CAJ | 학술논문

复杂网络模拟实际系统时，常采用带有直接免疫的传染模型或带传染媒介的传染模型。这些模型只侧重实际系统的某一方面的因素。针对这一不足，提出一个新的SIRS类传染病模型，即带有传染媒介和直接免疫的SIRS模型。利用平均场理论建立相应的常微分方程系统，并讨论该类系统的传播动力学行为。研究结果表明，均匀网络情况下，该模型存在一个有限的传播阈值，并且传染媒介也会加速疾病的传播；非均匀网络情形时，传播阈值主要与网络的拓扑结构有关。
복잡망락모의실제계통시，상채용대유직접면역적전염모형혹대전염매개적전염모형。저사모형지측중실제계통적모일방면적인소。침대저일불족，제출일개신적SIRS류전염병모형，즉대유전염매개화직접면역적SIRS모형。이용평균장이론건립상응적상미분방정계통，병토론해류계통적전파동역학행위。연구결과표명，균균망락정황하，해모형존재일개유한적전파역치，병차전염매개야회가속질병적전파；비균균망락정형시，전파역치주요여망락적탁복결구유관。
When simulating practical system with complex networks,it usually uses the infection models with either direct immunisation orinfective medium.These models only focus on the factor of certain aspect in the practical system.Aiming at this insufficiency,the paper pro-poses a novel SIRS (susceptible infected removed susceptible)epidemic model,i.e.an SIRS model with infective medium and direct im-munisation.By using mean-field theory,we establish a corresponding ordinary differential equation system,and discuss the transmission dy-namics behaviour of the system.Research results show that there is a limited transmission threshold in the model under the condition of uni-form networks,and the infective medium can also accelerate the disease spread,and the transmission threshold of the model in non-uniformnetworks is mainly related to the topology of the networks.