CAJ | 학술논문

空间传染病模型可用于估计空间斑图的形成及传染病的传播速率，因此能更精确地描述传染病的传播过程。在自然界中，考虑到易感者有能力识别感染者群体并有远离他们的趋势，我们研究了两类具有自我扩散和交叉扩散的SIR传染病模型的空间斑图形成。通过在正平衡态处将模型线性化，分析相应的特征方程，得到了系统出现图灵不稳定的充分条件。数值模拟表明模型会出现点状斑图和条状-点状斑图。研究结果丰富了传染病动力学模型中的斑图形成，并可用于预测传染病在空间中的传播过程，为传染病的预防和控制的科学决策提供了理论依据。
공간전염병모형가용우고계공간반도적형성급전염병적전파속솔，인차능경정학지묘술전염병적전파과정。재자연계중，고필도역감자유능력식별감염자군체병유원리타문적추세，아문연구료량류구유자아확산화교차확산적SIR전염병모형적공간반도형성。통과재정평형태처장모형선성화，분석상응적특정방정，득도료계통출현도령불은정적충분조건。수치모의표명모형회출현점상반도화조상-점상반도。연구결과봉부료전염병동역학모형중적반도형성，병가용우예측전염병재공간중적전파과정，위전염병적예방화공제적과학결책제공료이론의거。
Spatial epidemic models are suitable for describing the dynamical process of infec-tious diseases since they can be used to estimate the formation of spatial patterns on a large scale and the transmission velocity of diseases. Considering the tendency that the susceptibles would keep away from the infectives for the reason that the susceptibles have ability to recognize the infected individuals, we deal with spatial pattern formation of two SIR epidemic models with self and cross diffusion. By performing a linear approach around the positive steady states of the models and analyzing the corresponding characteristic equations, suffcient conditions are ob-tained for the Turing instability. Numerical simulations are carried out to exhibit regular-spot and stripe-spot patterns. The results may enrich the pattern formation in epidemic models, and are useful for predicting how the infectious diseases trans-mit in space. Our results provide theoretical basis for the scientific decision-making of prevention and control of infectious diseases.