Retrospective Evaluation of the Effectiveness of COVID-19 Control Strategies Implemented by the Victorian Government in Melbourne—A Proposal for a Standardized Approach to Review and Reappraise Control Measures

Abstract

In evaluating the effectiveness of COVID-19 control measures, we propose a standardized approach to assess the impact of COVID-19 management on flattening the curve by analyzing the case data of Victoria, Australia. Its capital, Melbourne, is considered the most lock-downed city in the world. We used the daily case data from Victoria and their first time derivative and compared the dates when the six lockdowns were imposed with the start and end of the effective period, i.e., the period between the maximum and minimum acceleration. Lockdowns 1, 2 (Level 4 restrictions), 3, and 4 were found to be implemented too late, as they were expected to come into effect at the end or after the effective phase, and they were therefore ineffective. It was determined that Lockdown 2 (Level 3 restrictions) did not initiate the effective phase, and it was therefore ineffective, too. Lockdown 5 was expected to take effect in the second half of the effective phase, but showed no changes in the acceleration curve, and it was therefore also ineffective. Lockdown 6, implemented well before the effective period, did not flatten the curve, and was thus also found to be ineffective. The mask mandate between Lockdown 2 (Level 3 and 4 restrictions) initiated the effective phase (likely along with Lockdown 2, Level 3 restrictions), and was therefore found to effectively flatten the curve. The temporal relationship between the assumed cause (control measure) and the observed effect (flattening of the curve) is thus a crucial parameter for assessing the effect of control measures.

1. Introduction

After three years of the COVID-19 pandemic, daily case numbers are declining: while the trend of pre-Omicron waves showed increasing numbers over time, the trend of Omicron waves featured decreasing numbers [1]. As restrictions ease around the world, countries are considering, if not calling for, retrospective assessment and internal review of control measures for determining their effectiveness and their suitability of containment of the pandemic. Some reports on this topic are already available, and they are introduced subsequently—an independent report, a report of a medical association, and a government report.

For example, in October 2022, the independent “Fault Lines” review [2] examining Australia’s response to COVID-19 was published, prompting strong opposition from the Prime Ministers of Victoria and Queensland [3]. The review listed four areas where Australia should have done better: (1) “Economic supports should have been provided fairly and equitably”; (2) “Lockdowns and border closures should have been used less”; (3) “Schools should have stayed open”; and (4) “Older Australians should have been better protected”. This report [2], however, did not specifically address the control measures and their effectiveness.

In July 2023, the British Medical Association [4] issued a report about “The public health response by UK Governments to COVID-19”, and the Executive Summary of this report asks: “How effectively did the UK governments manage their public health responses to the COVID-19 pandemic?”. This report lists all of the control measures chronologically, and it finally suggests “Recommendations for Governments and questions for the public inquiries to answer”, such as “What was the effectiveness of local lockdowns on case rates…?”.

In March 2023, the Singaporean Government released a white paper on Singapore’s response to COVID-19 [5], evaluating public health control measures as well as economical, public health, and social issues. Singapore introduced a lockdown (“circuit breaker”) on 7 April 2020, and the report concluded that “As a result of the Circuit Breaker, the number of community cases tapered off and fatalities stayed low”. However, no explanation was given for the temporal and, thus, the causal connection between the control measures and the beginning of the decline in the daily number of cases.

In Germany, panel doctors are advocating close examinations of the effectiveness of the control measures [6] and comparing them with other countries in order to understand whether Germany mastered the pandemic better than other countries. In Austria, the government intends to launch a transparent process to assess various issues related to the COVID-19 pandemic, such as the controversial measures, with an estimated cost of half a million EUR [7,8]. This assessment process, specifically “understanding the relative contribution of each of these interventions”, has been described as ‘complicated’ or “complex”, as different interventions were introduced simultaneously or in stages [8,9]. This complexity is reflected in the methodology of Haug et al. [10], who assessed the effectiveness of 6068 non-pharmaceutical interventions on reducing the effective reproduction number of COVID-19.

