A comparison of five epidemiological models for transmission of SARS-CoV-2 in India

Many popular disease transmission models have helped nations respond to the COVID-19 pandemic by informing decisions about pandemic planning, resource allocation, implementation of social distancing measures and other non-pharmaceutical interventions. We compare five epidemiological models for forecasting and assessing the course of the pandemic. We compare how the models analyze case-recovery-death count data in India, the country with second highest reported case-counts in a world where a large proportion of infections remain undetected. A baseline curve-fitting model is introduced, in addition to three compartmental models: an extended SIR (eSIR) model, an expanded SEIR model developed to account for infectiousness of asymptomatic and pre-symptomatic cases (SAPHIRE), another SEIR model to handle high false negative rate and symptom-based administration of tests (SEIR-fansy). A semi-mechanistic Bayesian hierarchical model developed at the Imperial College London (ICM) is also examined. Using COVID-19 data for India from March 15 to June 18 to train the models, we generate predictions from each of the five models from June 19 to July 18. To compare prediction accuracy with respect to reported cumulative and active case counts and cumulative death counts, we compute the symmetric mean absolute prediction error (SMAPE) and mean squared relative prediction error (MSRPE) for each of the five models. For active case counts, SEIR-fansy yields an SMAPE value of 0.72, and the eSIR model yields a value of 33.83. For cumulative case counts, SMAPE values are 1.76 for baseline model, 23.10 for eSIR, 2.07 for SAPHIRE and 3.20 for SEIR-fansy. For cumulative death counts, the SEIR-fansy model performs the best, with an SMAPE of 7.13, as compared to 26.30 for the eSIR model. Using Pearson correlation coefficient and Lin concordance correlation coefficient, for cumulative case counts, the baseline model exhibits highest correlation (both Pearson as well as Lin coefficients), while for cumulative death counts, projections from SEIR-fansy exhibit the best performance: For cumulative cases, correlation coefficients computed for the baseline model are 1 (Pearson) and 0.991 (Lin). For eSIR, those values are 0.985 (Pearson) and 0.316 (Lin). For SAPHIRE, we compute 1 (Pearson) and 0.975 (Lin). Finally, for SEIR-fansy we have those values at 1 (Pearson) and 0.965 (Lin). Similarly, for cumulative deaths, correlation coefficients computed for eSIR is 0.978 (Pearson) and 0.206 (Lin), and for SEIR-fansy we have those values at 0.999 (Pearson) and 0.742 (Lin). Three models (SAPHIRE, SEIR-fansy and ICM) return total (sum of reported and unreported) counts as well. We compute underreporting factors on two specific dates (June 30 and July 10) and note that on both dates, the SEIR-fansy model reports the highest underreporting factor for active cases (June 30: 6.10 and July 10: 6.24) and cumulative deaths (June 30: 3.62 and July 10: 3.99) for both dates, while the SAPHIRE model reports the highest underreporting factor for cumulative cases (June 30: 27.79 and July 10: 26.74).