Infectious diseases are usually caused by microorganisms like viruses, bacteria or pathogens, which can spiral into epidemics or even pandemics. The SARS-CoV-2 is one for the record books. Advances in mathematical tools and computing abilities have made it a lot less tedious for researchers and scientists to predict disease outbreaks, understand virus behaviours and aid policymakers to make data-driven decisions and interventions. However, Artificial Intelligence and its components like machine learning and deep learning can speed up this process even further. As the world continues to battle the pandemic, with some nations disproportionately affected, timely decisions based on mathematical deductions and AI-based models are the need of the hour. 

Prof Deepak Subramani (left) & Prof. Sashikumaar Ganesan, Dept of Computational Data Science, IISc

Upon being roped in by a member of the Karnataka COVID19 Taskforce, Prof. Sashikumaar Ganesan and Prof. Deepak Subramani of the Department of Computational Data Science, Indian Institute of Science (IISc) built a partial differential equation model that aims to predict the trajectory of COVID19 across Indian states. The model provides mathematical insights on projected infection numbers should states go into lockdowns that are either 15 days, 21 days or 30 days in duration.

Here are some simplified excerpts from the illuminating interview conducted with Prof. Ganesan and Prof. Subramani on how math and AI are crucial to understanding the path of the virus, staying ahead of it and making sound, data-driven policy decisions. 

What is the mathematical model you have used to track COVID19 and what does it hope to achieve? 

DS: Our model is a partial differential equation model. It's a slightly different AI model from what is typically seen. PDE helps us get projections and scenario analyses for Indian states on how COVID19 will progress and hopefully dissipate in this second wave. 

How do mathematical models decode infectious diseases? 

DS: The process of understanding and predicting infectious diseases dates back to the late 1700s at least. One of the models that has served the research community well is the compartment model where the population is divided into several compartments like "susceptible", "infected", "recovered", "diseased" and "people exposed to a disease but aren't symptomatic". By using ordinary differential equations on this data, predictions are made that help understand how these compartments evolve over time based on the R0. R0 is a basic reproduction number that indicates how contagious a disease actually is. Every prediction hinges on how this number evolves over time. 

So how does your PDE model work? 

DS: The primary use of epidemiological models is mainly for hindsight analysis. This is what spurred the development of our model, and we wanted to use this data to eventually help predict how the ongoing COVID19 crisis would evolve. Forecasting models first need the know-how of a fundamental scenario stands, and how pharmaceutical interventions like vaccinations and non-pharmaceutical interventions like lockdowns will impact interactions between people in the future. The PDE takes data in initial conditions - ie the numbers of people infected, recovered, vaccinated - as the initial input to the model. Then, the model makes assumptions on the nature of interactions between people, recovery rate, death rate - all distributed across age and severity of infection. By now, data has shown us that 80% of affected individuals have mild or no symptoms and 20% need hospitalisation. Within this, nearly 5% need ICU beds and another 15 - 17% need oxygenated beds. Data derived from medical literature and anecdotal evidence from medical experts are also fed as primary model parameters. The model's equations can then map out the trajectory of the virus and outcomes based on different scenarios. The model also takes into account the number of unreported cases per reported case. 

What kind of predictions does this model make? 

SG: When the model makes a nationwide prediction, individual states are taken as sub-units. Predictions are also made for the states in an effort to calculate a national avg. Thereafter, scenario analysis takes place. Individual states are also given the same parameters, and to help map out the performance of every state against the national average. This is what you see under the India tab on our website. For instance, if you click on the Karnataka tab, districts are the individual units whose performance is mapped against the state average. The last data update was on Apr 27. This data helps us answer if a lockdown is needed? If so, in which areas and for how long should the lockdowns be imposed? What levels of reduction in caseload can we expect? We did 4 scenarios - if cities resumed their activities in business as usual mode, if they were under a 15-day lockdown, a 21-day lockdown and a 30-day lockdown. So, by May 26th, what will the numbers looks like? Are the different districts reaching their projections for the various duration lockdowns? This data mainly helps make predictions about ICU beds, O2 beds and to plan for vital resources. 

So what are your deductions on the pandemic so far? Are we looking at a third wave anytime soon? 

SG: Honestly, no one can predict how a third wave is going to be like, although there is enough evidence to indicate there will be another wave. But I'd like to emphasise more on what we've observed so far and how this can help us prepare for the future. For Bangalore Urban, we calculated the first wave from the first day of the first nationwide lockdown ie 23rd March 2020 until 22nd March 2021. The second wave is from 23rd March 2021 and we continue to map it. Our mathematical model reveals that the infection spread dynamics across these two waves are more or less similar. But the second wave has been way harsher on account of many reasons - non-linear transmission, virulent spread, the exponential growth of infections and the presence of new mutations. As a result the healthcare system is operating at maximum capacity and is under duress. Bangalore Urban is reporting more than 60% of active cases in the state, and its lockdown efficacy is 100%. But in the districts of Karnataka, lockdown efficacy is 50%. Naturally, we expect the cases to slow down in the city first, and then the rest of the state. This data is being fed to the COVID19 working committees in Karnataka regularly as shown from my Twitter post below.

What can we expect in the next couple of weeks? 

SG: The model shows that the infection curve was indeed following what we projected had there been a 15-day lockdown. Now, with the lockdown extending till the month-end, we need to see if the curve follows the model's projection for a 21-day and then 30-day scenario. These projections are working provided people follow COVID-appropriate behaviour. If you look at daily active cases on a given day, we're at the peak now and the cases will reduce from May 20th, provided these strict measures continue to be followed. 

Can you explain why this modelling is so critical to disease management?

SG: It is very important to first understand why infectious disease mathematical modelling is done. This is a scenario projection analysis for the future, not about being right or wrong. There are variables to be followed, parameters to be maintained for the model to make its projections. We're not doing this to induce panic among citizens but help policymakers stay ahead of a crisis. With data analysis and machine learning, it is possible to closely track a disease's trajectory in the population. 

DS: When we use modelling to aid policymaking, a counter factual should be considered too - this means policy makers must consider what would have happened to beneficiaries in the absence of the intervention, and estimating its impact by comparing counterfactual outcomes to those observed under the intervention. Mathematical models must be used to understand the scenario that lays ahead, it points policymakers in the right direction and tells them where to look more closely.