The Equilibrium Analysis for Competitive Spreading Over Networks With Mutations

IF 2.4 Q2 AUTOMATION & CONTROL SYSTEMS IEEE Control Systems Letters Pub Date : 2024-06-17 DOI:10.1109/LCSYS.2024.3415457
Xue Lin;Qiang Jiao
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Abstract

Epidemic models have been used to analyze various spreading phenomena in the population, and usually consider that the spreading object does not change in the spreading process. Yet generally, the virus may evolve due to the influence of environments and medical interventions, or the information may be modified by individuals in networks. In this letter, we investigate the spread of two competing viruses in a network, where one of the viruses can mutate into the other one with a certain probability. Based on the multi-group susceptible-infected-susceptible (SIS) model, a mathematical model is proposed to describe the spread of viruses with mutations. We provide a necessary and sufficient condition for the uniqueness of the zero equilibrium, and the conditions for the existence, uniqueness, and local exponential stability of the coexisting equilibrium. Our results demonstrate that the mutation can affect the spreading ability of the virus and the coexistence of viruses. Moreover, we show the effect of mutation on the proportion of infected individuals by comparing it with the model without mutation.
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有突变的网络上竞争性传播的均衡分析
流行病模型被用来分析人群中的各种传播现象,通常认为传播对象在传播过程中不会发生变化。然而,一般情况下,病毒可能会因环境和医疗干预的影响而发生演变,或者网络中的个体可能会修改信息。在这封信中,我们研究了两种相互竞争的病毒在网络中的传播,其中一种病毒会以一定的概率变异成另一种病毒。基于多群体易感-感染-易感(SIS)模型,我们提出了一个数学模型来描述病毒的变异传播。我们提供了零平衡唯一性的必要条件和充分条件,以及共存平衡的存在性、唯一性和局部指数稳定性条件。我们的结果表明,变异会影响病毒的传播能力和病毒的共存。此外,我们还通过与无变异模型的比较,展示了变异对受感染个体比例的影响。
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来源期刊
IEEE Control Systems Letters
IEEE Control Systems Letters Mathematics-Control and Optimization
CiteScore
4.40
自引率
13.30%
发文量
471
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