Abstract
Echinococcus multilocularis, a major cause of echinococcosis in human, is a parasitic sylvatic disease between two major hosts in a predator-prey relation. A new model for the transmission dynamics of Echinococcus multilocularis in the population of red foxes and voles with environment as a source of infection is formulated and rigorously analyzed. The model is used to access the impact of treatment on red foxes and environmental disinfection as control strategies on the disease dynamics. The control reproduction number is computed and is used to rigorously prove the local and global dynamics of models' equilibria. Using available data on Echinococcus, elasticity indices and partial rank correlation coefficients of control reproduction number and cumulative new cases in red foxes and voles are computed. Parameters that have high influence locally and globally are identified. Numerical experiments indicate that administering disinfection of environment only induces more positive impact than applying treatment only on red foxes in controlling the infection. Generally, interventions towards treating red foxes and environmental disinfection could be sufficient in tackling transmission of disease in the populations.