Highly dynamic animal contact network and implications on disease transmission

Chen, Shi; White, Brad J.; Sanderson, Michael W.; Amrine, David E.; Ilany, Amiyaal; Lanzas, Cristina

where b 0 was the transmission coefficient (a constant), C ji,t represented the number of pairwise contacts of animal i in time t, I j,t and N t represented jth infected animal and total animals in time t, respectively. Because of the closed population, N t ; N for any given t. Thus we could re-organize the expression to b i,t~b 0 0 X j C ji,t I j,t . To simplify the model, recovery was considered independent of contact; an infected individual had a constant recovery probability (c) in any time, and once it recovered from the infected state, it would stay in the recovered state, assuming no leaking or waning immunity. Two sets of parameters, b ' 0~2 :5|10 {6 ; c~10 {3 and b ' 0~1 0 {5 ; c~2|10 {3 , were fed into the model, representing diseases with smaller and larger basic reproduction numbers (R 0 ). A total of 100 individuals were simulated with one infected at the beginning of simulation; the other 99 animals were initially susceptible. The simulation lasted for 100 days, with a 1-h time step. The hourly number of contacts for each individual was simulated from the fitted distribution (see SI figure 2) using the mean and variance of contacts in each hour, and the number of contacts was assumed frequency-dependent and independent of population size, according to the observed data (e.g. pen #3 had 27 animals but the number of contacts was not higher than pen #1 and pen #2, which both had 21 animals). We used this assumption to simplify the model, but as discussed later, the model could be altered to be density-dependent or for more complicated conditions for the specific disease system at hand. The degree order was simulated through a random permutation (from 1 to population size N 5 100) in each hour. The time series of mean disease prevalence, and contribution of new infection from each individual were investigated.