摘要
利用反应扩散方程单调方法和不变区域理论,研究具有饱和传染力的反应扩散方程D-SIS流行病模型,证明了解的存在惟一性,得到了疾病绝灭与持续的阈值———基本再生数,分别证明了无病平衡点和地方病平衡点的全局渐近稳定性.该研究将相应常微分方程模型的研究结果推广到了偏微分方程D-SIS模型,对疾病的预防与控制具有实用参考价值.
Based on the invariant region theory, a reaction diffusion equations D-SIS epidemic model with saturated rate is investigated by monotone methods. The existence and uniqueness of the solution for the model are proved. The basic reproduction number which determines whether the disease exists or not is got, and the globally asymptotical stability of the disease-free equilibrium and the endemic equilibrium are obtained. The concluded results of the corresponding ordinary differential equations model are expanded to the present D-SIS model, it is of benefit to disease control.
出处
《西安交通大学学报》
EI
CAS
CSCD
北大核心
2006年第6期734-737,共4页
Journal of Xi'an Jiaotong University
基金
国家自然科学基金重点资助项目(10531030)
国家"十五"医学科技攻关课题资助项目(2004BA719A01)
关键词
流行病
反应扩散方程
阈值
全局渐近稳定性
疾病控制
epidemics
reaction-diffusion equation
threshold
global asyrnptotical stability
disease control
