具有公共健康教育的随机潜蚤病模型动力学行为研究  

Dynamic Behavior of a Stochastic Tungiasis Model with Public Health Education

作　　者：孔丽丽 李录苹 陈慧琴 康淑瑰 KONG Lili;LI Luping;CHEN Huiqin;KANG Shugui(School of Mathematics and Statistics,Shanxi Datong University,Datong 037009,China)

机构地区：[1]山西大同大学数学与统计学院,大同037009

出　　处：《应用数学学报》2023年第2期277-290,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金项目(批准号:11871314);山西省高等学校科技创新项目(批准号:2022L416);大同市科技计划项目(批准号:2020147,2022056)资助项目。

摘　　要：潜蚤病是加勒比、拉丁美洲和撒哈拉以南的非洲等经济条件较差地区的一种常见的人畜共患病,其因发病率高,传染快受到人们的关注.而在这些经济贫困地区及时的公共健康教育是控制疾病的一种手段.基于此,本文研究了一类具有公共健康教育和饱和治疗率的随机潜蚤病模型的动力学行为.利用It?公式和构造Lyapunov函数等方法,首先证明了随机系统全局正解的存在唯一性;接着,分析了随机系统的正解围绕确定性系统的无病平衡点和地方病平衡点的渐近行为.最后,通过数值模拟验证了理论结果的正确性。Tungiasis is a common zoonotic disease in economically disadvantaged regions such as the Caribbean,Latin America and sub-Saharan Africa.It is of great concern due to its high incidence and rapid transmission.Timely public health education is a means to control the disease in these economically poor areas.Based on this,in this paper,the dynamic behavior of a stochastic model of tungiasis with public health education and saturation treatment rates was studied.By using Itôformula and constructing Lyapunov function,the existence and uniqueness of global positive solutions for stochastic systems are firstly proved;then,the asymptotic behavior of the positive solution of the stochastic system around the disease-free equilibrium and endemic equilibrium of the deterministic system is analyzed.Finally,the correctness of the theoretical results is verified by numerical simulation.The conclusion of theoretical research and numerical simulation shows that increasing the intensity of random interference is a means to accelerate the extinction of diseases.

关 键 词：随机潜蚤病模型 公共健康教育 LYAPUNOV函数 It?公式 

分 类 号：O175.1[理学—数学]