Although noted as complicated, there is a simplicity to this process regarding assessing whether the control measures were implemented at the right time and to what extent they actually and effectively contributed to flattening the curve (Figure 1a). The curve to be flattened corresponds to the cumulative case data of a single COVID-19 wave, whereas the first derivative of the cumulative data constitutes the daily case date (the velocity data) [11,12], i.e., the speed that the virus is spreading (Figure 1b). The first time derivative of the velocity data determines the acceleration [11,12] (Figure 1c) of the cumulative case data. The acceleration time curve has two distinct markers—namely, the maximum and minimum acceleration peaks (Figure 1c), which define the beginning and the end of the effective phase, and it is in this time window that the acceleration shows a negative slope [11,12]. During the effective phase, the curve of the cumulative cases flattens out (Figure 1a), which is the outcome that the implementation of control measures is supposed to achieve. In this context, the term “flattening the curve” refers to breaking the exponentially or sub-exponentially increasing velocity curve by reducing acceleration [12]. This is achieved by an effective control measure that reduces the acceleration and thereby creates a positive acceleration peak. Using the effective reproductive number R_eff (Figure 1d), which is proportional to the derivative of the logarithm of the velocity, for establishing a causal and temporal relationship between control measures and curve flattening fails, and this failure is a result of the fact that clear markers comparable to those of the acceleration are not reflected in the R_eff curve [12].

If a larger control measure, such as a lockdown, is implemented after the end (day 25 in Figure 1c) of the effective phase [11] of a COVID-19 wave, it cannot contribute to the flattening of the curve, since the flattening process was already initiated at the beginning (day 15 in Figure 1c) of the effective phase ([12]; Figure 1a,c). It should be noted that the effective phase (start and end) is invisible when relying on the effective reproductive number R_eff (Figure 1d). It should also be borne in mind that the curve can be flattened out even with very relaxed and voluntary government-based measures, as the example of Sweden shows [13].

After dividing the control measures into effective and ineffective measures, the individual contribution of each effective measure can be evaluated. For example, Trauer et al. [9] applied compartmental modelling to the second COVID-19 wave in Victoria (2020), and they estimated individual contributions of 37.4% by physical distancing and of 45.9% by wearing face masks.

The aim of this study is to propose, as a first step in reviewing the control measures that were adopted, a standardized approach to assess the temporal and causal relationship of the control measures and the flattening effect on the cumulative case curve. To exemplify this standardized approach, we evaluated the government’s COVID-19 management in the Australian state of Victoria. There are two reasons why Victoria was chosen for this analysis: its capital, Melbourne, is considered the most locked-down city in the world [14], and the three authors of this study also lived in Melbourne during the six lockdowns, which is an experience that is helpful in understanding the dynamics of all six lockdowns.

The need for a standardized approach is obvious: if each country uses different methods to examine the effectiveness of control measures, the results of these methods will not be comparable. From a global perspective, it would be beneficial to understand and compare [6] the effect of different measures, extract common mistakes, and thereby be prepared for future pandemics [2].

2. Method

We obtained Victoria’s cumulative case data from the COVID-19 Data Repository of the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University [15]. The raw data were processed according to the method of Fuss et al. [11,12] by calculating the daily case data (velocity) and then filtering the data with a running quadratic filter (a second-order Savitzky–Golay filter) over a window of 13 data to obtain the velocity data and their 95% confidence interval. The dynamics of the cumulative case curve and its derivatives are illustrated in Figure 1.

For assessing the effectiveness of the control measures, we compared the dates of their implementation to the responses of the acceleration curve. Since the first effect of a control measure is not expected before one serial interval (SI) after its implementation, we defined the time period in which the effect can be expected 5 (SI) to 10 days after implementation [12]. The mean (or median) of the serial interval (in days) varies between different sources: 3.95 in Tianjin [16], 3.96 [17], 4.0 [18], 4.46 [19], 4.6 [20], and 5.2 in Singapore [16], and 7.5 [21]. Additional delays beyond 10 days could result from processing and reporting the PCR tests.

