Model the COVID-19 pandemic
There has been a lot of press about disease modelling over the last week. The Government has releasing the modelling it has used to inform its current response. You don’t need to be clairvoyant to see how uncomfortable they were doing so, even though their modelling is basically sound. The fact of the matter is that good disease modelling is one of the few reliable tools we have for working out how best to respond. Last week in the Financial Review I presented some thoughts on the costs of different approaches to managing the pandemic based on our modelling. How does this compare with what the Government has done?
The basics of disease modelling
It helps to know how disease models work. There are a variety of approaches, but they have common elements.
The starting point is to understand how people interact. How many people will you or I contact on a typical school day, weekend or vacation day? This is difficult and costly to measure but it has been done, notably in the UK, and has been extended to different countries with different characteristics including Australia. Once you know how many contacts people make every day, you can start to plot how a disease will spread. Figure 1 shows estimated contact rates on a normal school day in Australia. By far the highest contact rates are between school age children. The next highest contact rates are work related. And broadly, most contacts are between people of similar age. The elderly have the lowest contact rates.
You also need to know how the disease spreads through a population with no immunity. We do this using an estimate of the R0 for the disease, which indicates how many other people you will directly infect if you are infected provided none of your contacts are immune. The R0 for COVID-19 is probably between 2.0 and 2.8, but estimates vary. We have used 2.4 as the central value in these illustrations.
As the number of immune within the population rises, whether because we are lucky enough to have a vaccine or because people have had the disease and recovered, the proportion of those susceptible to infection falls. If 50% of the population are immune, the effective R0 will fall to 1.2 because half the people you meet are immune. Once the R0 falls below 1, the disease will peter out. Pandemics are therefore self-limiting, but the harm they can cause on the way can be devastating.
To understand how fast the disease will spread, you need to know the duration of the exposure period (when the person is exposed but shows no symptoms and cannot spread the disease to others), and the duration of infectiousness which follows (when the infected person can infect others and may show symptoms). For COVID-19, estimates for these are around 5 days and 11 days respectively. It will take just over 2 weeks for an infected person to infect the 2.4 others indicated by the R0. Figure 2 shows the number of new symptomatic infections we could expect each day in Australia if we did nothing (clearly an unrealistic scenario). It would peak at around 210,000 in late May and decline thereafter. You would get a higher peak, a shorter pandemic and a higher number of infections overall with higher R0 values, and the converse with lower values.
Once we understand the rate of spread, we can determine the consequences. We start with the proportion of infections that are symptomatic, and the proportion of those cases that will die (sometimes referred to as the case fatality rate, CFR). For COVID-19 we assume that around 70% of infections are symptomatic and, of those, 0.5% will die provided that intensive care beds (ICU) are available for all that need them. We can assess demand for ICU from the expected proportion of ICU admissions that die (we assume 25% but there are higher estimates in the literature). We can assess the number of hospital admissions from the proportion of severe hospitalised cases that require ICU; we have assumed 30%. We also assume that all deaths occur in ICU if beds are available.
Figure 3 shows demand for ICU beds in Australia if there is no intervention. It peaks at around 32,000 per day. This aligns closely to the Governments own modelling. Australia had only 2,300 ICU beds at the outset of the pandemic, a 14-fold shortfall. Demand would be higher with a higher case fatality rate or a higher R0.
Hence all the talk about ‘flattening the curve’, bringing the number of daily infections down so that ICU demand does not rise above the dashed line.
If severe cases can’t get ICU, their risk of dying increases; we have assumed that severe cases are twice as likely to die without ICU, but the precise impact on mortality is not yet clear. Figure 4 shows the expected number of deaths each day without intervention; ‘Deaths’ refers to the number of deaths assuming all patients receive intensive care, ‘Excess deaths’ are the additional deaths because intensive care is not available. ICU shortages, absent intervention, would increase the CFR from 0.5% to 0.9%.
In order to effectively target interventions that minimise health impacts, we need two further pieces of information, the impact of age and comorbidities on mortality, and the susceptibility of different population cohorts to infection. Data from China indicates that people over 70 are 8-10 times more likely to die than healthy young adults and children, and that a single comorbidity increases the risk of a severe infection (requiring hospitalisation and ICU) and death 1.8-fold. This is not always the profile in a pandemic; mortality was very high in younger adults in the 1918 influenza pandemic. There is also evidence emerging that children are less susceptible to infection, but until that is confirmed, we have not included it in our modelling.
Finally, we believe that it is important to understand the cost and economic impact of the pandemic and of different interventions. We estimate benefits in terms of physical measures such as number of deaths, outpatient visits and hospitalisations; on cost measures including the direct cost of treatment; and on lost quality of life, where each quality adjusted year of life lost (QALY) is deemed to be worth $50,000. The last of these places a higher value on saving a young person’s life than an older person’s.
