Malware attacks in today's vast digital ecosystem pose a serious threat. Understanding malware propagation dynamics and designing effective control strategies are therefore essential. In this work, we propose a generic SEIRV model formulated using ordinary differential equations to study malware spread. We establish the positivity and boundedness of the system, derive the malware propagation threshold, and analyze the local and global stability of the malware-free equilibrium. The separatrix defining epidemic regions in the control space is identified, and the existence of a forward bifurcation is demonstrated. Using normalized forward sensitivity indices, we determine the parameters most influential to the propagation threshold. We further examine the nonlinear dependence of key epidemic characteristics on the transmission rate, including the maximum number of infected, time to peak infection, and total number of infected. We propose a hybrid gradient-based global optimization framework using simulated annealing approach to identify effective and cost-efficient control strategies. Finally, we calibrate the proposed model using infection data from the "Windows Malware Dataset with PE API Calls" and investigated the effect of intervention onset time on averted cases, revealing an exponential decay relationship between delayed intervention and averted cases.

翻译：当今庞大数字生态系统中的恶意软件攻击构成严重威胁。因此，理解恶意软件传播动力学并设计有效的控制策略至关重要。本研究提出一个基于常微分方程构建的通用SEIRV模型来研究恶意软件传播。我们建立了系统的正性与有界性，推导了恶意软件传播阈值，并分析了无恶意软件平衡点的局部与全局稳定性。识别了控制空间中定义流行区域的分界线，并证明了前向分岔的存在性。通过归一化前向敏感度指数，我们确定了对传播阈值影响最大的参数。进一步研究了关键流行特征对传播率的非线性依赖关系，包括最大感染数量、感染峰值时间及总感染数量。我们提出了一种基于模拟退火方法的混合梯度全局优化框架，以识别高效且成本可控的控制策略。最后，利用"Windows恶意软件数据集与PE API调用"中的感染数据对模型进行校准，并研究了干预启动时间对避免病例数的影响，揭示了延迟干预与避免病例数之间的指数衰减关系。