Computing R ₀ of dynamic models by a definition-based method

Computing the basic reproduction number (R ₀) 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 R ₀ but only a threshold quantity with little interpretation. In this paper, a definition-based method (DBM) is proposed to solve such a problem.

Start with the definition of R ₀, 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.

DBM and NGM give identical expressions for single-host models with single-group and interactive R 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 R ₀ derived by DBM with true epidemiological interpretations are better.

DBM is more suitable for single-host models, especially for models partitioned into subgroups. However, for multi-host dynamic models where the true R ₀ is failed to define, we may turn to the NGM for the threshold R ₀.