A new method for the estimation of stochastic epidemic descriptors reinforced by Kalman-based dynamic parameter estimation. Application to mpox data.

In the realm of epidemiology, it is essential to accurately assess epidemic phenomena through the adoption of innovative techniques that yield reliable predictions. This article introduces an advanced method that merges the Extended Kalman Filter approach with recursive algorithms to compute critical stochastic attributes important for evaluating epidemics. A new three-dimensional discrete Markov chain is presented, according to which the total number of infections, deaths, and the duration of epidemic outbreaks are estimated. This approach represents a notable improvement over the standard estimation procedure, which relies on Markov-based stochastic models with fixed parameters. Furthermore, it constitutes a real-time estimation process, as opposed to the standard method, which is more suitable for offline applications. The proposed methodology marks an original attempt to integrate computational techniques for modeling stochastic epidemic characteristics with dynamic parameter estimation procedures. An additional advantage is the reduction of noise in the system's states enhancing the overall precision. The method's performance is thoroughly assessed through 3 simulated epidemic instances. Furthermore, its application to the actual 2022 monkeypox (mpox) data from the Czech Republic demonstrates promising effectiveness. In comparison to the standard methodology, our approach yields estimates with deviations of only 4.383 weeks, 3.542 infections, and 0.266 deaths, as opposed to the standard method where we observe deviations of 15.372 weeks, 5.786 infections, and 0.501 deaths. Overall, the proposed estimation procedure proves to be a valuable tool for investigating epidemic phenomena characterized by fluctuating dynamics, potentially providing valuable insights for addressing the associated public health challenges. MSC: 62M20, 60J22, 65C40, 62G30, 62P10.