Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2306.15011

A two-strain model of infectious disease spread with asymmetric temporary immunity periods and partial cross-immunity

Matthew D. Johnston·Bruce Pell·David A. Rubel
View original source ↗Read source document ↗Export metadata ↓

Abstract

We introduce a two-strain model with asymmetric temporary immunity periods and partial cross-immunity. We derive explicit conditions for competitive exclusion and coexistence of the strains depending on the strain-specific basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. The results of our bifurcation analysis suggest that, even when two strains share similar basic reproduction numbers and other epidemiological parameters, a disparity in temporary immunity periods and partial or complete cross-immunity can provide a significant competitive advantage. To analyze the dynamics, we introduce a quasi-steady state reduced model which assumes the original strain remains at its endemic steady state. We completely analyze the resulting reduced planar hybrid switching system using linear stability analysis, planar phase-plane analysis, and the Bendixson-Dulac criterion. We validate both the full and reduced models with COVID-19 incidence data, focusing on the Delta (B.1.617.2), Omicron (B.1.1.529), and Kraken (XBB.1.5) variants. These numerical studies suggest that, while early novel strains of COVID-19 had a tendency toward dramatic takeovers and extinction of ancestral strains, more recent strains have the capacity for co-existence.

Explore related subjects

math.DSq-bio.PE

Keep this discovery

BibTeXRIS

Matthew D. Johnston, Bruce Pell, David A. Rubel. 2023-06-26. A two-strain model of infectious disease spread with asymmetric temporary immunity periods and partial cross-immunity. https://arxiv.org/abs/2306.15011

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

KEEP EXPLORING

Related papers

arXiv2026

Admissible Fourier Lengths, KAM Reducibility, and Spectral Applications

We develop a perturbative KAM reducibility theory for one-frequency $\mathrm{SL}(2,\mathbb{R})$ cocycles based on an admissible Fourier length $\ell$. The regularity relevant to the iteration is measured by positive adapted Fourier width rather than ordinary smoothness in the Euclidean length $|n|$. The same length governs Fourier decay, truncation and resonance scales, and the arithmetic condition controlling the small divisors. This framework contains the classical analytic and Gevrey settings, while non-monotone choices of $\ell$ allow classical nowhere differentiable Weierstrass-type perturbations and continuous perturbations outside every positive H\"older class. As spectral applications, we obtain purely absolutely continuous spectrum for every phase and $1/2$-H\"older continuity of the integrated density of states for the associated quasiperiodic Schr\"odinger operators. The Aubry dual has pure point spectrum for Lebesgue almost every dual phase, with eigenfunctions exponentially localized in the metric induced by $\ell$. We also construct nowhere differentiable quasiperiodic potentials with purely absolutely continuous Cantor spectrum.

math.DS↗
arXiv2026

Dynamics inside the attracting basins of some skew products

Polynomial skew products in $\mathbb{C}^2$ are maps of the form $F(z,w)=(P(z),Q(z,w))$, where $P$ and $Q$ are polynomials. Their local dynamics have been widely investigated. In this paper, we study the global dynamics inside Fatou components of some skew products. We consider all the inverse images in a Fatou component of a given point and use the Kobayashi metric to measure the distance between points. In the cases we consider, there are always arbitrarily large Kobayashi balls in the complement of these inverse sets.

math.DS↗
arXiv2026

Ergodicity of dynamical systems without uniqueness of orbits

Recently, there has been considerable interest in the study of non-deterministic dynamical systems. To analyze the chaotic behavior of such systems from a measure-theoretic viewpoint, it is desirable to consider ergodicity. However, the classical definition of ergodicity involves invariant sets, whose definition is not unique for non-deterministic dynamical systems. Thus, we are led to the question of which invariance yields an interesting definition of ergodicity. Here, we propose a definition based on the strong backward invariance and show that analogs of classical results hold. We also consider implications of the Birkhoff ergodic theorem for systems without uniqueness of orbits.

math.DS↗