Regression model for the reported infected during emerging pandemics under the stochastic SEIR

The COVID-19 pandemic revealed the necessity of measuring the statistical relationship between the transmission rate of epidemic diseases and the social/behavioral, logistical, and economic variables of the affected region. This paper introduces a regression model to estimate the impact of such covariates on the infectious rate of epidemiological agents. Hidden logistical predictor components, such as weekly seasonality of reported data, can also be accessed with the proposed methodology. For this, we assume that the dynamics of officially reported data of emerging pandemics, related to infected groups, follows a stochastic SEIR model. The main advantage of our method is that it is based on a new three-step algorithm that combines the classical likelihood principle, the minimization of the mean squared error, and a tri-section algorithm to estimate, simultaneously, the coefficients of the covariates and the parameters of the compartmental model. Simulation studies are provided to certify the accuracy of the proposed inference methodology. The model is further applied to analyze the official statistical reports of COVID-19 data in the state of São Paulo, Brazil. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s40314-023-02241-w.