Ziheng Cheng, Hanqing Hu, Teng Ma, Huangjie Zheng
Abstract:
Malware transmission remains a serious threat to computer networks,
particularly in heterogeneous environments.
We propose a three community SIP model (Susceptible-Infected-Protected) that includes
both intra and intercommunity transmissions.
The basic reproduction number \(\mathcal{R}_0 \) is derived using the next-generation
matrix method and serves as the threshold between extinction and persistence of malware.
Analysis shows that the malware-free equilibrium is globally stable when
\(\mathcal{R}_0 < 1\), while an endemic equilibrium exists and remains stable when
\(\mathcal{R}_0 >1\).
Numerical results support the theory and highlight that stronger protection and
limited cross-community connections can effectively suppress malware spread.
Submitted
Submitted Mach 25, 2026. Published September 10, 2026.
Math Subject Classifications: 34D20, 65L07, 92D30.
Key Words: Malware transmission; susceptible-infected-protected model;
reproduction number.
DOI: 10.58997/ejde.2026.69
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Ziheng Cheng School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240, China email: harryczh@sjtu.edu.cn |
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Hanqing Hu School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240, China email: hhqhaha666@sjtu.edu.cn |
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Teng Ma School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240, China email: dlutecnu@sjtu.edu.cn |
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Huangjie Zheng School of Mathematical Sciences Shanghai Jiao Tong University Shanghai 200240, China email: huangjie7796@sjtu.edu.cn |
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