We base the economic costs on loss of labour calculated directly from the time that infected individuals in the work force are absent from work due to illness, hospitalisation, intensive care and death. And on the labour that is lost as a result of social distancing measures and quarantine if they are put in place. We translate these into an impact on GDP using the labour contribution to GDP in Australia, which is around 47%. This is a simplification but points clearly in the right direction.
Flattening the curve
The concept of ‘no intervention’ is untenable. No government could or should allow the unhindered spread of a disease with these consequences. And even if they contemplated doing so, the evidence from Mexico in the 2009 swine flu pandemic is that the population self-isolates with a degree of panic, staying away from school and work. Australia has rightly responded to the pandemic with strict social distancing measures aimed at reducing spread and ‘flattening the curve’. Schools are closed; non-essential work has ceased; all gatherings have stopped; and everyone is forced to stay at home.
We model these changes by reducing contact rates in the school, workplace and community in line with the social distancing measures adopted. In this example, we have assumed 90% compliance, with contacts outside the workplace and in the community reduced by 90%. Figure 5 shows the dramatic effect of these measures on contact rates.
Figure 6 shows the impact of these measures on demand for ICU beds. It certainly flattens the curve. Over the duration of the modelling (just over a year), it dramatically reduces deaths from 137,000 to 22,000 and completely eliminates the excess deaths caused by lack of ICU. Over the year, it reduces the direct costs of health interventions by $10bn and saves QALYs worth $131bn ($1.1m per life saved).
The social distancing measures are in place for 10 months (from the beginning of March to the end of the year). They reduce labour availability by 675m working days, reducing GDP by around 19% (1.9% per month of application) worth around $390bn. That translates into a cost to the economy of around $3.4m per life saved.
Unfortunately, we cannot assume that COVID-19 will simply disappear at some future date. Figure 7 shows what happens if current social distancing measures remain in place until November and are then removed in their entirety. There is a resurgence of infections — a second wave — which arises because the proportion of susceptible people in the population is still very high and the virus is still around. This second wave overwhelms our ICU capacity once again.
We have, in a sense, the worst of both worlds: we have spent $290bn or 14% of GDP to merely delay the peak by 6 months but in the end we only save 70,000 lives, 45,000 fewer than would be saved if there was no second wave, a net cost per life saved of around $4.2m. Indeed, this figure is conservative in that it does not include all the deaths that would occur in the second wave after February 2021, not does it include the cost to the economy of extending social distancing to prevent the second wave.
If this was an influenza pandemic, even a severe one, we could relax the social distancing measures once a vaccine is given. But in the absence of a vaccine or a cure, sudden cessation of social distancing appears very unwise. But by the same token, keeping them all in place looks very expensive.
Different social distancing measures have different costs and benefits. For example, quarantining those at risk and those over 65 so that they have little or no contact with infected people will reduce the risk that they will get infected. Since this cohort has a high COVID-19 mortality rate, this has a large impact on the overall number of deaths. In contrast, relaxing school closures would have a much smaller impact on COVID-19 deaths even though it will substantially increase rates of social contact. This is because mortality rates are low in school children and in those they contact (mostly younger healthy adults). This will be the case provided, of course, we can ensure that those at risk, particularly those over 65, remain isolated; this is the reason we isolate care homes from visitors. Figure 8 and Table 1 show the effect of different social distancing measures individually on the number of daily deaths and the cost per life saved.
The most effective measures for reducing deaths are age-based isolation — because it targets a cohort with the highest mortality and because few in this cohort are working — and household isolation where there is an infection. The most expensive and least effective are school closures and workplace restrictions. Restrictions on all other activities, the current ‘stay at home’ policy, is effective at reducing deaths but has a higher cost per life saved.
Gradual Removal scenario
Modelling allows us to examine different timing and combinations of social distancing. Under a ‘Gradual Removal’ scenario, schools are re-opened after 3 weeks (which in this analysis would be at the end of the current Easter vacation), work constraints are removed 5 weeks later in late-May and constraints on community activities are removed after a further 12 weeks (taking us to September). Isolation of the at-risk ceases at the end of November, at which time we could even allow international visitors to return. Household quarantine where there is a symptomatic case (ideally confirmed with testing) continues throughout the modelling period and is extended to 21 days per case found.
In addition to these changes in social distancing and in line with government announcements, the number of ICU beds is increased from 2,300 to 7,000 by the time constraints on community activities are removed. Figure 9 shows the impact of all these collectively on demand for ICU beds. The increase in ICU bed availability is essential in order to allow relaxation of social distancing without overwhelming the health system and to eliminate all excess deaths.
The number of lives saved is smaller than if social distancing were in place for the whole year, as shown in in Figure 6. Gradual relaxation results in 52,000 deaths in contrast to the 22,000 deaths if social distancing stays in place until the end of the year.
