Stochastic dynamics of an epidemics with recurrent spillovers from an endemic reservoir

Marina Voinson; Alexandra Alvergne; Sylvain Billiard; Charline Smadi

As illustrated in Figure 3 , three patterns are observed (i) a stuttering chain of 150 transmission that goes extinct, i.e. infection spreads inefficiently, (corresponding to Stage II in Wolfe's classification, see Figure 1 ), (ii) a large outbreak and few stuttering chains of transmission (corresponding to Stage III, see Figure 1 ) and (iii) a single large outbreak consuming a large number of susceptible individuals (corresponding to Stage IV see Figure 1 ). 155 Figure 4 shows the roles of R 0 and Ï„ in the occurrence of the patterns. Stuttering chains of transmission occur when the pathogen is barely contagious between individuals (small R 0 ) and when the recurrent emergence of the pathogen (Ï„ ) is low. At the opposite, when the pathogen is highly contagious (large R 0 ) or when the spillover transmission is high (Ï„ ), only one large outbreak is ob-