Modeling for uncertain times: Approaches, behaviors, and outcomes
The spread of the pandemic or Covid-19 – first in China and South Korea and then in Europe and the United States – was swift and caught most governments, companies, and citizens off-guard. This global health crisis developed into an economic crisis and a supply chain crisis within weeks. Less than 100,000 global confirmed cases in early March 2020 has ballooned to more than 101 million by January 28, with more than 2.1 million deaths.
Every aspect of life for almost every individual on this planet has been impacted by COVID-19. From direct impact (e.g., death, hospitalization, infection) to indirect impact (e.g., loss of job, working from home, mental health) the virus has affected almost everyone on this planet. Uncertainty touched every aspect of life under COVID-19 – from health, to behavior to economic impact. Uncertainty often feeds emotional reactions such as fear, anger and frustration and such emotionally-driven behavior [Firth-Butterfield-etal-2020] has often taken precedence over rational decisions and actions.
In addition to the uncertainty, individuals, companies, policy makers and governments have all had to make decisions with little or no prior experience, with very little historical data, and also in a very short time. Advanced analytics and AI models have been used extensively to help address some of these uncertainties [Rao-etal-2020]. Models, a formal mathematical representation that can be applied to or calibrated to fit data, have been used extensively. In the history of humanity, perhaps no data models have been more recognizable than COVID-19’s infection and death curves. Virtually everyone, from the farmer in India to the director of the Center for Disease Control and Prevention (CDC) in the US, is now familiar with them. But the models have also drawn criticisms for inconsistencies in their predictions.
So, what are the models trying to capture? What decisions can they help us with? What techniques are we using to build these models?
A systems view of the impact of COVID19
The impact of COVID-19 has been broad, globally and across many facets of life, as well as deep, impacting lives and our livelihood. The best way to model all of the different aspects of impact is to take a systems level view, and isolate the key systems and the interactions between these systems. Once we have the macro-level view, we can build more granular micro-level views of just those systems that are directly relevant to specific decisions we want to make at the consumer, corporate, or national level. This will allow us to be resilient – taking into account the key drivers from other related systems, and also dynamic where we can focus on the immediate decisions at hand. Figure 1 shows the system level view of all the macro and micro factors under consideration.
Covid-19 disease progression is undoubtedly the key system that influences all the other macro-level systems. A number of pandemic level uncertainties like – uncertainties around the disease (e.g., infection rates, incubation time, diffusion process, growth rate, hospitalization rate and fatality rate), testing (e.g., diagnostic testing, antibody testing, accuracy), data (e.g., number of hospitalizations, deaths), and cure (e.g., therapeutic drugs – their efficacy and when they will be available, vaccines – their efficacy, trials, approval, and availability at scale) influence the disease progression. These uncertainties are very localized and time-dependent e.g., impact different countries, states, and even neighborhoods differently at different times.
The disease progression undoubtedly influences the government interventions which is our second macro-level system. State-based social distancing, curtailment and enablement of economic activity, like opening and closing of schools, bars, restaurants, etc., when and for how long a lockdown is imposed or lifted all have an impact on both the economic activity and the behavior of people.
Citizen behavior, surprisingly, has turned out to be one of the most significant macro-level system components of the pandemic – both the spread of the disease and the ability of the economic activity to rebound or falter [Firth-Butterfield-etal-2020]. While some countries and some states in the US have been very successful in enforcing restrictions of movement, with their citizens complying with the government interventions, other states have either failed to place restrictions and/or citizens have failed to comply. This macro-level dynamic makes it extremely important and challenging when we consider its micro-level impact on companies through consumer demand, workforce safety, and eventually the financial viability of companies.
The economy driven by the government interventions to either inhibit or enhance economic activity due to the pandemic, the behavior of its citizens, and the fiscal stimulus by governments to alleviate the economic pain on citizens and companies is another major macro-level system component.
All four of these macro-level system components interact with the micro-level system components. Customers, workforce, companies, demand, and supply are four key micro-level components. Customers and workforce are micro-level variants of citizens. Citizens within a region or zip code are considered as customers when they engage in consuming products and services and also act as the workforce when they are engaged in economic activity working for a company. Companies satisfy the demand of their consumers and also produce goods or intermediate goods that become supplies for other companies. Companies also employ the workforce to produce goods and services. All of these interactions are mediated through cash which underpins the economy.
At the micro-level, uncertainty in demand (e.g., the significant drop in demand for some products and services like air travel and tourism or the significant increase in demand for products like toilet rolls), supply chain disruption, workforce safety, productivity, and scheduling were major influencers of economic activity. These combined with the presence or absence of fiscal support from governments resulted in the financial viability of the companies (i.e., profits, margins, liquidity, and bankruptcy) and also the purchasing power, income levels and employment status of individuals.
Making strategic or operational decisions requires one to not only have an appreciation of the systems level view and the interactions between the components, but also to understand the key drivers and the nature of these interactions (e.g., virtuous or vicious feedback loops). Given the speed at which decisions need to be made, executives need to focus on the salient impacts of the pandemic and how the normal feedback loops are altered by the pandemic.
