Wastewater-based epidemiology (WBE) has emerged as a promising approach for monitoring the COVID-19 pandemic, since the measurement process is cost-effective and is exposed to fewer potential errors compared to other indicators like hospitalization data or the number of detected cases. Consequently, WBE was gradually becoming a key tool for epidemic surveillance and often the most reliable data source, as the intensity of clinical testing for COVID-19 drastically decreased by the third year of the pandemic. Recent results suggests that the model-based fusion of wastewater measurements with clinical data and other indicators is essential in future epidemic surveillance. In this work, we developed a wastewater-based compartmental epidemic model with a two-phase vaccination dynamics and immune evasion. We proposed a multi-step optimization-based data assimilation method for epidemic state reconstruction, parameter estimation, and prediction. The computations make use of the measured viral load in wastewater, the available clinical data (hospital occupancy, delivered vaccine doses, and deaths), the stringency index of the official social distancing rules, and other measures. The current state assessment and the estimation of the current transmission rate and immunity loss allow a plausible prediction of the future progression of the pandemic. Qualitative and quantitative evaluations revealed that the contribution of wastewater data in our computational epidemiological framework makes predictions more reliable. Predictions suggest that at least half of the Hungarian population has lost immunity during the epidemic outbreak caused by the BA.1 and BA.2 subvariants of Omicron in the first half of 2022. We obtained a similar result for the outbreaks caused by the subvariant BA.5 in the second half of 2022. The proposed approach has been used to support COVID management in Hungary and could be customized for other countries as well.

In this paper, we propose a model-based method for the reconstruction of not directly measured epidemiological data. To solve this task, we developed a generic optimization-based approach to compute unknown time-dependent quantities (such as states, inputs, and parameters) of discrete-time stochastic nonlinear models using a sequence of output measurements. The problem was reformulated as a stochastic nonlinear model predictive control computation, where the unknown inputs and parameters were searched as functions of the uncertain states, such that the model output followed the observations. The unknown data were approximated by Gaussian distributions. The predictive control problem was solved over a relatively long time window in three steps. First, we approximated the expected trajectories of the unknown quantities through a nonlinear deterministic problem. In the next step, we fixed the expected trajectories and computed the corresponding variances using closed-form expressions. Finally, the obtained mean and variance values were used as an initial guess to solve the stochastic problem. To reduce the estimated uncertainty of the computed states, a closed-loop input policy was considered during the optimization, where the state-dependent gain values were determined heuristically. The applicability of the approach is illustrated through the estimation of the epidemiological data of the COVID-19 pandemic in Hungary. To describe the epidemic spread, we used a slightly modified version of a previously published and validated compartmental model, in which the vaccination process was taken into account. The mean and the variance of the unknown data (e.g., the number of susceptible, infected, or recovered people) were estimated using only the daily number of hospitalized patients. The problem was reformulated as a finite-horizon predictive control problem, where the unknown time-dependent parameter, the daily transmission rate of the disease, was computed such that the expected value of the computed number of hospitalized patients fit the truly observed data as much as possible.

Optimal intervention planning is a critical part of epidemiological control, which is difficult to attain in real life situations. Ordinary differential equation (ODE) models can be used to optimize control but the results can not be easily translated to interventions in highly complex real life environments. Agent-based methods on the other hand allow detailed modeling of the environment but optimization is precluded by the large number of parameters. Our goal was to combine the advantages of both approaches, i.e., to allow control optimization in complex environments. The epidemic control objectives are expressed as a time-dependent reference for the number of infected people. To track this reference, a model predictive controller (MPC) is designed with a compartmental ODE prediction model to compute the optimal level of stringency of interventions, which are later translated to specific actions such as mobility restriction, quarantine policy, masking rules, school closure. The effects of interventions on the transmission rate of the pathogen, and hence their stringency, are computed using PanSim, an agent-based epidemic simulator that contains a detailed model of the environment. The realism and practical applicability of the method is demonstrated by the wide range of discrete level measures that can be taken into account. Moreover, the change between measures applied during consecutive planning intervals is also minimized. We found that such a combined intervention planning strategy is able to efficiently control a COVID-19-like epidemic process, in terms of incidence, virulence, and infectiousness with surprisingly sparse (e.g. 21 day) intervention regimes. At the same time, the approach proved to be robust even in scenarios with significant model uncertainties, such as unknown transmission rate, uncertain time and probability constants. The high performance of the computation allows a large number of test cases to be run. The proposed computational framework can be reused for epidemic management of unexpected pandemic events and can be customized to the needs of any country.