A generalized Chebyshev operational method for Volterra integro-partial differential equations with weakly singular kernels.

Volterra integro-partial differential equations with weakly singular kernels (VIPDEWSK) are utilized to model diverse physical phenomena. A matrix collocation method is proposed for determining the approximate solution of this functional equation category. The method employs shifted Chebyshev polynomials of the fifth kind (SCPFK) to construct two-dimensional pseudo-operational matrices of integration, avoiding the need for explicit integration and thereby speeding up computations.

Within-host delay differential model for SARS-CoV-2 kinetics with saturated antiviral responses.

The present study discussed a model to describe the SARS-CoV-2 viral kinetics in the presence of saturated antiviral responses. A discrete-time delay was introduced due to the time required for uninfected epithelial cells to activate a suitable antiviral response by generating immune cytokines and chemokines. We examined the system's stability at each equilibrium point.

Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes.

In this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability.