Shot noise processes are introduced to model aggregated parasitic count data arising from clumped superinfections coupled with different decay mechanisms of the ingested parasite clumps. The corresponding likelihood functions are derived by using Laplace transforms. The models are fitted to samples with Echinococcus granulosus parasites in dogs from Kazakhstan, Tunisia and China. It is shown that parameter estimates take plausible values and that the decay dynamics is comparable in the three samples. The results indicate that dogs cease to be infectious after about 8 months, and that infections of dogs occur at a low rate, but the ingested parasite load per clump is in the thousands.