Computing of dynamic models by a definition-based method.

Objectives: Computing the basic reproduction number ( ) 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 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 , 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 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 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 is failed to define, we may turn to the NGM for the threshold .