The exact dates of the different control measures come from the diaries of the three authors of this study, who lived in Melbourne during the six lockdowns.

3. Results

3.1. Lockdown 1

The Victorian Government declared a State of Emergency on 16 March 2020 (day 76, Figure 2), followed by national Stage 1 restrictions on 23 March 2020 (day 83: closure of sports, entertainment, and dining facilities). On 26 March 2020 (day 86), national Stage 2 restrictions were introduced (stay-at-home advice unless impossible, and restrictions on the number of people in indoor and outdoor gatherings). On 31 March 2020 (day 91), the Victorian Government imposed Lockdown 1, Stage 3 restrictions, under a stay-at-home order, and permitted people to only leave the house for four reasons: (1) food and supplies, (2) exercise, (3) medical care, and (4) work and education, if required [22]. In addition, non-essential shops and educational institutions had to be closed [23]. Furthermore, fines were imposed for violations of public health protection measures [22,23].

Figure 3 shows the daily case numbers, their 13-day second-order polynomial filter, and the first time derivative thereof. The effective phase lasted from 18 March 2020 (day 78) until 2 April 2020 (day 93). Stage 1 and Stage 2 restrictions were introduced after the beginning of the effective phase, and the onset of their specific effects (the light and dark green bars in Figure 3) were expected to take effect retrospectively one serial interval after their introduction and further delays (i.e., 5 to 10 days) after their introduction. The acceleration increased slightly from day 86 (26 March 2020) and peaked on day 88 (28 March 2020). It is likely that the Stage 1 restrictions resulted in a decrease in acceleration after the peak, and that the Stage 2 restrictions decreased the acceleration further from day 89, with a steeper gradient (more efficient) than the gradient in the first half of the effective phase. Lockdown 1 was introduced two days before the end of the effective phase, and the lockdown was expected to take effect retrospectively on 5 April 2021 (day 96), i.e., three days after the end of the effective phase on 2 April 2020 (day 93). Lockdown 1 was introduced too late, and could no longer help to flatten the curve as the negative acceleration (deceleration) was already increasing and approaching zero.

3.2. Lockdown 2

The Victorian Government introduced the Stage 3 restrictions on 1 July 2020 (day 183), similar to the Stage 3 restrictions of Lockdown 1 (just four reasons to leave the home, and leaving for food and supplies was limited to one person per household once per day), but schools were not closed (yet). Stage 3 restrictions in Lockdown 2 were introduced on 9 July 2020 (day 191). The mask mandate was introduced on 23 July 2020 (day 205). The State of Disaster was declared on 2 August 2020 (day 215), and Stage 4 restrictions were implemented on 3 August 2022 (day 216): there was a curfew from 8 a.m. to 5 a.m.; shopping and exercise could take place no further than 5 km from the place of residence; non-essential retail and educational facilities, including kindergarten and childcare, were closed; and outdoor exercise was restricted to one hour per day with one other person.

Figure 4 shows that the effect of the Stage 3 restrictions was expected on day 188 (6 July 2020). There is a slight decrease in the acceleration, but this decrease did not reach the zero line, and instead fluctuated around a constant acceleration value (approximately 15 case numbers per day squared). Stage 3 restrictions in Lockdown 2 failed to interrupt these fluctuations. The retrospectively expected onset of the effect of the mask mandate (day 210, 28 July 2020) coincided with the start of the effective phase (day 209, 27 July 2020) and the decline of the acceleration. This result is a causal dependency of the decreasing acceleration and the prescribed mask order. In contrast, Stage 4 restrictions in Lockdown 2 were expected to take effect retrospectively on 7 August 2020 (day 220), i.e., at the end of the effective phase. Stage 4 restrictions in Lockdown 2 were therefore introduced too late and could not contribute to the flattening of the curve, as the negative acceleration (i.e., deceleration) was already increasing and approaching zero, which is similar to what happened during Lockdown 1.

3.3. Lockdown 3

Due to the COVID-19 outbreak at the Holiday Inn quarantine hotel at Melbourne Airport, a 5-day snap lockdown under Stage 4 restrictions was imposed on 13 February 2021 (day 410). The restrictions included: the four reasons to leave home, no public gatherings, a travel limit of 5 km, a mask mandate, the closure of educational institutions and non-essential businesses, but no curfew.

As shown in Figure 5, there were two preceding spikes around day 367 (1 January 2021) and 383 (17 January 2021), with the effective phases each lasting 8 days. The effective phase of the February 2021 spike started on 10 February 2021 (day 407). Note the average daily caseload of 2.5 cases per day at the peak of the spike. The restrictions of the snap Lockdown 3 with Stage 4 restrictions were expected to take effect retrospectively on 18 February 2021 (day 415), i.e., two days after the end of the effective phase on 16 February 2021 (day 413). Stage 4 restrictions in Lockdown 3 were therefore introduced too late and could not contribute to the flattening of the curve, as the negative acceleration (i.e., deceleration) was already increasing and approaching zero, which is similar to what happened during Lockdowns 1 and 2.

3.4. Lockdown 4

On 28 May 2021 (day 514), an initial 7-day circuit breaker Lockdown with Stage 4 restrictions was introduced, which was extended by a further 7 days. The restrictions were similar to Lockdown 3, but as part of the stay-at-home orders, the four reasons to leave the house were expanded to five, and now included permission to leave the home for obtaining a COVID-19 vaccination. The COVID-19 vaccination program started in Victoria in February 2021 [24].

As shown in Figure 6, the effective phase began on 22 May 2021 (day 508) and ended on 30 May 2021 (day 516). Lockdown 4 was introduced 2 days before the end of the effective phase. Lockdown 4 with Stage 4 restrictions was expected to take effect retrospectively on 2 June 2021 (day 519), i.e., three days after the end of the effective phase on 30 May 2021 (day 516). The negative peak of acceleration marks the end of the effective phase, from which acceleration increases and approaches zero. As shown in Figure 6, this return to zero exhibits a steep gradient and, after an overshoot, reaches a positive peak on 2 June 2021 (day 519). After the end of the effective phase, such overshoots occur quite frequently, as the acceleration fluctuates around the zero line. However, the positive peak on 2 June 2021 (day 519) coincides with the onset of the effect of Lockdown 4, and this was followed by a deep acceleration low. It is thus likely that this trough was caused by Lockdown 4.

3.5. Lockdown 5

On 16 July 2021 (day 563), the Victorian Government ordered a further 12-day circuit breaker lockdown under Stage 4 restrictions, and Lockdown 4 restrictions were repeated in this one.

As shown in Figure 7, the start of the effective phase coincided with the introduction of Lockdown 5. As Lockdown 5 with Level 4 restrictions was not expected to take effect until at least one series interval after its implementation, the start of the effective phase was not initiated by Lockdown 5. Lockdown 5 was expected to take effect retrospectively on 21 July 2021 (day 568), i.e., four days before the end of the effective phase on 16 July 2021 (day 563). Since the acceleration gradient was steeper in the first half of the effective phase, and flatter in the second half, Lockdown 5 was unable to help to flatten the curve, and it was thus introduced too late. This result is supported by the fact that after the average daily case numbers hit a local minimum of approximately 2.5 cases per day on 31 July 2021 (day 578), the daily cases started to rise again, leading to Lockdown 6 five days later.

3.6. Lockdown 6

As the daily case numbers increased again four days after the end of Lockdown 5, Lockdown 6 was introduced on 5 August 2021 (day 583) under Stage 4 restrictions. The restrictions were similar to the previous lockdowns. Since the daily number of cases continued to rise, a curfew from 9 p.m. to 8 a.m. was introduced on 17 August 2021 (day 595) together with government permits required for working outside the home and for travelling to work.

