Pith. sign in

REVIEW 3 cited by

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2306.15011 v1 pith:OWWUB2BL submitted 2023-06-26 math.DS q-bio.PE

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 This is my paper
classification math.DS q-bio.PE
keywords strainscross-immunityimmunityperiodstemporaryanalysismodelpartial
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
Share X Bluesky LinkedIn Reddit HN
read the original 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.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A Perron-Volterra Lyapunov function for mathematical epidemiology reaction networks (MERN) with non-interacting rank-one strains

    math.DS 2026-05 unverdicted novelty 7.0

    A new Perron-Volterra Lyapunov construction unifies stability proofs for rank-one epidemic models and establishes the competitive exclusion partition property for two-strain cases.

  2. A Perron-Volterra Lyapunov function for mathematical epidemiology reaction networks (MERN) with non-interacting rank-one strains

    math.DS 2026-05 unverdicted novelty 7.0

    Proves parameter-space partitions into regions with unique stable equilibria in n-strain models via explicit Perron-Volterra Lyapunov functions for boundary and coexistence equilibria.

  3. A Perron-Volterra Lyapunov function for mathematical epidemiology reaction networks (MERN) with non-interacting rank-one strains

    math.DS 2026-05 conditional novelty 6.0

    For multi-strain epidemic models with independent rank-one transmission blocks, explicit Lyapunov functions prove competitive exclusion: generically one strain persists, coexistence only on lower-dimensional tie surfaces.