Implementation of a triangular probabilistic distribution for optimal parametrization of the SEIR model recovery rates with delay.

Dynamical analysis of epidemiological models received significant attention after the global disaster of the Covid-19 pandemic. Although much of the attention has focused on choosing the appropriate model to describe and interpret the epidemiological data and on predicting the spread of the disease, working on uncovering the hidden dynamics by analyzing the predictive data and studying the algebraic properties of the models such as the invariant spaces, the center manifolds, and the Lyapunov functions in the general parameter space still have the potential to make a significant contribution to our understanding of the dynamics of spread. In this paper, in order to determine the recovery rate based on characteristic model parameters, the triangular probabilistic distribution is implemented in an epidemic delay differential equation with delays.

Biochemical models of SIR and SIRS: Effects of bilinear incidence rate on infection-free and endemic states.

Understanding and forecasting the progression of disease epidemics is possible through the study of nonlinear epidemic biochemical models that describe the relationship among susceptible, infected, and immune individuals in a population. In this paper, by determining the algebraic invariant planes and studying the Hopf bifurcation on these invariant planes, we study the stability of the Hopf bifurcation in the infection-free and endemic states of the SIR and SIRS epidemic models with bilinear incidence rate. We analyze the stability of the limit cycles of the bilinear incidence SIR and SIRS models at the steady state point where infection vanishes and at the endemic steady state point where the system behaves in an oscillatory manner.

Chaotic behavior of light-assisted physical aging in arsenoselenide glasses.

The theory of strange attractors is shown to be adequately applicable for analyzing the kinetics of light-assisted physical aging revealed in structural relaxation of Se-rich As-Se glasses below glass transition. Kinetics of enthalpy losses is used to determine the phase space reconstruction parameters. Observed chaotic behaviour (involving chaos and fractal consideration such as detrended fluctuation analysis, attractor identification using phase space representation, delay coordinates, mutual information, false nearest neighbours, etc.

Possible stretched exponential parametrization for humidity absorption in polymers.

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.