A Stochastic Hantavirus Model with Environmental Reservoir

Hantaviruses circulate in an ecological web linking rodent population dynamics, contaminated environmental substrates and the accidental human host, causing two severe syndromes for which no licensed antiviral therapy exists [15,22]. We formulate and rigorously analyse a coupled SEIR-SEIV model joining a rodent reservoir with chronic lifelong shedding and no recovery, an environmental viral compartment V accumulating shed material, and a dead-end human SEIR population. For the deterministic system we establish well-posedness and derive, by the next-generation method [39], a basic reproduction number that decomposes additively, R 0 = R dir 0 + R 0 ind , separating the direct rodent-to-rodent route from the indirect environmental one. We prove that R 0 is the exact threshold, the disease-free and endemic equilibria being globally asymptotically stable for R 0 ≤ 1 and R 0 > 1 respectively, through Volterra-type Lyapunov functions. Under multiplicative Brownian noise on (S R , E R , I R , V ) the system remains globally positive. We show that the classical Itô-corrected threshold R s < R 0 , standard in this literature, is necessary but not sucient for extinction once more than one infected compartment is present its usual derivation counts the Itô correction twice and we exhibit an explicit counterexample. We replace it by a variational exponent Λ, computable by nested one-dimensional bisection, that bounds the top Lyapunov exponent of the infected block: Λ < 0 forces global almost-sure exponential extinction even when R 0 > 1. Under small noise the solution stays within an O( ∑ i σ i 2 ) mean-square deviation of the endemic equilibrium up to its exit time; the criterion is one-sided, since persistence is documented numerically but not proved. Forcing the environmental decay rate with the observed temperature cycle of Shaanxi Province (China) reproduces the documented winter peak of HFRS incidence. As the forced system is nonautonomous, we compute its periodic reproduction number by Floquet analysis and obtain R per 0 ≈ 2.15 against R 0 = 1.63. A complementary rainfall forcing with a one-year lag captures the interannual peaks (20052016), while the residual uctuations, explained by neither driver, provide an empirical rationale for the stochastic framework.