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Ergodic stationary distribution of a stochastic hepatitis B epidemic model with interval-valued parameters and compensated Poisson process. (English) Zbl 1431.92138

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 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.

MSC:

92D30 Epidemiology
60G51 Processes with independent increments; Lévy processes
60H30 Applications of stochastic analysis (to PDEs, etc.)
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