Convergence of Bi-Virus Epidemic Models With Non-Linear Rates on Networks—A Monotone Dynamical Systems Approach
Convergence of Bi-Virus Epidemic Models With Non-Linear Rates on Networks—A Monotone Dynamical Systems Approach
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DOI：
10.1109/tnet.2022.3213015
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发表时间：
2022-10
期刊：
影响因子：
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通讯作者：
Vishwaraj Doshi;Shailaja Mallick;Do Young Eun
中科院分区：
文献类型：
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作者：
Vishwaraj Doshi;Shailaja Mallick;Do Young Eun
我们研究了易感-感染-易感（SIS$）型的竞争流行病模型的收敛性。SIS流行病模型在模拟传染病（如病毒、传染病，甚至是接触网络上的谣言/意见）的传播动态方面得到了广泛的普及（图表）。我们分析了两个这样的病毒在重叠图上传播的情况，感染传播和恢复的非线性率。我们称其为非线性双病毒模型，并在最近的结果基础上，获得了三分法可能结果（无病毒状态、单病毒状态和共存状态）的解的全局收敛的精确条件。我们的技术是基于单调动力系统（MDS）理论，与李亚普诺夫为基础的技术相比，在确定竞争流行病背景下的收敛特性方面只取得了部分成功。我们证明了现有的工作如何未能成功地描述双病毒流行病的模型参数空间的一个大子集，包括导致流行病共存的所有情景。据我们所知，我们的结果是第一个在一般图上提供具有非线性感染和恢复率的双病毒系统的完全收敛分析。
We study convergence properties of competing epidemic models of the Susceptible-Infected-Susceptible ( $SIS$ ) type. The SIS epidemic model has seen widespread popularity in modelling the spreading dynamics of contagions such as viruses, infectious diseases, or even rumors/opinions over contact networks (graphs). We analyze the case of two such viruses spreading on overlaid graphs, with non-linear rates of infection spread and recovery. We call this the non-linear bi-virus model and, building upon recent results, obtain precise conditions for global convergence of the solutions to a trichotomy of possible outcomes: a virus-free state, a single-virus state, and to a coexistence state. Our techniques are based on the theory of monotone dynamical systems (MDS), in contrast to Lyapunov based techniques that have only seen partial success in determining convergence properties in the setting of competing epidemics. We demonstrate how the existing works have been unsuccessful in characterizing a large subset of the model parameter space for bi-virus epidemics, including all scenarios leading to coexistence of the epidemics. To the best of our knowledge, our results are the first in providing complete convergence analysis for the bi-virus system with non-linear infection and recovery rates on general graphs.