What does this research mean for the field?

An SIS epidemic model with a constant importation or removal rate of infected individuals possesses fully characterizable topologically distinct phase portraits in the Poincaré disc, completely describing its qualitative dynamics. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To fully characterize all topologically distinct phase portraits in the Poincaré disc for an SIS epidemic model that incorporates constant importation or removal rates of infected individuals.

September 8, 2026International Journal of Bifurcation and Chaos

An SIS Model with Importation and Removal

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To fully characterize all topologically distinct phase portraits in the Poincaré disc for an SIS epidemic model that incorporates constant importation or removal rates of infected individuals.
Formulated a nonlinear ordinary differential equation system representing susceptible-infectious-susceptible dynamics with constant migration (importation or removal) of infectives.
Conducted qualitative phase-space analysis on the Poincaré disc to map all trajectories, including boundary behaviors at infinity.
Identified and classified every topologically distinct phase portrait possible under the governing parameter spaces of the model.
Established the first comprehensive qualitative description of all orbital trajectories, capturing paths that approach or emerge from infinity.

Authors

JLJaume LlibreUniversitat Autònoma de Barcelona HZHui ZengSun Yat-sen University

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Implication

Mathematical analysis reveals all topologically distinct phase portraits in an SIS model with constant importation or removal, highlighting complete global dynamics across all orbits.

Cite This Study

Llibre et al. (2026) studied this question.

synapsesocial.com/papers/6a9fd7c658e84d0ff5b46c5e https://doi.org/10.1142/s0218127426502238

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Implication

Mathematical analysis reveals all topologically distinct phase portraits in an SIS model with constant importation or removal, highlighting complete global dynamics across all orbits.

An SIS Model with Importation and Removal

Key Points

Discussion

Implication

Cite This Study

An SIS Model with Importation and Removal

Key Points

Discussion

Implication

Cite This Study

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