未感染概率为一般函数的离散S-I-R模型
A Discrete S-I-R Model with a General Function of Remaining Susceptible Probability
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摘要: 研究了一个离散S-I-R传染病模型,其中未感染概率为关于被感染人群的一般函数. 建立了模型的基本再生数, 得到了平衡点的存在性和稳定性只依赖于此再生数. 此外, 还得到了系统一致持久和全局渐近稳定的条件. 模型的数学结论表明种群密集是疾病传播的原因, 提高医疗技术有利于疾病控制.Abstract: This paper studies a discrete S-I-R disease transmission model, in which the probability of remaining susceptible is a general function of the infected population. The basic reproduction number is established. Existence and stability of equilibria are studied with conditions only related to this number. Conditions for permanence and global stability of the system are also obtained. The mathematical results of the model suggest that overcrowded population may be the reason for disease spread and improving the medical technology is effective for disease control.
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