Stability Analysis of Delayed COVID-19 Models

Abstract

We analyze mathematical models for COVID-19 with discrete time delays and vaccination. Sufficient conditions for the local stability of the endemic and disease-free equilibrium points are proved for any positive time delay. The stability results are illustrated through numerical simulations performed in MATLAB.

Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

“…Remark 3. If ψ(t) = t and α = 1, then the fractional system (17) reduces to the classical PK/PD model (3) [43].…”

“…The field of Pharmacokinetics and Pharmacodynamics plays a crucial role in understanding the behavior of drugs in biological systems [37]. Traditional PK/PD models have predominantly relied on integer-order derivatives to describe various processes involved in drug absorption, distribution, metabolism, and elimination [13,31,43]. However, these models often fall short in accurately capturing the complexity of Pharmacokinetic behaviors [8,19].…”

“…In this article, we propose a novel fractional four-compartmental PK/PD model for the induction phase of anesthesia, employing the ψ-Caputo fractional derivative. This innovative approach involves replacing each ordinary derivative in the classical PK/PD model investigated in [41,43] with the ψ-Caputo fractional derivative of order α ∈ (0, 1] [1].…”

Global Dynamics of a Within‐Host COVID‐19/AIDS Coinfection Model with Distributed Delays

“…Mathematical models that consist of a system of differential equations have proven their efectiveness in studying the interactions between viruses and their hosts and the common interactions between diseases (see e.g., [12,[18][19][20][21][22][23][24]). HIV within-host models have been widely investigated and great results have been reached [18,19,[25][26][27][28].…”

“…Terefore, mathematicians have frequently used diferent types of delays to make biological models more realistic. In [26,28,35], HIV models with time delay were introduced, whilst modeling and analysis of COVID-19 based on a time delay dynamic model are presented in [12,23]. Although there are some publications that combine the coinfection between viruses in the presence of time delay, there are still no models of coinfection between SARS-CoV-2 and HIV with time delay.…”