Compared to the effective phase (Figure 8) from 29 September 2021 (day 638) to 26 October 2021 (day 665), Lockdown 6 and its extensions to curfew and permits did not contribute to the effective phase, and they therefore did not contribute to flattening the curve. The effective phase started approximately 30 days later than expected, with approximately 17-fold more cases compared to the case numbers during the expected onset of the effective phase. Due to a high percentage of first-dose vaccinations, the control measures were relaxed before the start of the effective phase [25]. At the end of the effective phase, the same high percentage of double-dose vaccinations was achieved [26].

4. Discussion

The contributions of the lockdowns and other critical control measures to the flattening of the curve are listed in

Table 1. Summary of the control measures, their dates, their actual timing, and their actual effects.

Control Measure	Date	Timing	Effect
Stage 1 restrictions Stage 2 restrictions	23 March 2020 26 March 2020	Did not initiate the effective phase	Likely supporting the second half of the effective phase
Lockdown 1	31 March 2020	Introduced too late; effect expected after effective phase; and did not flatten the curve	NONE
Stage 3 restrictions	1 July 2020	Did not initiate the effective phase; did not flatten the curve	Acceleration did not increase further but was constant on average
Lockdown 2, Stage 3	9 July 2020	Did not initiate the effective phase or reduce the constant acceleration; and did not flatten the curve	NONE
Mask Mandate	23 July 2020	Initiated the effective phase	Flattened the curve, likely in combination with preceding measures
Lockdown 2, Stage 4	3 August 2020	Introduced too late; effect expected at end of effective phase; and did not flatten the curve	NONE
Lockdown 3	13 February 2021	Introduced too late; effect expected after effective phase; and did not flatten the curve	NONE
Lockdown 4	28 May 2021	Introduced too late; effect expected after effective phase; and did not flatten the curve	Likely supported faster return to zero cases after the effective phase
Lockdown 5	16 July 2021	Introduced too late; effect expected in 2nd half of effective phase but invisible; and did not flatten the curve	NONE
Lockdown 6 (curfew, permits)	5 August 2021 17 August 2021	Introduced far before the effective phase; did not flatten the curve	NONE

.

In summary, none of the six lockdowns (Lockdown 2 divided into Stage 3 and 4 measures) directly helped to flatten the curve (Table 1), let alone initiated the flattening. Lockdown 4 could have contributed to a faster return to zero cases after the effective phase. Two different control measures introduced days before the lockdowns were identified as at least partially successful. Stage 1 restrictions in the advent of Lockdown 1 were likely supporting the second half of the effective phase, an effect that was actually expected from Lockdown 1 itself. The mask mandate introduced ten days before Lockdown 2, Stage 4 restrictions, seems to have initiated the flattening of the curve, based on a temporal–causal relationship.

A reasonable counter-argument at this point might be that without lockdowns, there would have been more daily cases and more deaths. However, the sheer lack of effect of a lockdown inevitably leads to more cases and more deaths. It would have been far better if the unsuccessful lockdown had initiated the effective phase as expected, and had thereby flattened the curve.

Caution should be exercised when using the effective reproduction number R_eff to assess the effectiveness of control measures. While the acceleration shows clear time markings (minimum and maximum peak data; zero transition) throughout the duration of a wave (Figure 1), R_eff only offers the transition from >1 to <1, which evidently coincided with the peak velocity data. If only the amount of decrease in R_eff (ΔR_eff, e.g., [10,27]) is used, this amount should actually be related to the time window in which R_eff decreases, i.e., the gradient of the R_eff-time curve. However, this gradient decreases over time, as R_eff, if >1, varies from +ꝏ to 1, and if <1, it varies from 1 to 0. Using the gradient of the logarithm of R_eff is not helpful either, as this gradient is constant (Figure 1) in a Gaussian shaped wave.

