In this study, we examined a continuous-time Markov chain (CTMC) model, conducted a five-type branching process, and studied the influence of seasonal forcing to analyze the different facets of the transmission of Cystic Echinoccocosis among definitive, intermediate, and accidental hosts. First, we studied the deterministic model related to the disease, derived the basic reproduction number, and analyzed the stability of the equilibria to understand the long-term behavior of the infected classes. We then aligned with the CTMC formulation that captured the stochastic amplification of infected definitive hosts, accompanied by a lower burden of infected carcasses than the corresponding deterministic model. The branching process analysis near the disease-free equilibrium quantifies outbreak and extinction probabilities and shows that early epidemic outcomes are primarily driven by the initial numbers of infected definitive hosts and environmental egg burden rather than accidental host infection. Sensitivity analysis identified the death rate of intermediate hosts and environmental parameters as the most critical factors for CE transmission. Moreover, the results of incorporating seasonal forcing highlighted the importance of temporally adaptive control strategies in this context due to the influence of meteorological conditions on parasite egg viability and host behavioral patterns. Overall, the results of our multimodal approach provide rigorous guidance for robust modeling and effective control.