Differential susceptibility epidemic models
Differential susceptibility epidemic models
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DOI：
10.1007/s00285-004-0301-7
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发表时间：
2005-06-01
影响因子：
1.9
通讯作者：
Li, J
中科院分区：
文献类型：
--
作者：
Hyman, JM;Li, J
我们建立了房室微分易感性（DS）的易感性-感染-去除（SIR）模型，将易感人群分为多个亚组，根据每个组中的个人的易感性。我们分析的情况下，每个人的接触的数量是恒定的或成比例的总人口的疾病引起的死亡率的影响。通过研究无感染平衡点的局部稳定性，我们得到了每个模型的感染再生数的显式公式。我们进一步证明了每个模型的无感染平衡点是全局渐近稳定的定性分析模型系统的动力学，并利用适当选择的Liapunov函数。我们证明了，如果再生数大于1，则本文所研究的所有DS模型都存在唯一的地方病平衡点。我们证明了无疾病死亡率和接触数与总人口成比例的模型的地方病平衡点是局部渐近稳定的。我们还提供了充分条件的地方病平衡点的稳定性的其他情况。简要讨论了DS模型在最优疫苗策略中的应用，并给出了DS模型与多食饵种群的捕食-食饵模型和多宿主的宿主-寄生虫相互作用模型之间的联系。
We formulate compartmental differential susceptibility (DS) susceptible-infective-removed (SIR) models by dividing the susceptible population into multiple subgroups according to the susceptibility of individuals in each group. We analyze the impact of disease-induced mortality in the situations where the number of contacts per individual is either constant or proportional to the total population. We derive an explicit formula for the reproductive number of infection for each model by investigating the local stability of the infection-free equilibrium. We further prove that the infection-free equilibrium of each model is globally asymptotically stable by qualitative analysis of the dynamics of the model system and by utilizing an appropriately chosen Liapunov function. We show that if the reproductive number is greater than one, then there exists a unique endemic equilibrium for all of the DS models studied in this paper. We prove that the endemic equilibrium is locally asymptotically stable for the models with no disease-induced mortality and the models with contact numbers proportional to the total population. We also provide sufficient conditions for the stability of the endemic equilibrium for other situations. We briefly discuss applications of the DS models to optimal vaccine strategies and the connections between the DS models and predator-prey models with multiple prey populations or host-parasitic interaction models with multiple hosts are also given.