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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 R0 index provide perspectives on the severity and future of the COVID-19 pandemic. [ABSTRACT FROM AUTHOR]

The paper concerns a new forecast model that includes the class of undiagnosed infected people, and has a multiregion extension, to cope with the in‐time and in‐space heterogeneity of an epidemic. The model is applied to the SARS‐CoV2 (COVID‐19) pandemic that, starting from the end of February 2020, began spreading along the Italian peninsula, by first attacking small communities in north regions, and then extending to the center and south of Italy, including the two main islands. It has proved to be a robust and reliable tool for the forecast of the total and active cases, which can be also used to simulate different scenarios. In particular, the model is able to address a number of issues, such as assessing the adoption of the lockdown in Italy, started from March 11, 2020; the estimate of the actual attack rate; and how to employ a rapid screening test campaign for containing the epidemic. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019 (COVID‐19) is a viral disease which is declared as a pandemic by WHO. This disease is posing a global threat, and almost every country in the world is now affected by this disease. Currently, there is no vaccine for this disease, and because of this, containing COVID‐19 is not an easy task. It is noticed that elderly people got severely affected by this disease specially in Europe. In the present paper, we propose and analyze a mathematical model for COVID‐19 virus transmission by dividing whole population in old and young groups. We find disease‐free equilibrium and the basic reproduction number (R0). We estimate the parameter corresponding to rate of transmission and rate of detection of COVID‐19 using real data from Italy and Spain by least square method. We also perform sensitivity analysis to identify the key parameters which influence the basic reproduction number and hence regulate the transmission dynamics of COVID‐19. Finally, we extend our proposed model to optimal control problem to explore the best cost‐effective and time‐dependent control strategies that can reduce the number of infectives in a specified interval of time. [ABSTRACT FROM AUTHOR]