Epidemic models with heterogeneous mixing and treatment
Epidemic models with heterogeneous mixing and treatment
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DOI：
10.1007/s11538-008-9326-1
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发表时间：
2008-10-01
影响因子：
3.5
通讯作者：
Brauer, Fred
中科院分区：
文献类型：
--
作者：
Brauer, Fred
我们考虑了一个带有治疗的两组传染病模型，并建立了一个最终的大小关系，给出了流行病的程度。可以利用组之间的任意混合来建立这种关系，即使可能不可行地确定模型的再现次数。如果两组的混合是成比例的，则繁殖数有一个明确的表达式，并且最终的大小关系可以用繁殖数的分量来表示。我们还将结果推广到具有比例混合的两组流感模型。一些数值模拟表明：(I)如果疾病死亡率很小，无疾病死亡的假设是一个很好的近似；(Ii)一组模型是两组模型的近似，但两组模型是比较靶向治疗策略所必需的。
We consider a two-group epidemic model with treatment and establish a final size relation that gives the extent of the epidemic. This relation can be established with arbitrary mixing between the groups even though it may not be feasible to determine the reproduction number for the model. If the mixing of the two groups is proportionate, there is an explicit expression for the reproductive number and the final size relation is expressible in terms of the components of the reproduction number. We also extend the results to a two-group influenza model with proportionate mixing. Some numerical simulations suggest that (i) the assumption of no disease deaths is a good approximation if the disease death rate is small and (ii) a one-group model is a close approximation to a two-group model but a two-group model is necessary for comparing targeted treatment strategies.