Modelling COVID-19 in Australia
Updated: Apr 9, 2020
COVID-19 has taken the world by storm. A little more than three months after the first case was observed, it has become all that the world is talking about. Aside from the obvious health impacts that have led to more than 80,000 deaths at the time of writing, the economic impact of COVID-19 cannot be understated.
With over 25% of all recorded cases, the US is currently leading this tragic race. Unemployment claims in the US hit their peak at 6.6 million in the week ending 28th March, the most filed in history. Even in the wake of the 2008 global financial crisis, this number peaked at approximately 600,000. Economists in the US are already making comparisons to the Great Depression.
Australia's geographic isolation from the rest of the world is no safety against the economic downturn that has already begun and surely has some way to go yet. Upto a million jobs could fall victim to COVID-19 based on current estimates. Stimulus packages promised by the government will decrease these numbers, but any further increases in COVID-19 transmission rates will likely trigger stricter lockdown measures and undermine any government economic response.
In this uncertain environment, businesses are required to forecast cashflow and expenditure to decide what actions to take with employees and products. Layoffs have already begun and many employees are forced to take pay cuts to keep their employers afloat. With things changing so quickly, companies must stay ahead of the COVID-19 curve and take proactive action to ensure they will still be here to watch the rebound on the other side of the pandemic.
In this post we present the SIR model, which is one way companies can monitor what Australia's curve is doing on a daily basis.
S-I-R Model
The Susceptible-Infectious-Recovered (SIR) model is an epidemiological tool to model the spread of an infectious disease in a large population. It belongs to the 'compartmentalised' class of modelling strategies, where the entire population is discretely categorised and individuals move between the categories as time passes. For the SIR model, these categories are:
Susceptible (S) - the subset of the population that can be infected when exposed.
Infectious (I) - the subset of the population carrying the pathogen.
Recovered (R) - the subset of the population that has previously been infected and is now unable to spread the pathogen, through either immunity or death.
The SIR model and its derivatives were inspired by chemical kinetics models; as with those models, the dynamics (in this case the movement of individuals between the different categories) are governed by three differential equations and several empirical constants:
The empirical constants in the equations are:
μ - birth rate of susceptible individuals
δ - natural death rate
β - infectivity rate per contact
a - death rate of infected hosts
γ - recovery rate of infected hosts
Assumptions
Given the speed at which COVID-19 is spreading, the natural birth and death rates (μ and δ) are set to 0. These would play roles in longer pandemics and may become important should the spread not be arrested by the end of the year.
a is approximated as 0 to reflect the low mortality of COVID19 in Australia (0.8%).
From an infection perspective, 'recovery' refers to a low propensity of an individual to transmit the disease, which is not necessarily the same as a return to good health. For COVI19, 1/γ is estimated to be in the range 1.7-5.6 days. For this study, 1/γ is assumed to be 3.3.
The time for a return to good health is estimated to be approximately 2 weeks for mild cases and 3-6 weeks for severe cases. A middle-of-the-range assumption is made of 4 weeks.
Basic Reproduction Number
β and γ together represent the most important prediction of the SIR model for our purposes - the basic reproduction number of the pathogen, R0. R0 is a dimensionless number that indicates the expected number of secondary infections that result from a single infection in a completely susceptible population. Quite simply, it can be thought of as the number of people that each infected individual will pass the disease on to.
R0 is calculated as the ratio β/γ. When R0 is less than 1, the epidemic is stemmed and the population returns to normalcy. When R0 is greater than 1, the epidemic grows until the entire population is infected.
R0 varies through the course of an epidemic as it depends not only on the properties of the pathogen but also on the response of the host such as the use of masks, social distancing, and hand-washing. In the early stages of an epidemic when information is not easily available and government responses have not yet been formulated, R0 may be high. As the epidemic grows, public policy and personal behaviour act to reduce R0. The extent to which R0 is reduced and the timing of that reduction determine how far the disease spreads.
The figure below shows the expected number of positive cases of COVID-19 in Australia given certain constant values for R0 beginning with the number of infected from April 7th - 5919. R0 values below 1 show the epidemic decaying. With an R0 of 0.5, the expected number of infections after 2 weeks is just 700. R0 values above 1 paint a more depressing scenario - an R0 of 1.4 would see us at 32,000 cases.
The future trajectory of R0 is not known to us but we do know the history of our infection curve. Given that, and the 28-day recovery assumption, the value of β can be optimised to produce characteristics of the epidemic that best match the available data. This allows the retrospective calculation and visualisation of R0.
Findings
The plot below shows R0 for the COVID-19 pandemic in Australia thus far (red) and also the total number of cases in Australia (blue) - note the log scale on the latter. R0 for a given day is evaluated based on infection data from the previous 5 days. To ensure robust statistics, R0 is only calculated from the day when Australia's case count reached 100.
Are there reasons to be optimistic? Cautiously, yes. R0 has been dropping fairly consistently for nearly two weeks and we are yet to see the full effect of the recent bans of large gatherings in Australia and the further travel restrictions imposed. These will apply additional downward pressure to R0. However, R0 remains significantly above 1 which indicates the epidemic still has legs in Australia. As seen earlier in this post, R0 values even marginally above 1 can be disastrous. Should current mitigation policies fail to reduce this to very nearly 1, further measures are likely which will impose even greater strain on the Australian economy.
What does this mean for businesses? Traditional methods of running a business do not account for the difficult and uncertain future that looms. More than ever, businesses need to optimise operations to reduce expenditure, make efficient use of their assets to increase revenue, and rely on agile predictive modelling to make quick, smart decisions in this volatile situation. The current crisis not only affects bottom lines, but also the livelihoods of the millions of employed Australians. It is vital that we get this right. We will be monitoring R0 for COVID-19 on a daily basis at our Australian dashboard. Visit it to see what progress our policies and behaviour are making towards flattening the curve.
The Australian government has also released its own modelling findings for the spread of COVID-19 in Australia. It models different scenarios and drives home the importance of physical distancing measures. It is available here.
Supplementary information
For reference, below is a plot of R0 for Australia compared to other countries that have been hit hard by the virus.
In the early stages, countries are unprepared and social distancing has not yet been implemented; R0 starts out at high values. As the supply of medical PPE catches up to demand, countries increase testing, and people begin working from home and limiting face-to-face social interaction, R0 is forced downwards.
China has had a low value of R0 - very nearly 1 - for over a month now but some doubt has been cast over the reliability of these numbers. It is however conceivable that their early and aggressive measures to slow down the outbreak has resulted in some very low R0 numbers.
South Korea and Iran bore the brunt of the early global outbreak. Subsequently however, South Korea's widely-praised mass testing and isolation has seen their R0 drop to marginally above China's and remain there for 3 weeks. Iran's introduction of social distancing laws had a similar, but smaller effect - their R0 has hovered around 1.25 for 2 weeks now after a significant drop from the early days.
Spain and Italy have both had high values of R0 for long periods of time. They are now #2 and #3 respectively on the global case count list. Their aggressive lockdown measures have resulted in significant reductions in these numbers but the early and quick spread means their daily increase in case count remains high.
The US, meanwhile, has had a high R0 for over 5 weeks and, while this number is dropping, it is still at around 1.5 - higher than any of the other countries on the plot. Additionally, testing there has thus far been inadequate, so this estimate of R0 is likely to be optimistic.