Quasilinearized Genocchi-polynomial collocation for efficient simulation of a nonlinear SIRV anthrax transmission model

Mathematical models of anthrax transmission often involve strong nonlinearities that challenge standard solvers and can limit robust inference. We present a four-compartment (SIRV) animal anthrax model and an efficient numerical framework that combines quasilinearization with a shifted Genocchi-polynomial collocation scheme (Genocchi–QLM). We provide convergence and error analyses for the approximations on a finite interval and construct a residual-error diagnostic to certify solution quality. Across representative parameter sets, Genocchi–QLM achieves rapid convergence and close agreement with a benchmark Runge–Kutta implementation (ode45), while maintaining numerical stability over long horizons. We further assess practical relevance by comparing simulated infected-case trajectories to reported outbreak patterns from endemic settings, observing qualitative agreement in rise-and-decay phases consistent with recovery, mortality, vaccination, and waning-immunity mechanisms. Sensitivity exploration highlights how vaccination rate and immunity waning jointly shape persistence. Because the method converts a nonlinear initial-value problem into a sequence of linear systems with sparse structure, it is readily extensible to higher-dimensional or controlled models and can be adapted to fractional or stochastic variants. These results indicate that Genocchi–QLM is a fast, accurate, and scalable tool for solving nonlinear epidemiological systems and for supporting data-informed analysis of anthrax control strategies.