Dynamics of a network-based SIR epidemic model with double impulsive controls

Gui Guan; Zhenyuan Guo; Yanyu Xiao; Yuming Chen; Gui Guan; Zhenyuan Guo; Yanyu Xiao; Yuming Chen

doi:10.3934/mbe.2026086

Mathematical Biosciences and Engineering

2026, Volume 23, Issue 8: 2367-2392. doi: 10.3934/mbe.2026086

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Research article

Dynamics of a network-based SIR epidemic model with double impulsive controls

1.
School of Mathematics, Hunan University, Changsha 410082, China
2.
Faculty of Mathematics and Physics, Huai'an University, Huai'an 223003, China
3.
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA
4.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Received: 27 March 2026 Revised: 21 May 2026 Accepted: 10 June 2026 Published: 30 July 2026

A network-based susceptible-infected-recovered (SIR) epidemic model is proposed to study the spread of infectious diseases, thereby incorporating vertical transmission and a saturated incidence rate. Additionally, it introduces double impulsive control strategies, including pulse vaccination and screening with treatment at distinct fixed intervals. Dynamical behaviors of the formulated model are analyzed using two types of transmission thresholds, namely $ R^0_{k_i} $ and $ \widehat{R^0_{k_i}} $. By applying the Floquet theorem and comparison principle, the system admits a disease-free periodic solution that is globally asymptotically stable if $ \max\limits_{i = 1, 2, \ldots, n}\widehat{R^0_{k_i}} < 1 $. The persistence of disease is confirmed from the uniform persistence of the Poincaré map when $ \frac{1}{1+\alpha}\max\limits_{i = 1, 2, \ldots, n}R^0_{k_i} > 1 $, where $ \alpha $ is the saturated coefficient in the saturation infection. Scenario studies are performed to numerically evaluate the impact of various parameters on the disease dynamics, and the effectiveness of double impulsive controls. It can be concluded that synthetical double impulsive controls are more efficient at eradicating the disease compared with only either of them.
- complex network,
- disease modeling,
- pulse,
- stability,
- uniform persistence
Citation: Gui Guan, Zhenyuan Guo, Yanyu Xiao, Yuming Chen. Dynamics of a network-based SIR epidemic model with double impulsive controls[J]. Mathematical Biosciences and Engineering, 2026, 23(8): 2367-2392. doi: 10.3934/mbe.2026086

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Abstract

A network-based susceptible-infected-recovered (SIR) epidemic model is proposed to study the spread of infectious diseases, thereby incorporating vertical transmission and a saturated incidence rate. Additionally, it introduces double impulsive control strategies, including pulse vaccination and screening with treatment at distinct fixed intervals. Dynamical behaviors of the formulated model are analyzed using two types of transmission thresholds, namely $ R^0_{k_i} $ and $ \widehat{R^0_{k_i}} $. By applying the Floquet theorem and comparison principle, the system admits a disease-free periodic solution that is globally asymptotically stable if $ \max\limits_{i = 1, 2, \ldots, n}\widehat{R^0_{k_i}} < 1 $. The persistence of disease is confirmed from the uniform persistence of the Poincaré map when $ \frac{1}{1+\alpha}\max\limits_{i = 1, 2, \ldots, n}R^0_{k_i} > 1 $, where $ \alpha $ is the saturated coefficient in the saturation infection. Scenario studies are performed to numerically evaluate the impact of various parameters on the disease dynamics, and the effectiveness of double impulsive controls. It can be concluded that synthetical double impulsive controls are more efficient at eradicating the disease compared with only either of them.

References

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