Estimating the Transmittable Prevalence of Infectious Diseases Using a Back-Calculation Approach

  • Lee, Youngsaeng (ICT Convergence Research Center for Smart Appliances, Chonnam National University) ;
  • Jang, Hyun Gap (JW LEE Center for Global Medicine, College of Medicine, Seoul National University) ;
  • Kim, Tae Yoon (Department of Statistics, Kyemyong University) ;
  • Park, Jeong-Soo (Department of Statistics, Chonnam National University)
  • Received : 2014.05.20
  • Accepted : 2014.08.24
  • Published : 2014.11.30


A new method to calculate the transmittable prevalence of an epidemic disease is proposed based on a back-calculation formula. We calculated the probabilities of reactivation and of parasitemia as well as transmittable prevalence (the number of persons with parasitemia in the incubation period) of malaria in South Korea using incidence of 12 years(2001-2012). For this computation, a new probability function of transmittable condition is obtained. The probability of reactivation is estimated by the least squares method for the back-calculated longterm incubation period. The probability of parasitemia is calculated by a convolution of the survival function of the short-term incubation function and the probability of reactivation. Transmittable prevalence is computed by a convolution of the infected numbers and the probabilities of transmission. Confidence intervals are calculated using the parametric bootstrap method. The method proposed is applicable to other epidemic diseases in other countries where incidence and a long incubation period are available. We found the estimated transmittable prevalence in South Korea was concentrated in the summer with 276 cases on a peak at the $31^{st}$ week and with about a 60% reduction in the peak from the naive prevalence. The statistics of transmittable prevalence can be used for malaria prevention programs and to select blood transfusion donors.


Supported by : National Research Foundation of Korea (NRF)


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