arXiv subjects

R. P. Gupta

Publications and source records attributed to R. P. Gupta.

2 recordsLinked to original sources

arXiv2023

Dynamics of an SIR epidemic model with limited medical resources, revisited and corrected

This paper generalizes and corrects a famous paper (more than 200 citations) concerning Hopf and Bogdanov-Takens bifurcations due to L. Zhou and M. Fan, "Dynamics of an SIR epidemic model with limited medical resources revisited", in which we discovered a significant numerical error. Importantly, unlike the paper of Zhou and Fan and several other papers that followed them, we offer a notebook where the reader may recover all the results and modify them for analyzing similar models. Our calculations lead to the introduction of some interesting symbolic objects, "Groebner eliminated traces and determinants" - see (4.5), (4.6), which seem to have appeared here for the first time and which might be of independent interest. We hope our paper might serve as yet another alarm bell regarding the importance of accompanying papers involving complicated hand computations by electronic notebooks.

math.DS↗

arXiv2022

Testing a varying-$Λ$ model for dark energy within Co-varying Physical Couplings framework

The Co-varying Physical Couplings (CPC) framework is a modified gravity set up assuming Einstein Field Equations wherein the quantities $\{G,c,Λ\}$ are promoted to space-time functions. Bianchi identity and the requirement of stress-energy tensor conservation entangle the possible variations of the couplings $\{G,c,Λ\}$, which are forced to co-vary as dictated by the General Constraint (GC). In this paper we explore a cosmological model wherein $G$, $c$ and $Λ$ are functions of the redshift respecting the GC of the CPC framework. We assume a linear parametrization of $Λ$ in terms of the scale factor $a$. We use the ansatz $\dot{G}/G = σ\left( \dot{c}/c \right)$ with $σ=$ constant to deduce the functional forms of $c=c(z)$ and $G=G(z)$. We show that this varying-$\{G,c,Λ\}$ model fits SNe Ia data and $H(z)$ data with $σ= 3$. The model parameters can be constrained to describe dark energy at the background level.

gr-qc↗