COVID-19 Modeling and Decision Making
Having identified the key system level components of COVID-19 we now look at the specific models that have been built and also the decisions that they help us to make.
Disease Progression: Epidemiological Models
The classic way of modeling the progression of an infectious disease has been called the SIR model. The three letters capture the different states of an individual as they progress through an infection, e.g., being Susceptible, then getting Infected, and finally Recovering from it. Further refinements of this type of modeling capture additional states like the SEIRD model (Susceptible, Exposed, Infected, Recovered, and Dead) capturing the exposure and death states. The COVID-19 pandemic has resulted in a number of these models – built for different countries – that capture additional states. For example, one paper [Khalil-etal-2012] captures the above SEIRD states as well as contact, quarantined, not quarantined, and immunized. Some others [Kompella-etal-2020; Silva-et-al-2020] capture pre-symptomatic and pre-asymptomatic, symptomatic and asymptomatic states, hospitalization, and critical states as well. The more states of infection a model captures, the more it facilitated fine-grained decision-making. It does make the model more complex and also requires a lot more data to calibrate the model.
The reason for modeling the disease progression is to enable different interventions that can help reduce infections, hospitalizations, deaths etc., as well as to get back to work and restart the economy. This leads us to the next set of models.
Government Interventions & Effectiveness: Behavioral Models
Behavioral models capture the different restrictions and interventions that can be put in place and how effective they are in reducing the spread of the disease. These models simulate interventions, such as the Stay-at-home orders (SHOs) or social distancing restrictions and evaluate how they impact the disease progression as described by the epidemiological models. Many of these models [Chen-etal-2020] have a spatio-temporal dimension and can estimate the compliance with such orders by location and by political affiliation. Mobility data from smartphones can help track movement of citizens, without necessarily identifying them, to evaluate the effectiveness of lockdown and even social distancing interventions. The role of misinformation [Leitner-2020] on the compliance of individuals and the progression of the disease can also be studied using these approaches.
Economic impact: Economic Models
The epidemiological models when combined with behavioral models can also be used to analyze the economic impact of different interventions. Such models [Silva-etal.2020] allow policy makers to analyze different scenarios of social distancing interventions, with varying epidemiological and economic effects. Silva, et.al., consider seven different scenarios in their model (1) do nothing, (2) lockdown, (3) conditional lockdown, (4) vertical isolation, (5) partial isolation, (6) use of face masks, and (7) use of face masks together with 50% of adhesion to social isolation.
These models are not only useful to reduce the spread of the disease through various intervention mechanisms, but can also be used to return back to work in a safe manner. The paper by Wang, et.al., for example, evaluates the phased reopening strategy of New York City and its impact on public transit, car traffic, and micro mobility modes within the city.
Modeling Approaches for Uncertain Times
Three specific modeling approaches or techniques have been used for building these epidemiological, behavioral, and economic models. Historically, equation based approaches have been used to model the spread of infectious diseases [Duan-etal-2015, Hunter-etal-2018]. Differential equations are used to define the rate at which the population within each state (e.g., susceptible, infectious etc) changes over time. These equations are then solved over time to understand the dynamics of the disease. More states in the model means more equations required to capture the dynamics of the interaction and hence more complex is the model. Equation based approaches are also referred to as System Dynamic (SD) models.
The second approach that has been used to build the epidemiological models has been Agent-based Model (ABM). In agent-based models, each individual is represented as an agent and they interact with other agents and the environment. Agents change from one state (e.g., susceptible, infectious etc) to another and running a number of these agents provides the overall dynamics of the spread of the disease. Equation based approaches treat all individuals within each state as a single "compartment" and do not allow for any individual variations. However, in agent based models each agent can be unique which allows us to model more of the behavioral aspects, discussed earlier, more naturally.
More recently, machine learning – deep learning and reinforcement learning – are being used to build these models. Recent approaches are integrating COVID-19 cases and deaths with socioeconomic, health and behavioral risk factors at a local level, and using deep learning [Fox-etal-2020] to better predict the disease progression. Similarly, reinforcement learning [Kompella-etal-2020] is being used to optimize the mitigation policies.
In summary, the necessity to understand the dynamics of the disease progression and its impact on the behavior of individuals and the economy have resulted in a resurgence of agent-based, system dynamic, and machine learning models. The rich interplay between assumptions, data, models, government interventions and human behaviors makes these models challenging to build, but very useful to evaluate different strategies in a methodical fashion.
REFERENCES
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Rao, A. and Firth-Butterfield, K. "3 ways COID19-is transforming advanced analytics and AI" World Economic Forum. Global Agenda, July 23, 2020.
Khalil, Khaled M. et al. "An Agent-Based Modeling for Pandemic Influenza in Egypt." Intelligent Systems Reference Library (2012): 205–218.
Leitner, Stephan. "On the Dynamics Emerging from Pandemics and Infodemics." Mind & Society (2020):
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Silva, Petrônio C.L. et al. "COVID-ABS: An Agent-Based Model of COVID-19 Epidemic to Simulate Health and Economic Effects of Social Distancing Interventions." Chaos, Solitons & Fractals 139 (2020): 110088.
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