Alveolar echinococcosis (AE) is a zoonotic parasitic diseases caused by a cestode parasite known as Echinococcus multilocularis. The parasite has a wildlife cycle with definitive hosts (foxes) and small mammals as intermediate hosts (rodents) while humans are the accidental hosts. Parasite infection pressure relation to time of the year and age dependent infection pressure for parasite abundance also depend on the urbanization. The aim of current work is forecasting the thresholds via the computational analysis of the disease spread which is a useful approach since it can help to design the experimental settings with better planning and efficiency. Network analysis when interlinked with the computational techniques provides better insight into the spatial and temporal heterogeneities. In the present study, a mathematical framework that describes the transmission dynamics and control measures of E. multilocularis in foxes is documented. We used treatment of foxes with baits for the prevention of the E. multilocularis infection. A novel approach of networking, called Petri net (PN), based on density dependent differential equations, is utilized during this research. The accurate description of the transmission of the parasite and the effect of drug on it is provided to the readers in this article. The transitions, which are difficult to analyse theoretically, are presented with the aid of the discrete approach of networking. A discrete mathematical framework can prove to be an accurate and robust tool to analyse and control the parasite dynamics.