Ergodic stationary distribution of a stochastic hepatitis B epidemic model with interval-valued parameters and compensated Poisson process (Q2299978)

Summary: Hepatitis B epidemic was and is still a rich subject that sparks the interest of epidemiological researchers. The dynamics of this epidemic is often modeled by a system with constant parameters. In reality, the parameters associated with the hepatitis B model are not certain, but the interval in which it belongs to can readily be determined. Our paper focuses on an imprecise hepatitis B model perturbed by Lévy noise due to unexpected environmental disturbances. This model has a global positive solution. Under an appropriate assumption, we prove the existence of a unique ergodic stationary distribution by using the mutually exclusive possibilities lemma demonstrated by \textit{L. Stettner} [On the existence and uniqueness of invariant measure for continuous-time Markov processes. Techn. Rep., Brown University (1986)]. Our main effort is to establish an almost perfect condition for the existence of the stationary distribution. Numerical simulations are introduced to illustrate the analytical results.