Shi Zhao1,2, Jinjun Ran3, Guangpu Yang4,5, Peihua Cao6. 1. JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China. 2. Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China. 3. School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China. 4. Department of Orthopaedics and Traumatology, Chinese University of Hong Kong, Hong Kong, China. 5. SH Ho Scoliosis Research Lab, Joint Scoliosis Research Center of Chinese University of Hong Kong and Nanjing University, Hong Kong, China. 6. Clinical Research Centre, Zhujiang Hospital, Southern Medical University, Guangzhou, China.
We read with interests Huang et al.'s article ‘Seasonality of the transmissibility of hand, foot and mouth disease: a modelling study in Xiamen City, China’ [1]. Huang et al. modelled the long-term transmission dynamics of hand, foot and mouth disease (HFMD) in Xiamen, China. However, we suspected that there was an inconsistency between the model formulation and the effective reproduction number, Reff, in [1]. As such, we highlighted the importance of following the next generation matrix (NGM) analytic procedure to find reproduction numbers in compartmental models.The NGM approach is widely adopted to derive the reproduction numbers in modelling infectious disease epidemiology [2-9]. With this approach, we re-analysed the ‘SEIAR’ model in [1], and found the effective reproduction number, denoted by reff in this letter to distinguish from Reff in [1], in Eqn (1).Here, all notations have the same definitions as in Huang et al. [1]. We found that reff was different from that in Huang et al. [1]. For a sufficiently small value of the human natural death rate (dr), we have an approximated version of reff as in Eqn (2), and it has an analytic form closer to the Reff in [1].It was notable that the denominator of the first fractional term in the brackets, i.e. [⋅], has an additional term ‘f’ in Eqn (2), compared to the Reff in [1]. This difference implied that the HFMD-induced fatality rate (f) was neglected in Huang et al. [1]. Furthermore, according to Table 1 in [1], the value of f was set to be (0.03% =) 0.0003 that appears relatively small compared to the main ‘removing’ rates (γ and γ′) of HFMD infections. This setting suggested that the Reff in [1] could be treated as a reasonable simplification from its theoretical version. Hence, this inconsistency between the model formulation and the reproduction number was unlikely to affect the main conclusions.In conclusion, we call for caution in deriving and simplifying reproduction numbers from compartmental models.