Transmission matrix parameter estimation of COVID-19 evolution with age compartments using ensemble-based data assimilation

The COVID-19 pandemic, with its multiple outbreaks, has posed significant challenges for governments worldwide. Much of the epidemiological modeling relied on pre-pandemic contact information of the population to model the virus transmission between population age groups. However, said interactions underwent drastic changes due to governmental health measures, referred to as non-pharmaceutical interventions. These interventions, from social distancing to complete lockdowns, aimed to reduce transmission of the virus. This work proposes taking into account the impact of non-pharmaceutical measures upon social interactions among different age groups by estimating the time dependence of these interactions in real time based on epidemiological data. This is achieved by using a time-dependent transmission matrix of the disease between different population age groups. This transmission matrix is estimated using an ensemble-based data assimilation system applied to a meta-population model and time series data of age-dependent accumulated cases and deaths. We conducted a set of idealized twin experiments to explore the performance of different ways in which social interactions can be parametrized through the transmission matrix of the meta-population model. These experiments show that, in an age-compartmental model, all the independent parameters of the transmission matrix cannot be unequivocally estimated, i.e., they are not all identifiable. Nevertheless, the time-dependent transmission matrix can be estimated under certain parameterizations. These estimated parameters lead to an increase in forecast accuracy within age-group compartments compared to a single-compartmental model assimilating observations of age-dependent accumulated cases and deaths in Argentina. Furthermore, they give reliable estimations of the effective reproduction number. The age-dependent data assimilation and forecasting of virus transmission are crucial for an accurate prediction and diagnosis of healthcare demand.