The use of mathematical models to simulate control options for echinococcosis.

In many parts of the world Echinococcus granulosus is a widespread infection in sheep and dogs with a consequential spill over into the human population. In the past, mathematical models have been derived to define the transmission dynamics of this parasite, principally in the sheep-dog life cycle. These models have characterized the cycles of infection as lacking in density dependent constraints in both the definitive or intermediate hosts. This suggested that there was little, if any, induced host immunity by the parasite in either host in natural infections. However, recent evidence from both Tunisia and Kazakhstan, where young dogs are the most heavily parasitised, suggests the possibility of significant definitive host immunity. This may have an effect on the control effort needed to destabilize the parasite. A preliminary computer simulation model (based on an Excel spreadsheet) to attempt to predict the results of a control programme has been written. This demonstrates that there could be significantly different results if there is indeed protective immunity in the dog than in the absence of immunity. In the former the parasite needs a greater control effort to push the parasite towards extinction than in the latter. The computer simulation is based on a mathematical model of the parasite's life cycle and is flexible so that different values of parameters can be used in different situations where the transmission of the parasite may be at different levels. Because of the flexibility of the computer simulation it is anticipated that this programme can be applied in most situations, although initial parameters for a particular location or strain of the parasite will have to be first predetermined with base line field surveys and possibly experimental infections. The programme also has an additional flexibility to enable simulations if some parameters cannot be accurately estimated through Monte-Carlo techniques. In the latter situation, worst and best case scenarios can be estimated and likely frequency distributions of the unknown parameters can be included in the model.