SUMMARYHundreds of small-scale influenza outbreaks in schools are reported in mainland China every year, leading to a heavy disease burden which seriously impacts the operation of affected schools. Knowing the transmissibility of each outbreak in the early stage has become a major concern for public health policy-makers and primary healthcare providers. In this study, we collected all the small-scale outbreaks in Changsha (a large city in south central China with ~7·04 million population) from January 2005 to December 2013. Four simple and popularly used models were employed to calculate the reproduction number (R) of these outbreaks. Given that the duration of a generation interval Tc = 2·7 and the standard deviation (s.d.)σ = 1·1, the mean R estimated by an epidemic model, normal distribution and delta distribution were 2·51 (s.d. = 0·73), 4·11 (s.d. = 2·20) and 5·88 (s.d. = 5·00), respectively. When Tc = 2·9 and σ = 1·4, the mean R estimated by the three models were 2·62 (s.d. = 0·78), 4·72 (s.d. = 2·82) and 6·86 (s.d. = 6·34), respectively. The mean R estimated by gamma distribution was 4·32 (s.d. = 2·47). We found that the values of R in small-scale outbreaks in schools were higher than in large-scale outbreaks in a neighbourhood, city or province. Normal distribution, delta distribution, and gamma distribution models seem to more easily overestimate the R of influenza outbreaks compared to the epidemic model.
Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel
