VIPER: a new compartment model for prediction of infected and recovered patients in pandemics with case studies on COVID-19

We propose a compartment model called the Vaccine Immunization with Partial Effective and Restrictions (VIPER) model, which specifically accounts for two features in the recent transmission of COVID-19, namely partially effective vaccines and non-pharmaceutical interventions. Compared with existing compartment models, our proposed VIPER facilitates more complex transitions between states to improve its practical applicability. We conduct a comparative analysis using data from four countries, each from a different continent, demonstrating the improvement achieved by the VIPER model over a similar compartment model proposed in a recent study with the same compartments (SVEIHDR: Susceptible, Vaccinated, Exposed, Infected, Hospitalized, Death, Recovered) but simpler transition routes. We also compare against other common prediction approaches, including the long short-term memory (LSTM) and auto-regressive integrated moving average (ARIMA) models. In addition to predicting the number of recovered cases, as in most existing studies, we also focus on the infected cases, which are more variable and critical for medical resource planning and allocation purposes. Our results show that the VIPER significantly outperforms the original SVEIHDR model in predicting the numbers of both infected and recovered individuals, with the estimation error reduced by at least \(20\%\) $20\%$ across all cases, and by over \(90\%\) $90\%$ in the case of Canada. Our proposed VIPER model consistently achieves accuracy that is better or comparable to LSTM and ARIMA across all cases. Additionally, VIPER provides deeper insights, as its compartmental approach is based on epidemiological processes, with parameters that have clear epidemiological significance. The implications of these results suggest that the VIPER model is an accurate and interpretable framework for understanding general pandemic dynamics, with a flexible structure that can be tailored to the specific epidemic conditions of different countries. The accuracy, interpretability, and flexibility of the VIPER model could lead to more effective decision-making in future public health responses.