Study on pest management SI epidemic model with instantaneous and non-instantaneous impulsive effects

Hu Pu; Sergey Meleshko; Eckart Schulz; Jianjun Jiao; Hu Pu; Sergey Meleshko; Eckart Schulz; Jianjun Jiao

doi:10.3934/math.20251072

AIMS Mathematics

2025, Volume 10, Issue 10: 24179-24207. doi: 10.3934/math.20251072

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Research article

Study on pest management SI epidemic model with instantaneous and non-instantaneous impulsive effects

Hu Pu ^1,2,
Sergey Meleshko ^{1
,
,},
Eckart Schulz ^{1
,
,},
Jianjun Jiao ^{3
,
,}

1.
School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon, Ratchasima 30000, Thailand
2.
Department of Mathematics, School of Science, Xingyi Normal University for Nationalities, Xingyi 52400, China
3.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China

Received: 01 August 2025 Revised: 22 September 2025 Accepted: 09 October 2025 Published: 23 October 2025
MSC : 34A37, 34C25, 34D05, 92D45

In this study, we propose and analyze a Susceptible-Infected (SI) epidemic model applied to pest management, focusing on the nonlinear release of infected pests and an instantaneous pulse of pesticide spraying. Additionally, the mortality rates of both susceptible and infected pests following the pesticide application are modeled as non-instantaneous pulses. Utilizing the comparison theorem for pulse differential equations and Floquet theory, we derive a threshold condition for the eradication of susceptible pests. We also demonstrate that all solutions are uniformly ultimately bounded. Furthermore, we establish conditions for the globally asymptotic stability of the pest-free boundary periodic solution and the permanence of the system. Finally, numerical simulations are conducted to verify the theoretical findings, and the key parameters affecting the pest extinction threshold were obtained, thereby providing a solid theoretical basis for the development of effective pest management strategies.
Citation: Hu Pu, Sergey Meleshko, Eckart Schulz, Jianjun Jiao. Study on pest management SI epidemic model with instantaneous and non-instantaneous impulsive effects[J]. AIMS Mathematics, 2025, 10(10): 24179-24207. doi: 10.3934/math.20251072

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Abstract

In this study, we propose and analyze a Susceptible-Infected (SI) epidemic model applied to pest management, focusing on the nonlinear release of infected pests and an instantaneous pulse of pesticide spraying. Additionally, the mortality rates of both susceptible and infected pests following the pesticide application are modeled as non-instantaneous pulses. Utilizing the comparison theorem for pulse differential equations and Floquet theory, we derive a threshold condition for the eradication of susceptible pests. We also demonstrate that all solutions are uniformly ultimately bounded. Furthermore, we establish conditions for the globally asymptotic stability of the pest-free boundary periodic solution and the permanence of the system. Finally, numerical simulations are conducted to verify the theoretical findings, and the key parameters affecting the pest extinction threshold were obtained, thereby providing a solid theoretical basis for the development of effective pest management strategies.

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