Scott et al. [28] attempted to relate the effect of mandatory masks (Lockdown 2 in Victoria; Figure 4) by calculating the R_eff before and after a ‘hinge day’ (31 July 2020), and obtained average R_eff values of >1 (1.16–1.28) and <1 (0.91–0.88), respectively. They concluded that, “The mandatory mask use policy … was associated with a significant decline in new COVID-19 cases after introduction of the policy” [28]. This result is expected, as the ‘hinge day’ was close to the peak of the velocity curve between 1 and 2 August 2020. R_eff is, by definition, unity at any velocity peak. The cumulative case curve begins to flatten out before the velocity peak, particularly at the positive acceleration peak at the beginning of the effective phase. The retrospectively expected onset of the effect of the mask mandate (28 July 2021) coincided with the start of the effective phase (27 July 2021) and the decline in acceleration (Figure 4). The transition of R_eff from >1 to <1 occurs at the velocity peak, which is the only clear marker seen on the R_eff curve (Figure 1). The positive and negative acceleration peaks, i.e., the start and end of the effective phase, cannot be detected on the R_eff curve. In this regard, the Victorian Government erred in claiming that Lockdown 2, Stage 4 restrictions were responsible for flattening the curve [29] and in placing the start date of Lockdown 2 before the velocity peak, even though it was clearly after the velocity peak (Figure 4). Details of this error are given in [12].

In the context of the second COVID-19 wave in Victoria, Trauer et al. [9] used a simulation based on a compartmental model, and they “estimated significant effects for each of the calibrated time-varying processes, with estimates for the individual-level effect of physical distancing of 37.4% (95% CrI 7.2–56.4%) and of face coverings of 45.9% (95% CrI 32.9–55.6%)”. The latter result reflects our observation and conclusion that the effective phase of Lockdown 2 was initiated by the mask mandate.

The decision criteria for classifying the effect of a control measure depend on the timing of cause (control measure) and effect (flattening of the curve). In this connection, Fuss et al. [12] defined several scenarios related to the chronological sequence of control measures and the onset of their effect:

• If the effective phase starts before or on the day the control measure is introduced, there is no causal connection between the control measure and the initiation of the effective phase.
• If the effective phase starts within one average SI after the day the control measure is introduced, there is an unlikely causal connection as the relationship between epidemiological indicators of infection cannot be an immediate one due to the serial interval (SI).
• If the effective phase starts between the end of SI and the following 5 days, there is very likely a connection.
• If the effective phase starts after the end of one SI + 5 days, there is an unclear connection, depending on the circumstances, which could be interpreted as a severe delay of the intervention’s effect, or even as an unsuccessful effect not entirely connected to the intervention, considering that relaxed measures (comparable to the ones introduced in Sweden) also initiated the effective phase.

The effect is a specific change in a parameter (e.g., the decline of the acceleration after the start of the effective phase), and the cause is supposed to be a control measure. If the cause precedes the effect, a causal relationship is likely considering the delay due to the SI. If the “cause” occurs after the effect, we cannot even speak of a cause. If a lockdown were introduced, to take one example, in the middle of the effective phase, and its effect was thus expected, e.g., at the end of the effective phase, this very lockdown could not have helped to flatten the curve as it was introduced too late, and was therefore ineffective and, as a result, in vain. If a control measure introduced at a certain point of time, despite considering the time delays, does not have the expected effect over a longer period of time, a causal relationship is questionable. It is less likely, if not impossible, regarding Lockdown 6 that the beginning of the effective phase with a 30-day delay was causally linked to the control measure itself. We thus expect the immediacy principle that constructs the causal relationship. The immediate effect is explained by Rothman and Greenland [30] as the causal light-switch/light-bulb effect, which involves more factors than just a switch to turn on the light. These additional factors in the context of control measures that could help to tip the acceleration curve faster are prior control measures already in place, seasonal effects, improved compliance, immunization, and a latent factor that explains the flattening of the curve without control measures. The latter is probably responsible for COVID-19 control in Sweden [13] in the sense of self-imposed but not government-imposed compliance. In these circumstances, it is likely that the vaccination status in Victoria in September/October 2021 initiated the effective phase (Figure 4) rather than a very delayed effect of Lockdown 6. Furthermore, why would a control measure (Lockdown 6 in this case) succeed a month after its introduction at excessive daily case numbers, which are decisively more difficult to control (exponentially increasing velocity if constant R_eff), if it failed in the first place with 17 times fewer case numbers at the expected onset of the effect? In short, the longer an effect is delayed, the less likely that there is a temporal cause.

