First reported in Wuhan back in December 2019, the coronavirus disease (COVID-19) has since escalated into a pandemic which has impacted countries across the globe economically and socially. As of the time of writing, there have been 95 million cases and 2.03 million deaths recorded worldwide.
Until an effective vaccine become widely available, authorities are likely to keep preventive measures like social distancing and city lockdowns in place, albeit at the expense of the country’s economic wellbeing.
It is only obvious, then, that such reduction in social consumption has corresponded to a decline in economic growth, as well as in social dissatisfaction.
With common social distancing regulations ensuring that large gatherings are limited, public events restricted, and schools and some workplaces closed down, the impact of these policies have resulted in a sharp contraction of economic activities, especially for service-oriented economies like the United States (US).
Statistics have shown a 5% drop in the monthly Gross Domestic Product (GDP) growth in the US, with the economic cost of the first two months of the pandemic amounting to $2.14 trillion, roughly 10% of the GDP.
Naturally, the trade-off between economic and public health is highly relevant to many governments, who have struggled to maintain economic stability while attempting to minimize infection and death rates. A recent paper, Efficient Social Distancing for COVID-19: An Integration of Economic Health and Public Health, written by SPMS Assistant Professor Pun Chi Seng and his co-authors from The Chinese University of Hong Kong, aims to investigate an efficient social distancing policy (ESDP) with stochastic epidemic modeling and deep learning algorithms.
SPMS Asst Prof Pun Chi Seng
To begin with, the conventional SIRD modeling approach categorizes individual cases into categories – susceptible (S), infectious (I), recovered (R) and deceased (D). More specifically, a discrete-time SIRD model is being used, which is more intuitive to capture the changes in COVID-19 processes –
Although the model can be incorporated with more compartments, the SIRD model is more accessible as it requires only the number of reported cases, active cases, and deaths for COVID-19, which are readily available online.
Compared to most other studies, the infection, recovery, and death rates are assumed to be stochastic, where the randomness is introduced through their log-odds (i.e. β, γ, δ while fβ, fγ, fδ take the sigmoid function to ensure the rates to be in a natural range of [0, 1]) to provide a better fit of the observed COVID-19 data.
Another modelling insight is that the observed time series data are significantly affected by the government’s timely mobility control policy; thus, feeding data directly into the model fails to reflect on the endogenous epidemic process.
To tease out its dependence on the mobility controls, the model is further refined by making use of the Google community mobility reports as explanatory factors. It can be intuitively observed that community mobility affects infection but not recovery and death, as evidenced by simple regressions. It is noteworthy that the regression of the infection log-odds on the mobility indices achieves R-squared of about 0.85.
With the insights above, the stochastic model of COVID-19 process is practical and interpretable, therefore it can be used to evaluate different existing social distancing policy by simulation as the paper illustrated with the US COVID-19 data.
Assuming that the government can control the community mobility by imposing a social distancing policy, it is desirable to know what level of mobility control is optimal or efficient. To that end, a stochastic control problem can be formulated with the states of S, I, R and D, which are controlled by the mobility indices (via I). The problem formulation requires an objective, which is specified by the user (government). As discussed above, Asst Prof Pun and his fellow co-authors consider a trade-off between public health and economic health, which is expressed mathematically as
where α denotes the mobility control (social distancing policy) and λ ≥ 0 represents the economic risk aversion. In layman terms, when the value of λ = 0, it simply means that the policymaker is only focusing on improving public health at the expense of unlimited economic cost, and vice versa for an extremely large value for λ.
To identify the economic health risk caused by COVID-19, an ex-post regression of the daily S&P 500 index price on the COVID-19 statistics and mobility indices is conducted. During the pandemic (especially in the early stage), they are found to be strong indicators of the economy as evidenced by the R-squared of about 0.9 for the aforementioned regression. In the problem formulation above, public health risk is taken as the expected infection log-odds, while the economic health risk is modelled as tracking error between the COVID-19 driven economic growth and a pre-specified reasonable growth of S&P 500 index.
Efficient frontier of social distancing policies
Finally, the study solves for the complicated stochastic control problem under constraints on the social distancing policies. It is analytically challenging, and this paper adopts a deep learning approach. An efficient frontier of the social distancing policies can be presented as in the figure. A historical social distancing policy can be plotted on the feasible region and the policymaker can see from the graph to understand how far it is deviated from an efficient policy in the sense that the infection rate, the economic risk, or both could be lower. The algorithm also provides the corresponding ESDP to achieve it.
When an effective vaccine becomes available to most people, it is expected that susceptible individuals (S) and death rate (δ) will reduce significantly, while the recovery rate (γ) increases. As a result, the algorithm in the paper will suggest the resumption of our activities to the days before the emergence of COVID-19.
Although this study is targeted for COVID-19, the general methodology of finding ESDP can potentially be used for future unexpected pandemics, especially ones where there are no available effective vaccines.
On a separate note, the primary research interest of Asst Prof Pun is not in epidemic modelling but from this study, one can see the incorporation of the interdisciplinary knowledge from statistics, stochastic processes, deep learning, and financial mathematics, which were key motivators in driving Asst Prof Pun’s research in financial problems.
Check out Asst Prof Pun’s website for more information about how such techniques are used in the emerging FinTech industry.