Computing R0 of dynamic models by a definition-based method


Objectives: 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. Methods: 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. 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 R 0 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 R 0 is failed to define, we may turn to the NGM for the threshold R 0.

Infectious Disease Modelling
2022 重点研发专项