The paper is concerned with R. Bartoszyński’s rabies model [Math. Biosciences 24, 355-377 (1975; Zbl 0324.92028)] which is well-known to be a particular case of a continuous-state branching process. A one-one correspondence with compound Poisson processes is obtained and used to obtain various limit theorems for the population size and the jump times. A particular interesting feature is the existence of a last jump time T, and the asymptotics include limit results conditionally upon \(T>t\).