percent of the Australian population to reduce the spread of COVID-19.

If social distancing measures were adopted by at least 80 percent of the Australian population, we could expect to see a control of the spread of the COVID-19 pandemic in just over three months, new research by the University of Sydney has found.

Led by Complex Systems academic and pandemic modeling expert, Professor Mikhail Prokopenko, the study also revealed that social distancing would be an unproductive measure if adopted by less than 70 percent of the population.

“If we want to control the spread of COVID-19 – rather than letting the disease control us – at least eighty percent of the Australian population must comply with strict social distancing measures for at least four months,” said Professor Mikhail Prokopenko.

“However, if ninety percent of the population complies, then the duration could be as short as thirteen to fourteen weeks – meaning if we began tomorrow we could expect a control of COVID-19 by July,” he said.

“Conversely, if less than seventy percent of the population is adopting social distancing measures, we cannot suppress the spread of the pandemic and any social distancing could be a fruitless effort,” he said.

“There is a clear trade off – stricter measures imposed earlier would reduce how long our lives are impacted by this disease. On the contrary, laxer protocols could mean a longer, more drawn out and ineffective struggle against COVID-19,” he said.

Study suggests tough measures early on

The research also found that for every day the stricter social distancing measures are delayed, society would need to endure several more days under a longer suppression policy.

This shows a COVID19 spread model

The research found that if 90 percent of the Australian population adopted social distancing, the spread of COVID-19 could be controlled by July 2020, whereas social distancing of less than 70 percent would not suppress the pandemic. The image is credited to Professor Mikhail Prokopenko, University of Sydney.

“There’s good reason for imposing tough measures early on. The longer we delay the peak, the more time our healthcare system has to prepare for it by accessing more resources such as ICU beds, ventilators, antivirals and trained health workers,” said Professor Prokopenko.

The researchers also found that while school closures had the potential to compensate for ten percent of a lack of social distancing compliance, they only delayed the peak of the pandemic by two weeks.

They also found that school closures did not significantly reduce new cases for older adults, but slightly increased the fraction of new cases in children around the peak of the pandemic in Australia.

How the modeling worked

The AceMod simulator comprises over twenty-four million software agents, each with attributes of an anonymous individual, such as age, gender, occupation, susceptibility and immunity to diseases.

Contact rates within different social contexts, such as households, household clusters, local neighbourhoods, schools, classrooms and workplaces are also built into the program.

This shows a graph

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. The image is credited to Professor Mikhail Prokopenko, University of Sydney.

The set of generated agents captures average characteristics of the real population and is calibrated to 2016 Australian Census data with respect to key demographic statistics.

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

In this scenario, 80 percent social distancing could either mean – any person in one household could go out once in five days, or, one member per family of five could go out daily, but the other four stay at home all the time.


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 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 high- resolution 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.

Technical preliminaries and model calibration

In this paper, we present results of the high-resolution (individual-based) pandemic modelling in Aus- tralia, 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 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 R0, 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 R0, 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 pan- demic, 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) R0 = [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 R0 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 R0 = 2.4, while examining values between 2.0 and 2.6 [26].

In our model, R0 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 R0 = 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 incidence C˙ 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.

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, 36, 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 R0 = 2.27, was found to produce the 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 Fergusson 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, σc = 0.134 for children, and σa = 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” [37].

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 R0 = 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 rate C˙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 R0, and the incubation and generation periods.

Intervention strategies

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 Fergusson 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. [38], “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 working group 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 is considered in this study, unlike the model of Fergusson 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, 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.

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 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.

Results

The comparative analysis is carried out by AceMod, across all intervention strategies, for the calibrated set of parameters, including R0 = 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 σc = 0.134 for children, and σa = 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.

Baseline
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 reiterate, 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 incidence C 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.

Case isolation

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.

School closures: SC

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 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.

Social distancing: SD

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. 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 F, 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.
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.

Summary

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. 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.

Conclusions

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 vary- ing 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 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 Australia1.

Another avenue leads to analysis of precursors and critical thresholds for possible emergence of new strains [39, 40, 41], given genomic surveillance data interpreted as complex networks [42, 43, 44, 45, 46], and dynamic models of social behaviour in times of health crises [47, 16, 48, 49].

Acknowledgments

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 gen- eral.

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.

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