What question did this study set out to answer?

Formulate and analyze a non-Markovian SIR epidemic model on complex networks incorporating saturated treatment capacity to evaluate disease transmission dynamics and persistence.

August 19, 2026SIAM Journal on Applied Mathematics

Global Dynamics of a Non-Markovian Epidemic Model on Complex Networks

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Authors

JYJunyuan Yang MMMaia Martcheva JZJun Zhang

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Overview

Mathematical modeling study demonstrates how treatment delays cause backward bifurcation in complex contact networks, indicating that limited healthcare capacity complicates disease eradication.

Key Points

Formulate and analyze a non-Markovian SIR epidemic model on complex networks incorporating saturated treatment capacity to evaluate disease transmission dynamics and persistence.
Developed a susceptible-infectious-recovered network model using general recovery distributions and a saturation treatment function to reflect resource constraints.
Established model well-posedness and disease-free equilibrium stability using semigroup theory and comparison principles.
Analyzed bifurcation behavior near the disease-free equilibrium using an updated Lyapunov–Schmidt reduction method and verified dynamics via numerical simulations.
Proved the global stability criteria for the disease-free equilibrium under non-Markovian recovery dynamics.
Demonstrated that excessive delayed treatment effects trigger backward bifurcation near the disease-free equilibrium, allowing disease persistence despite basic reproduction metrics.
Showed through simulations that contact network topology combined with non-Markovian recovery processes alters outbreak trajectory and control thresholds.

Cite This Study

Yang et al. (2026) studied this question.

synapsesocial.com/papers/6a85643903308d306e2d7c9c https://doi.org/10.1137/24m1711546

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August 19, 2026SIAM Journal on Applied Mathematics

Global Dynamics of a Non-Markovian Epidemic Model on Complex Networks

View Full Paper

Ask AI

Bookmark

Authors

JYJunyuan Yang MMMaia Martcheva JZJun Zhang

Discussion

Member takes

Overview

Mathematical modeling study demonstrates how treatment delays cause backward bifurcation in complex contact networks, indicating that limited healthcare capacity complicates disease eradication.

Key Points

Formulate and analyze a non-Markovian SIR epidemic model on complex networks incorporating saturated treatment capacity to evaluate disease transmission dynamics and persistence.
Developed a susceptible-infectious-recovered network model using general recovery distributions and a saturation treatment function to reflect resource constraints.
Established model well-posedness and disease-free equilibrium stability using semigroup theory and comparison principles.
Analyzed bifurcation behavior near the disease-free equilibrium using an updated Lyapunov–Schmidt reduction method and verified dynamics via numerical simulations.
Proved the global stability criteria for the disease-free equilibrium under non-Markovian recovery dynamics.
Demonstrated that excessive delayed treatment effects trigger backward bifurcation near the disease-free equilibrium, allowing disease persistence despite basic reproduction metrics.
Showed through simulations that contact network topology combined with non-Markovian recovery processes alters outbreak trajectory and control thresholds.

Cite This Study

Yang et al. (2026) studied this question.

synapsesocial.com/papers/6a85643903308d306e2d7c9c https://doi.org/10.1137/24m1711546

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