arXiv subjects

Keoni Castellano

Publications and source records attributed to Keoni Castellano.

3 recordsLinked to original sources

arXiv2025

Investigation of a two-patch within-host model of hepatitis B viral infection

Chronic infection with hepatitis B virus (HBV) can lead to formation of abnormal nodular structures within the liver. To address how changes in liver anatomy affect overall virus-host dynamics, we developed within-host ordinary differential equation models of two-patch hepatitis B infection, one that assumes irreversible and one that assumes reversible movement between nodular structures. We investigated the models analytically and numerically, and determined the contribution of patch susceptibility, immune responses, and virus movement on within-patch and whole-liver virus dynamics. We explored the structural and practical identifiability of the models by implementing a differential algebra approach and the Monte Carlo approach for a specific HBV data set. We determined conditions for viral clearance, viral localization, and systemic viral infection. Our study suggests that cell susceptibility to infection within modular structures, the movement rate between patches, and the immune-mediated infected cell killing have the most influence on HBV dynamics. Our results can help inform intervention strategies.

q-bio.OT↗

arXiv2023

Multiplicity of endemic equilibria for a diffusive SIS epidemic model with mass-action

We study a diffusive SIS epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on previous studies related to disease extinction or persistence when $\mathcal{R}_0<1$ and the multiplicity of EE solutions when $\mathcal{R}_0>1$. Interestingly, even with such a simple nonlinearity induced by the mass-action, we show that the diffusive epidemic model may have an S-shaped or backward bifurcation curve of EE solutions.

math.AP↗

arXiv2021

Remarks on the preservation and breaking of translational symmetry for a class of ODEs

In this paper, we provide both a preservation and breaking of symmetry theorem for $2π$-periodic problems of the form \begin{align*} \begin{cases} -u''(t) + g(u(t)) = f(t)\cr u(0) - u(2π) = u'(0) - u'(2π) = 0 \end{cases} \end{align*} where $g: \mathbb{R} \to \mathbb{R}$ is a given $C^1$ function and $f: [0,2π] \to \mathbb{R}$ is continuous. We provide a preservation of symmetry result that is analogous to one given by Willem (Willem, 1989) and a generalization of the theorem given by Costa-Fang (Costa and Fang, 2019). Both of these theorems use group actions that are not normally considered in the literature.

math.AP↗