Population dynamics in echinococcosis and cysticercosis: mathematical model of the life-cycles of Taenia hydatigena and T. ovis.

It is shown that under the conditions that prevailed in New Zealand in the late 1950s, Taenia hydatigena was hyperendemic, the life-cycle being regulated by a density-dependent constraint in the form of acquired immunity, and T. ovis was rare. The control measures that caused Echinococcus granulosus, which was endemic at the time, to decline towards extinction reduced T. hydatigena and T. ovis to endemic status only. A non-linear integrodifferential equation model, which was previously linearized to describe the life-cycle of E. granulosus in dogs and sheep in New Zealand, is used to describe the life-cycles of T. hydatigena and T. ovis. The model is then used to compare and contrast the population dynamics of these three species. The model is used to demonstrate that the endemic steady state is structurally unstable, and may be asymptotically unstable to small perturbations. It is also shown that despite the lower infection pressure experienced by the intermediate host in the endemic state, the numbers of larvae in sheep may be higher than in the hyperendemic state. Finally it is shown that the partial success of the control measures against T. hydatigena may have caused an increase in the numbers and prevalence of T. ovis larvae in sheep due to the reciprocal immunity between the two species.