两类具有空间扩散的SIR传染病模型的斑图形成

摘要

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。%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.