Zoonotic Spillover and Multirooted Transmission: A Stochastic Modeling for Nipah Virus Persistence with Nonlinear Incidence and Vaccination Feedback

Nipah virus (NiV) spreads from bat-to-human spillover and limited human-to-human

transmission, till this moment surveillance in endemic is quite weak and the virus can persist despite high

mortality. We study a stochastic compartmental system that couples the human host (susceptible,

exposed, infectious, removed and vaccinated) with bat reservoir (susceptible, infected), with the help of

a saturating non-linear incidence to capture compact contact efficiency at high prevalence. The

deterministic equations are lifted to stochastic differential equations driven by independent Wiener

processes and we prove unique global positive solution with the help of Ito calculus and stopping-time

arguments.

Lyapunov-based analysis yields threshold conditions separating almost-sure extinction from persistence

and we establish an ergodic stationary distribution under an explicit bound on basic reproduction number

and diffusion matrix spectrum. Numerical addition with Milstein scheme, calibrated with serological and

outbreak data from South and Southeast Asia, reproduces the analytical thresholds. Sensitivity analysis

shows noise intensity and vaccination timing can shift outcomes from persistence elimination even when

deterministic reproduction number exceeds one, highlighting need for timely interventions in

resource-limited settings.