Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2112.14876

Dynamic Systems Framework for Modeling COVID-19 with Lévy Noise

Daniel Tesfay·Almaz Tesfay·James Brannan
View original source ↗Read source document ↗Export metadata ↓

Abstract

Natural fluctuations have played a crucial role in affecting the dynamics of pervasive diseases such as the coronavirus. Examining the effects of irregular unsettling disturbances on epidemic models is important for understanding these dynamics. In this study, we introduce a mathematical model for the SIR (Susceptible-Infectious-Recovered) dynamics of the coronavirus, incorporating perturbations in the contact rate through Levy noise. The utilization of the Levy process is essential for the protection and control of diseases. We delve into the dynamics of both the deterministic model and the global positive solution of the stochastic model, establishing their existence and uniqueness. Additionally, we explore conditions for the termination and persistence of the infection. Furthermore, we derive the basic reproduction number, a critical determinant of disease extinction or persistence. Numerical results indicate that COVID-19 dissipates from the population when the reproduction number is less than one in the presence of significant or minor noise. Conversely, controlling epidemic diseases becomes challenging when the reproduction number exceeds one. To illustrate this phenomenon, we provide numerical simulations, offering insights into the dynamics of the disease and the efficacy of control measures

Explore related subjects

math.DSphysics.soc-phq-bio.PE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Daniel Tesfay, Almaz Tesfay, James Brannan. 2024-12-16. Dynamic Systems Framework for Modeling COVID-19 with Lévy Noise. https://arxiv.org/abs/2112.14876

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Effective equidistribution of orbits under semisimple groups on congruence quotients

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group.This extends a previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we allow for periodic orbits of semisimple groups with nontrivial centralizer in the ambient group. Our proof uses crucially an effective closing lemma from work of the author with Lindenstrauss, Margulis,Mohammadi, and Shah.

math.DS↗
arXiv2026

Generalized entropy of measure-induced maps

A classical result by E. Glasner and B. Weiss states that the topological entropy of a map $f$ is zero if and only if the topological entropy of its measure-induced map $f_*$ is zero, where $f_*$ is defined as the push-forward of a measure. In this work, we use generalized entropy to distinguish the complexity of these maps and prove that the measure-induced map is much more complex than the original map. Moreover, we introduce the generalized mean dimension, an invariant that is useful for distinguishing dynamical systems with zero mean dimension, including those with the small-boundary property, and we show a relationship between this new invariant and generalized entropy.

math.DS↗
arXiv2026

The endpoint problem for $\varepsilon$-hypercyclicity

For a fixed $0<\varepsilon<1$, F. Bayart asked in 2024 whether there exists an operator $T$ such that, for every $0<δ<1$, $T$ is $δ$-hypercyclic if and only if $δ\in[\varepsilon,1)$. We answer this question affirmatively by constructing a weighted backward shift on $\ell_2(\mathbb N_0,\ell_2(\mathbb N_0))$ with this property.

math.DS↗