Vaccination of influenza a virus decreases transmission rates in pigs

Romagosa, Anna; Allerson, Matt; Gramer, Marie; Joo, Han Soo; Deen, John; Detmer, Susan; Torremorell, Montserrat

To estimate the transmission parameter β, a generalized linear model (GLM) with a complementary log-log link function and log I Δt/N as the offset variable (number of infectious pigs/total number of pigs) was used to calculate the estimates of the transmission parameter β by day (Δt = 1) [45] . Knowing the number of susceptible contact pigs and the number of infectious pigs at the start of each period Δt (S t-1 , I t-1 ), the number of new infections that appeared at the end of each period (C t ), and the total number of animals in each period (N), the probability that a pig became infected was 1-e -IβΔt/N and the number of animals infected during each time period was E(C)= S(1-e -IβΔt/N ) [18] . The logistic regression model cannot provide a direct estimate of the transmission rate β, but with an alternative transformation known as the complementary loglog we calculated β from the equation log [-log (1-E(C)/ S)] = log (β) + log (IΔt/N). This model is similar to the linear model as follows: log [-log (1-E(C)/S)] = βo + β 1 X where the intercept coefficient βo = log (β), with corresponding β 1 = 1 including the predictor X = log (IΔt/N) as a fixed offset. With the transformation of log (β), the transmission parameter β could be estimated. The model entails some assumptions: (i) all susceptible animals are equally susceptible; (ii) all infected animals are equally infectious; (iii) each infected pig poses an independent risk of infection to each susceptible pig. Differences between β values were compared using chi-square comparisons and differences were considered statistically significant at p < 0.05.