标题： 一类疟疾流行动态模型的比较随机与确定性研究：探讨噪声对疾病根除和持续的影响 显示英文标题

标题： A comparative stochastic and deterministic study of a class of epidemic dynamic models for malaria: exploring the impacts of noise on eradication and persistence of disease

摘要： 对一组疟疾SEIRS流行动力学模型的比较随机和确定性研究被提出。 该族类型由疾病非线性发病率的定性行为决定。 此外，疟疾模型表现出三个随机延迟：其中两个延迟代表疾病在媒介和人类宿主体内的潜伏期，而第三个延迟是针对疾病的有效自然免疫力的时期。 通过在疾病传播和人类自然死亡率中包含随机环境波动，改进了随机疟疾模型。 通过比较分析该族随机和确定性模型，以及进一步对系统中白噪声强度在（1）平衡点的存在性和稳定性，以及（2）疟疾在人类群体中的根除和持续方面的显著性进行深入检查，获得了关于延迟和噪声对疟疾动态影响的见解。 在系统中存在常数或随机延迟的情况下，确定并比较了随机和确定性设置下疟疾的基本再生数和其他阈值。 给出了数值模拟结果。 显示英文摘要

摘要： A comparative stochastic and deterministic study of a family of SEIRS epidemic dynamic models for malaria is presented. The family type is determined by the qualitative behavior of the nonlinear incidence rates of the disease. Furthermore, the malaria models exhibit three random delays:- two of the delays represent the incubation periods of the disease inside the vector and human hosts, whereas the third delay is the period of effective natural immunity against the disease. The stochastic malaria models are improved by including the random environmental fluctuations in the disease transmission and natural death rates of humans. Insights about the effects of the delays and the noises on the malaria dynamics are gained via comparative analyses of the family of stochastic and deterministic models, and further critical examination of the significance of the intensities of the white noises in the system on (1) the existence and stability of the equilibria, and also on (2) the eradication and persistence of malaria in the human population. The basic reproduction numbers and other threshold values for malaria in the stochastic and deterministic settings are determined and compared for the cases of constant or random delays in the system. Numerical simulation results are presented.