A stochastic delay framework for East Coast fever dynamics with integrated vaccination, treatment, and acaricide...

East Coast fever (ECF) is a severe tick-borne disease of cattle in Africa caused by Theileria parva and transmitted primarily by the brown ear tick, Rhipicephalus appendiculatus. This study develops a stochastic delay differential equation model for ECF transmission between cattle and ticks by incorporating vaccination, treatment, natural recovery, carrier-mediated transmission, and acaricide-induced tick removal. Two biologically distinct delays are included: a cattle-side delay representing the incubation or prepatent period and a tick-side delay representing parasite development within the vector. Compartment-specific multiplicative Brownian perturbations are introduced to represent environmental and epidemiological uncertainty. The existence of a unique global nonnegative solution is established, finite-time explosion is excluded, and the total cattle and tick populations are shown to be bounded in expectation. The disease-free and endemic equilibria of the associated deterministic drift system are derived. A deterministic basic reproduction number and a local diffusion-adjusted stochastic threshold are obtained by accounting for the Itô corrections in the infected cattle, carrier cattle, and infectious tick compartments. The stochastic threshold characterizes local invasion potential near the disease-free reference state, while explicit Lyapunov-Krasovskii inequalities provide sufficient conditions for local mean-square extinction. A threshold value above unity is interpreted as indicating possible invasion and persistence rather than as an unconditional global persistence result. Numerical approximations are constructed using the Euler-Maruyama, drift-RK4-Euler, and positivity-preserving stochastic nonstandard finite difference schemes. The stochastic methods are compared using identical Brownian sample paths, parameter values, initial histories, delays, and time steps. The stochastic NSFD method preserves nonnegativity almost surely and maintains bounded total populations in expectation. Numerical experiments illustrate the effects of biological delays, stochastic intensity, vaccine effectiveness, treatment, and acaricide application on disease dynamics. The results suggest that integrated host-directed and vector-directed interventions can reduce the simulated infection burden under the selected parameter regimes. Selected field prevalence estimates are included only as descriptive epidemiological motivation and are not used for pooled statistical inference, parameter estimation, or model validation.