The connection between lockdowns alone with more efficient epidemiological control of COVID-19 was refuted by Fuss et al. [11], although it seems plausible that lockdowns must be more efficient. Rothman and Greenland [30] define “the problem with plausibility: it is too often not based on logic or data, but only on prior beliefs”. Assuming that lockdowns must be more efficient is a typical prior belief, but it was nevertheless challenged by Anders Tegnell, the Swedish state epidemiologist: “Lockdown, closing borders—nothing has a historical scientific basis” [13]. There are two issues with control measures in terms of cause and effect:

(1)

First, we have the advantage of being able to rely on data rather than belief. The acceleration data provide stronger evidence of the causal relationship between measures and data changes than the R_eff.

(2)

Second, even if the onset of the effect occurs at the expected time, there is always some probability that the apparent association is not real (and, rather, an illusion) if the latent factor mentioned above, explaining the flattening of the curve without control measures, outweighs all of the other control measures (i.e., self-imposed compliance rather than government-imposed compliance).

In summary, there are two reasons why lockdowns or other control measures are ineffective:

(1)

They were introduced too late, with effects expected towards the end, or even after the end, of the effective phase.

(2)

Alternatively, if introduced before the start of the effective phase, the compliance was poor. Murphy et al. [31] investigated the compliance of Australian citizens during the first lockdown, and they concluded that it was as low as 50% due to citizens socialising in-person with friends or relatives they did not live with and also leaving the house without a good reason.

The limitations of this study are as follows:

(1)

The causal relationship between the control measure and the start of effectiveness is construed by circumstantial evidence. This evidence fails if the latent factor mentioned above could have prepared the flattening of the curve over a longer period of time, so that a timely and quickly initiated control measure cannot do much to help.

(2)

The evaluation of a control measure with regard to its effectiveness, based on the method proposed in this study, is only a retrospective, and, therefore, it cannot be used for forecasting. It is thus not surprising that the timing of a control measure can fail in the sense that it is introduced too late and therefore proves ineffective. The reason that the method is a retrospective method is explained by the window width of the 13 data applied to the daily case data (velocity) filtering with a running quadratic filter. The optimal window width of 13 data was determined from a convergence test [11].

5. Conclusions

In this study, we have attempted to establish a likely causal effect or to refute an effect of a control measure, depending mainly on the criterion of temporality, by answering whether it is very likely that a specific control measure, or a plurality of measures, flatten the curve by initiating the effective phase. In the case of Victoria, Lockdowns 1, 2, 3, 4, and 5 did not start the effective phase as they were introduced too late. Lockdown 6 was inefficient because, if there was a causal link to the flattening of the curve, the effect came delayed by about a month after the lockdown was implemented and, paradoxically, after the restrictions were eased.

For the purpose of evaluating, reviewing, and reappraising the control measures and their various impacts (e.g., on mental health, economic burden, legal aspects, etc.), we have proposed a standardized approach to data processing and decision making. It is important to remember that any measure is a fine line between controlling a spreading disease and minimizing the burden on citizens. Severe restrictions can lead to legal action, as a successful class action lawsuit in Melbourne shows [32]. In the advent of Lockdown 2, “people were wrongly detained for up to 14 days and threatened with physical harm if they tried to leave” their homes [32]. As a result of this class action, “Thousands of residents … are set to collectively reap $5 m in compensation” [32]. Evidently, there is much more to evaluate in the aftermath of the COVID-19 pandemic, such as the impact on health (particularly the mental health) of citizens and on the economy, but all of the impacts need to be assessed in terms of the effect of the control measures, i.e., which control measures initiated the effective phase and, therefore, the flattening of the curve, and not with the mere reduction of R_eff. The latter approach grossly neglects the temporality principle of cause and effect.