In this paper, the author proposes a new SEIRS model that generalizes several classical deterministic epidemic models (e.g., SIR and SIS and SEIR and SEIRS) involving the relationships between the susceptible S, exposed E, infected I, and recovered R individuals for understanding the proliferation of infectious diseases. As a way to incorporate the most important features of the previous models...

In this paper, we study the long-time behavior of a nonautonomous SEIRS epidemic model. We obtain new su cient conditions for the permanence (uniform persistence) and extinction of infectious population of the model. By numerical examples we show that there are cases such that our results improve the previous results obtained in [T. Zhang and Z. Teng, On a nonautonomous SEIRS model in epidemiol...

A delayed SEIRS epidemic model with pulse vaccination and nonlinear incidence rate is proposed. We analyze the dynamical behaviors of this model and point out that there exists an infectionfree periodic solution which is globally attractive if R1 < 1, R2 > 1, and the disease is permanent. Our results indicate that a short period of pulse or a large pulse vaccination rate is the sufficient condi...

In this paper, we derive some threshold conditions for permanence and extinction of diseases that can be described by a nonautonomous SEIRS epidemic model. Under the quite weak assumptions, we establish some sufficient conditions to prove the permanence and extinction of disease. Some new threshold values are determined.

During COVID-19 the new normal became an increased reliance on remote connectivity, and that fact is far away to change any time soon. The increasing number of networked devices connected Internet causing exponential growth botnets. Subsequently, DDoS (Distributed Denial Service) attacks registered around world also increased, especially during pandemic lockdown. Therefore, it crucial understan...

Bulgaria has the lowest COVID-19 vaccination rate in European Union and second-highest mortality world. That is why we think it important better to understand reason for this situation analyse development of disease over time. In paper, an extended time-dependent SEIRS model SEIRS-VB used investigate long-term behaviour epidemic. This includes vital dynamics. To apply some numerical simulation ...

We consider the problem of identifying the time-dependent transmission rate from incidence data and from prevalence data in epidemic SIR, SIRS, and SEIRS models. We show closed representation formulas avoiding the computation of higher derivatives of the data or solving differential equations. We exhibit the connections between the formulas given in several recent papers. In particular we expla...