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

A stochastic SIR model was developed using the transmission and recovery parameters obtained from the previously described deterministic model and experimental study (parameters listed in Table 1 ). For all stochastic models, the initial number of infectious, susceptible, and recovered pigs was 1, 10, and 0, similar to that of the experimental study. In the stochastic models two events could occur, transmission (S I) and recovery (I R) within the SIR model (S I R). The transmission rate (β) was obtained from the deterministic model and the recovery rate (γ) was obtained from the experimental study (the inverse of the infectious period). The rate at which transmission occurred was βSI and the rate at which recovery occurred was γI. Each replicate for which transmission occurred in the experimental study was modeled separately with 10 000 simulations using the parameters obtained from the experimental deterministic model. Each simulation was run until the infectious process ended and a final size of the outbreak could be assessed. The number of new cases (contact infected susceptible individuals) observed for each simulation, given the parameters listed in Table 1 , was assessed for each replicate with the initial number of infectious, susceptible, and recovered individuals at 1, 10, and 0, respectively. The proportion and cumulative proportion of 10 000 simulations by the number of new cases for each replicate was displayed in graph format. The direct method of Gillespie was used to model the random events of transmission and recovery [46] . Reproduction ratio R by replicate. 4 Reproduction ratio R when replicates were combined by group. a,b,c Statistically significant differences (p < 0.05).