Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period - Mei Li; Jing Zhang (Axioms, 2025)
This paper investigates a stochastic semi-parametric SEIR model characterized by infectivity during the incubation period and influenced by white noise perturbations. First, based on the theory of stochastic persistence, we derive the conditions required for the disease to persist within the model. Under these conditions, we apply Khasminskii’s ergodic theorem and Lyapunov functions to establish that the model possesses a unique ergodic stationary distribution. Finally, we utilize Khasminskii’s periodic theorem to examine the corresponding stochastic periodic SEIR model derived from the stochastic semi-parametric SEIR model, identifying sufficient conditions for the existence of non-trivial periodic solutions. Our theoretical results are further validated through numerical simulations.