A Stochastic Model of East Coast Fever Incorporating a Wildlife–Livestock Interface

East Coast Fever (ECF) causes approximately one million livestock deaths annually in sub-Saharan Africa, posing a significant threat to livestock. The wildlife–livestock interface complicates disease management, as wildlife serve as reservoirs. This study developed a Continuous Time Markov Chain (CTMC) model incorporating the wildlife–livestock interface to analyze ECF dynamics. Using the Galton–Watson approximation, we assessed the probability of disease extinction following the introduction of infected hosts or vectors. The probability of disease extinction calculated from the branching process is shown to be in good agreement with the probability approximated from numerical simulations. The disease dynamics of the deterministic model and the CTMC model are compared to ascertain the effect of demographic stochasticity on ECF dynamics. Differences in model predictions and asymptotic dynamics between stochastic and deterministic models were evident. The deterministic and stochastic formulations should therefore be viewed as complementary modeling frameworks, with the deterministic model characterizing average epidemic dynamics and the CTMC model capturing the probabilistic variability and extinction behavior inherent in real transmission processes. These differences are crucial for intervention strategies earmarked to prevent outbreaks. Our analysis revealed a high probability of ECF extinction if the disease emerges from recovered carrier cattle. Finite time to ECF disease extinction is estimated using 10,000 sample paths, and it is shown that the epidemic duration is shortest if the disease is introduced by infectious cattle. The epidemic duration is longest when the disease is introduced by infectious ticks. Additionally, we observed that host interactions at the wildlife–livestock interface play a critical role in shaping ECF transmission and informing control strategies.