But the 22,000 deaths figure is not the right counterfactual, it ignores the deaths that would occur in the second wave very likely to arise when the mitigation measures are finally removed A more sensible counterfactual would recognise the high likelihood of a second wave in which case there would be 66,000 deaths. In terms of lives saved, Gradual Removal is very similar to later rapid removal and a second wave. The harsh reality is that without a cure or vaccine there is no way to eliminate all avoidable deaths without protracted and extended constraints on the economy, of the order 2% per month, until the restrictions are removed. Failing to recognise this would be a serious policy failure.
Under the ‘Gradual Removal’ policy the economic costs of the social distancing measures are limited to 6.4% of GDP, around $132bn. The cost per life saved is around $2.1m. In contrast, the cost of current social distancing to the end of the year would be around 19% of GDP, $390bn, resulting in a cost per life saved of $3.4m assuming somewhat unrealistically, that there is no second wave and there are only 22,000 deaths. If there is a second wave after December, then the cost per life saved rises to close to $6m.
Even if we were to assume that $3.4m per life saved is correct, as economists we also look at the cost of saving each additional life compared to the Gradual Removal policy. This is over $8m, well above our normal health cost-benefit threshold. The cost per additional life saved would be higher still if we needed to take further action to forestall a second wave.
Rapid Removal scenario
We also examined a faster phased relaxation of social distancing measures. In this scenario, schools re-open immediately and all workplace constraints are also relaxed. Constraints on community activity are relaxed at the end of June. Household quarantine and isolation of those at risk remain in place as before. Inevitably, demand for ICU beds rises more rapidly than under Gradual Removal, and for a short period of time, about six weeks, demand exceeds available capacity by around 10% resulting in excess deaths (see Figure 10).
There are more deaths in this case, 3,200 or about 5% more than under Gradual Removal, but the impact on GDP is much smaller (4.1% or $85bn as opposed to 6.3% or $132bn). The average cost per life saved under the Rapid Removal scenario is $1.4m. The cost of saving each additional life under the Gradual Removal policy is close to $15m. Under our normal health cost-benefit criteria, we would choose to accelerate the removal of social distancing. These results are summarised in Table 2 and Figure 11.
The foregoing points to the difficult trade-off between economic gains and lives saved from accelerated removal of social distancing constraints. We conclude that acceleration is the preferred option if we base our decisions on the normal health cost-benefit and value of life metrics used in decision making in Australia. We take no position on whether these metrics are appropriate for our economy or on whether there are compelling reasons for changing them in a pandemic.
There are some important additional considerations before deciding on how best to relax current social distancing measure. First, the timing of new ICU bed capacity: the foregoing assumes that new beds can be made available quickly, certainly by September. If this is not the case, then measures should be relaxed more slowly. Second, it depends on high rates of compliance in household quarantine where there is an infection and isolation of the at risk. In our analysis, a 15% reduction in compliance results in 3,000 additional deaths, increasing the cost of each life saved under the Gradual Removal scenario from $2.1m to $2.6m. If we cannot ensure compliance by measures such as strong government and social support for the isolated, we may need to prolong broader and more costly constraints on community activities.
We can and should use modelling to compare different intervention approaches. These are some examples of how disease modelling can inform our policies. A more thorough exposition would expand the range of scenarios and use techniques like Monte Carlo analysis. Variants of the modelling, such as greater geographical specificity or a stochastic element to the likelihood of infecting others, may also provide more nuance. And some of the key assumptions may change as we learn more about COVID-19 and our response to the current measures; this may lead to different choices.
Nevertheless, our modelling, which aligns well with the modelling results published by the Government but includes metrics on cost, points clearly to the need to relax social distancing and prepare for the disease to spread in a controlled manner. While Governments have not set out their anticipated program for relaxing social distancing, recent announcements suggest that they are aware. Moving early to relax school closures and work constraints is sound policy; it limits the economic costs and does not result in many more deaths. Expanding ICU beds is an important step in allowing this to work.
Relaxing constraints on public activities, sports, cinemas, pubs and clubs etc. is a more challenging decision. But our modelling indicates that the economic benefits of allowing these to restart relatively quickly are compelling. The cost for each additional life saved from their continuation is large. Opening these activities is key to ensuring, as quickly as possible, a managed transition to the point where we have herd immunity with a low risk of a second wave.
Case-related household quarantine and isolation of those at risk, particularly those over 65, is necessary until late in the year. These allow other social distancing measures to be relaxed while minimising the risk of an uncontrolled and unmanageable increase in severe cases. Better testing to identify households with an infection is important. Government action to ensure effective social support for the isolated is also essential to allow them to comply.
While it may be uncomfortable to consider, paying too much for protection in a pandemic today comes at the expense of those who would benefit from spending that same money elsewhere tomorrow. Protecting the economy is an imperative: to ensure in the future better health care, better road safety, better the myriad of other programs where we rely on public spending to ensure our wellbeing.
 For example, it does not consider any demand effects associated with isolation of the elderly or the proportion of elderly that remain in work. We also have to make assumptions on the impact of school closure on workplace availability for carers and on the impact of moving work from the workplace to home on productivity.