霍乱多斑块传播动力学建模及稳定性分析

Dynamic modeling and stability analysis of cholera transmission in multi-patches

针对霍乱疫情,建立了两斑块、多群体的SIR传染病动力学模型,并进行了稳定性分析.当两群体间不存在相互作用时,假设单群体的所有解都收敛到一个平衡点.当两个群体间存在相互作用且为弱连通时,其SIR流行病模型的解不仅会收敛到地方病平衡点,还可能会收敛到混合平衡点,其坐标在某一单群体中处于边界,而在另一单群体中处于内部.最后进行了数值模拟来验证理论结果.

A cholera transmission SIR epidemic model with two patches and reducible connected network consideration is formulated.When there is no interaction between the two patches,it is first assumed that all solutions of each single group converge to the unique disease-free equilibrium.When there are interactions between two patches and they are reducible connected,the solution of the SIR epidemic model will not only converge to the endemic equilibrium,but may also converge to the mixed equilibrium,whose coordinates are at the boundary in one single group and in another It is internal.Finally,a numerical simulation was performed to verify the theoretical findings.