A stochastic particle extended SEIRS model with repeated vaccination: Application to real data of COVID-19 in Italy

The prediction of the evolution of epidemics plays an important role in limiting the transmissibility and the burdensome consequences of infectious diseases, which leads to the employment of mathematical modeling. In this paper, we propose a stochastic particle filtering extended SEIRS model with repeated vaccination and time-dependent parameters, aiming to efficiently describe the demanding dynamics of time-varying epidemics. The validity of our model is examined using daily records of COVID-19 in Italy for a period of 525 days, revealing a notable capacity to uncover the hidden dynamics of the pandemic. The main findings include the estimation of asymptomatic cases, which is a well-known feature of the current pandemic. Unlike other proposed models that employ extra compartments for asymptomatic cases, which force the estimation of this proportion and significantly increase the model's complexity, our approach leads to the evaluation of the hidden dynamics of COVID-19 without additional computational burden. Other findings that confirm the model's appropriateness and robustness are its parameter evolution and the estimation of more ICU-admitted cases compared to the official records during the most prevalent infection wave of January 2022, attributed to the intensified increase in admissions that may have led to full occupancy in ICUs. As the vast majority of datasets contain time series of total recovered and vaccinated cases, we propose a statistical algorithm to estimate the currently recovered and protected through vaccination cases. This necessity arises from the attenuation of antibodies after vaccination/infection and is necessary for long-time interval predictions. Finally, we not only present a novel stochastic epidemiological model and test its efficiency but also investigate its mathematical properties, such as the existence and stability of epidemic equilibria, giving new insights to the literature. The latter provides additional details concerning the system's long-term behavior, while the conclusions drawn from the R-0 index provide perspectives on the severity and future of the COVID-19 pandemic.