Reconstruction of Epidemiological Data in Hungary Using Stochastic Model Predictive Control

Abstract

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.

Stochastic Modelling of Lassa Fever Epidemic Disease

“…In 2020, Bakare et al worked on the transmission dynamics of the disease and derived a nonlinear ordinary differential equation by introducing the seasonal parameters. Although stochastic methods are suitable for quantitative study via a mathematical model, they play an important role in data analysis, such as in environmental cases [3][4][5], finance [6], energy [7], and epidemiology [8]. For this purpose, some steps are recommended, such as preventive measures, educational campaigns, community hygiene, and isolation of infected humans [9].…”

Optimizing Symptom Based Testing Strategies for Pandemic Mitigation

“…In order to describe the evolution of the COVID-19 epidemic with adequate precision, we create a compartmental model based on the one originally published in [24], with its variations being used in [7] and [26] as well. In the original model, the total population is split into eight compartments: susceptible individuals (x S ), who have not contracted the disease yet, and neither have immunity due to vaccination; latent infected (x L ), who carry the disease, but have no symptoms, and are not yet infectious; asymptomatic (x A ) subjects are infected, but have no symptoms, their infection is not confirmed by testing, and eventually recover without intervention -nevertheless, they can transmit the disease to others; presymptomatic (x P ) people can already infect others, but their symptoms have not appeared yet; symptomatic infected (x I ) present symptoms of the disease, can infect others, and some of them require hospitalization to recover; hospitalised (x H ) patients can not infect others due to isolation, and might recover or die; recovered (x R ) people are considered to be totally immune to the disease (on the length of the control horizon); and there is a compartment for deceased individuals (x D ).…”