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As cities and nations around the world look to find the right balance between opening the economy and keeping the infections within manageable levels, application of model thinking can assist city administrators to make these decisions with greater confidence.
Traditional Models: Rigorous but Limited Decision Support
Most prominent models around the pandemic model the population across 4 broad compartments: those who are susceptible (S) to infection, those who have been infected (I), and those who have recovered (R) or died (D). Interactions across these compartments are then modelled and calibrated based on emerging data and then used for predictions of the infection. Let us call these models as SIRD models. While these are elegant models for epidemiology, these are not appropriate for assessing impact and making decisions in real scenarios. Critical shortcomings are the following:
- Focus on epidemiological segments instead of behavioural/ impact segments: Such models assume similar transmission parameters across these compartments. However, transmissions can vary due to socio-economic conditions and nature of work, primarily since these factors impact ability to practice preventive measures like social distancing and work from home. As an illustration, a food delivery employee will have to necessarily work outside while interacting with several different strangers, same for an Uber driver. However, an IT professional, or most white-collar employees can afford to severely limit physical interactions with people.
- Transmission as a smooth and often fixed parameter: SIRD models assume that transmission of the infection can be modelled through a smooth curve. This is intuitively not helpful as transmission is primarily a patchy curve (say flatter during lockdowns but steeper during open economy).
- Model calibration dependent on confirmed cases: For a disease like Covid, which has significant detection uncertainty (both around if one has one infection and when it can be detected), and has been catered to with varying testing protocols (initial emphasis on testing international travellers, later on moving to more wider testing based on healthcare readiness and anticipated community transmission), confirmed cases might not be gainfully employed to understand how the disease has propagated so far.
Since each city has a different proportion of behavioural segments (say white collar vs blue collar workers), has been experimenting with different set of control measures, as well as testing patterns, pure SIRD models fail to answer questions like the following:
- Which control measures will allow harmless interactions but prevent those that can result in an increased transmission of the disease?
- What is the impact on vulnerable communities and what state support can mitigate that (e.g., state owned insurance, availability of public sector beds, pricing of drugs etc.)?
- Given the state of affairs as of today (say stringent lockdown, followed by relaxed one), what is the state of infections and how is it going to be impacted by policy measures?
- What is the end game and phasing to ensure that each city contains Covid and puts in place a way to prevent new waves?
Adding Boosters to the SIRD model
To solve for some of these shortcomings, a few enhancements are proposed to the vanilla SIRD model for better decision discourse. I have chosen to also create a representative model for Delhi leveraging some of the data points available (which remains very, very limited or hard to find). Below are the proposed enhancements:
- Modelling socio-economic segments: The city (Delhi) has been divided into WhiteTown and BlueTown. BlueTown represents densely populated, often unplanned residential areas with most residents involved in activities requiring physical work, with relatively low socio-economic status. WhiteTown represents less dense areas, with residents involved in work which can be conducted within their houses (Work from Home), with relatively better socio-economic status. Transmission is modelled both within segments (say neighbours in closely packed slums using community facilities) as well as across segments (say a pizza delivery boy, from BlueTown infecting residents in WhiteTown, who have ordered food). While this is an abstraction, the intent is to model relevant socio-economic segments, perhaps more than just these two, in a real model.
- Incorporation of undertaken control measures: The model treats the overall duration till date as a set of intervals where transmission is correlated to the undertaken measures and observed impacts. As an illustration, the transmission intuitively slows during a rigorous lockdown but surges again once unlocking happen. For my toy model, 4 clear intervals with varying detections are modelled separated by critical events – first case detection, full lockdown, initial opening up for green zones, and extended lockdown with some relaxations
- Empirical calculation of transmission factors: While assessment of transmission rates remains widely uncertain, we can make some straightforward assumptions to simplify this. We can assume that transmission did slow down as number of contacts per person reduced (as in a lockdown scenario) and moved back again on opening. We can also assume that detection rate (cases per infections) changed in accordance with testing norms. Finally, transmission within WhiteTown, BlueTown and across them is estimated using interactions across a set of professions.
While a clear calibration of the model was difficult (due to asymptotic cases as well as delays in detection and reporting), the model was adjusted to reasonable limits through empirical estimates described above. The figure below illustrates resulting output. While the numbers don’t align due to calibration challenges, the output reflects the modelling flexibility vis-a-vis a SIRD model for Delhi with smooth transmission assumptions – as an illustration, the steepness shown in June would be very hard to discover in a classical SIRD model. Additionally, the dire impact of opening up (and within various segments) can be much better gleaned from this exercise, which can then create the necessary discourse of what can be done to prevent such uptick while opening up and if such measures will be sufficient and damage acceptable.

Creating the World of Alternatives
Extending the status quo and seeing where it leads us was then considered for impact assessment across the two fictional towns through simulating two scenarios. In the first scenario, it is assumed that post lockdown transmission rates will continue (those observed in June implicitly and which are still lower than those at the start of the pandemic when awareness was even lower). This then suggest a peak in February next year. In the other scenario, if we assume pre-lockdown transmission rates, we see the peak in August. As is also seen, the impact on BlueTown is much more than that on WhiteTown, expected due to high transmission rates estimated there. The results are plotted below.


While the model has focused on simulating impacts on two socio-economic segments, multiple segments as necessary could be identified useful for Decision Making – an illustration would be simulating shop owners in hotspots and then simulating their transmission parameters. Further, indications on infected personnel can help prepare for medical resources distribution across regions. All critical decisions can, hence, be decided by simulating alternatives and assessing relative impacts.
Takeaways for City Administrators
Good models can be helpful in decision making, even if their predictions are wrong. This one has a specific decision maker – city administrators looking to take decision to fight this pandemic, at its heart and is customized to help with the relevant decisions on policy ranging from total lockdown, healthcare readiness, allowance of services to even opening of borders. City administrators, hence, need to rely on models that represent their city and its affairs, and enable decision making across decisions that face them
The model also necessitates infusing various data sources within the paradigm of a traditional epidemiological model, which to me is a necessity in a crisis like this. City administrators need to work with all the data they have rather than relying on puritan traditional data as any decision they take will impact lives, livelihood as well as economy. In this context, it means that not only the official reported figures are considered, all state available data like the first reporting with symptoms of possible cases (at hospitals) as well as deaths is leveraged to adjust for lags in detection.
Lastly, while a modified model like this might still yield inaccurate numbers as our understanding of the disease, mortality rate and asymptotic population continues to evolve, having this socio-economic or segmental flavour can allow us to more consciously take decisions, while understanding the relative impacts across various segments. This can then inform more targeted interventions
Overall, as administrators struggle with political, social and emotional pressures, they should not forget that there is only one defining characteristic of a good decision – that it is consciously taken.
Hat tips:
- https://timesofindia.indiatimes.com/city/delhi/Half-of-Delhis-population-lives-in-slums/articleshow/16664224.cms
- https://www.sciencedirect.com/science/article/pii/S0307904X11005191
- https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7190554/
- https://science.thewire.in/the-sciences/basic-reproductive-ratio-value-india-estimate/
- https://assets.2030vision.com/files/resources/2030vision-full-report.pdf?416997c759
- https://www.lewuathe.com/covid-19-dynamics-with-sir-model.html
- https://www.thehindu.com/coronavirus/