A number of models have been developed in India to forecast the spread of the coronavirus disease or COVID-19 in the country. While these have largely been variants of the classical susceptible-exposed-infectious-recovered (SEIR) compartmental model, other approaches using time-series analysis, machine-learning, network models, and agent-based simulations have also helped to provide specific insights into questions of policy. Model building has had to incorporate our evolving knowledge of the disease, including the appearance of new variants, immune escape leading to reinfections, time-varying non-pharmaceutical interventions, the pace of the vaccination program, and breakthrough infections. The predictive power of these models has been hampered by the lack of availability of quality data on infection and deaths as a function of age, the nature of social contacts, demography, and the clinical consequence of infection. An early emphasis on "ensemble models," a thrust toward increased data availability, a greater engagement of modelers with the epidemiological and public health communities, and a more nuanced approach to communicating the limitations of modeling could have substantially increased the usefulness of models during the COVID-19 pandemic in India.
Most models were variants of the SEIR model where the individuals in the population move from S = susceptible to E = exposed to I = infectious to R = removed compartments. The time-evolution of the fraction of the population in each compartment is captured by a system of ordinary differential equations. Parameter estimation based on observables then enables the prediction of the future evolution of the pandemic.
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