COVID-19 infection dynamics and flattening of curveNovember 9, 2020
Information about the spread of COVID-19, such as the rate of infection, death rates and so on are important to all stakeholders, including the public and the policymakers. There have been several statistical approaches which have been used to model the spread, and data has been used to predict when the peak infection will be and when the curve will start flattening and so on.
Several graphs depicting the expected number of infections have been viral in the media and social networks right from the beginning of the pandemic. Such mathematical models have projected many ominous trends. These graphs, however, never received much attention, but now they are informing important decisions such as financial planning, healthcare allocations, public policy and even speculations. The government, policymakers and regulatory authorities have used such models to evaluate and plan mammoth changes in operations and economies affecting the 1.3 billion people in India, even before researchers have concrete models and understand the dynamics.
There is more than one way of modelling any epidemic, including pure mathematical abstractions or statistical models and those based on artificial intelligence and network theories. The current modellers are mixing several elements as they fumble in the darkness of this pandemic using different tools, creating new ones or adapting existing ones as more information becomes available. One of the most common approaches is called the compartmental model, in which a population is categorized into several groups with specific rules governing how these groups behave.
The first category or group is susceptible or S, the second is exposed (E), the third is infected (I) and the last one is recovered or removed (R). In this model, the E group or category was added later and the initial models were SIR models. When people got re-infected, it became a SIRS model. The addition of the ‘exposed’ group made it a SEIR or SEIRS model. This basic model usually has numbers and equations for each category and their transitions to the next. The graph generated for the R (removed) population will usually be a sigmoid or elongated S-curve as the number of dead or recovered increases initially and then plateaus or reduces gradually. Forecasting based on this approach depends heavily on several factors like biology, politics, the economy and the weather.
Institute for Health Metrics and Evaluation (IHME) used a different approach called the curve-fitting model which assumed that the situation in the U.S would resemble earlier infection curves and it did predict the trends till about 50,000 cases. In mid-April, the IHME model predicted that the death toll would reach 60,000 in mid-May. However, the actual number was around 80,000. Later they moved to a SEIR model and are now evolving a better predictive system. An independent data scientist from MIT developed the YYG system, where only daily deaths were used with a set of parameters such as the reproduction number and the infection mortality rate in a grid search. The SEIR model soon took centerstage as machine learning approaches were incorporated along with deep-learning and neural networks. In comparison to these data-driven methods, agent-based models developed by the University of Sydney had a three-layer system using demographics, mobility and disease characteristics.
Several countries have clearly passed the first wave of the epidemic and are potentially heading for the next one. The linear growth pattern of infection continues for several weeks and the implementation of non-pharmaceutical interventions (NPIs) such as social distancing and masks have certainly helped in keeping the infection rates down.
Going by basic epidemiological concepts, the growth patterns with extended linear regions should be rare, with mathematically linear growth for an extended period usually indicating the failure to implement solutions in the compartments or categories mentioned in the SEIR method. Therefore, there is a need to use newer methods such as network interactions to explain the long-term linear growth of infections. For example, the use of the social network graph theory gave a reasonable explanation. A concept called small-world network — which tries to capture the social links (degree), groups (or families), how long a person can be contagious and potential overlaps along with distant groups with leisure links — can give a better understanding and calibrated framework.
With a population of more than 1.3 billion and the second-highest number of registered COVID-19 cases so far, India needs to understand and develop containment strategies at national, state and local levels. It was clear that around 10% were the first wave of patients who were infected outside India and the rest were cases of local transmission. A recent article by Karikalan Nagarajan (BMC Medical Research Methodology 20, 233 (2020)) has used a network approach leveraging large-scale contact tracing data around COVID-19. The availability of such relational data consisting of linked patients and contacts enabled such network analytics to be performed. In their cohort, the majority (88.72%) of the patients did not transmit the infection. However, a small number of 0.65% of the source patients disproportionately transmitted the infection to 36.7% of target patients. As for the remainder, around 62% did not have any identified source of infection and 1.72% had more than one source of infection. The data also showed that there were differences among individual patients in terms of infecting others and transmitting through an intermediary to many others. The network hubs suggested that there are only a few actors in the network playing a very important role in being the source and intermediaries for the infection transmission (often called super-spreaders). This kind of network analysis gives precise data on individual-patient-level variations in transmission. The network model-based prediction methods could help in identifying key super-spreader patients and develop important public health planning systems to achieve a reduction in the spread of COVID-19 infection.