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Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function

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  • Zhou, Baoquan
  • Shi, Ningzhong

Abstract

This paper examines a stochastic SEIS epidemic model motivated by Black–Karasinski process. First, it is shown that Black–Karasinski process is a both biologically and mathematically reasonable assumption compared with existing stochastic modeling methods. By analyzing the diffusion structure of the model and solving the relevant Kolmogorov–Fokker–Planck equation, a complete characterization for explicitly approximating the stationary density function near some quasi-positive equilibria is provided. Then for the deterministic model, the basic reproduction number and related asymptotic stability are studied. Finally, several numerical examples are given to substantiate our theoretical findings.

Suggested Citation

  • Zhou, Baoquan & Shi, Ningzhong, 2024. "Analysis of a stochastic SEIS epidemic model motivated by Black–Karasinski process: Probability density function," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012657
    DOI: 10.1016/j.chaos.2024.115713
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