Objectives

Computing the basic reproduction number (R₀) in deterministic dynamical models is a hot topic and is frequently demanded by researchers in public health. The next-generation methods (NGM) are widely used for such computation, however, the results of NGM are usually not to be the true R₀ but only a threshold quantity with little interpretation. In this paper, a definition-based method (DBM) is proposed to solve such a problem.

Methods

Start with the definition of R₀, consider different states that one infected individual may develop into, and take expectations. A comparison with NGM has proceeded. Numerical verification is performed using parameters fitted by data of COVID-19 in Hunan Province.

Results

DBM and NGM give identical expressions for single-host models with single-group and interactive R_ij of single-host models with multi-groups, while difference arises for models partitioned into subgroups. Numerical verification showed the consistencies and differences between DBM and NGM, which supports the conclusion that R₀ derived by DBM with true epidemiological interpretations are better.

Conclusions

DBM is more suitable for single-host models, especially for models partitioned into subgroups. However, for multi-host dynamic models where the true R₀ is failed to define, we may turn to the NGM for the threshold R₀.

中文翻译：

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通过基于定义的方法计算动态模型的 R0

目标

在确定性动态模型中计算基本再生数 ( R ₀ ) 是一个热门话题，并且经常受到公共卫生研究人员的要求。下一代方法（NGM）被广泛用于此类计算，然而，NGM的结果通常不是真正的R ₀，而只是一个几乎没有解释的阈值量。在本文中，提出了一种基于定义的方法（DBM）来解决这样的问题。

方法

从R ₀的定义开始，考虑一个感染者可能发展到的不同状态，并采取预期。已经进行了与 NGM 的比较。使用湖南省 COVID-19 数据拟合的参数进行数值验证。

结果

DBM 和 NGM 对具有单组的单主机模型和具有多组的单主机模型的交互式R _{ij给出相同的表达式，而对于划分为子组的模型则出现差异。}数值验证显示了 DBM 和 NGM 之间的一致性和差异，这支持了DBM 推导出的具有真实流行病学解释的R ₀更好的结论。

结论

DBM 更适用于单主机模型，尤其适用于划分为子组的模型。然而，对于真正的R ₀无法定义的多主机动态模型，我们可以求助于 NGM 的阈值R ₀。