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Numerical analysis of linearly implicit Milstein method for stochastic SEIR models with nonlinear incidence rates

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  • Yang, Huizi
  • Yang, Zhanwen
  • Ming, Aoyun

Abstract

In this paper, we focus on the numerical analysis of stochastic SEIR models with nonlinear incidence rates. By reformulating the stochastic basic reproduction number R0S, it is shown that the disease extinction of deterministic models is preserved under stochastic noises. On the other hand, the total population of stochastic SEIR models is varying and even unbounded when there are some noises in the natural death rate. Therefore, as the fundamental approach, we have to present the boundedness in the 4th moment and Hölder continuity of the exact solutions for the numerical convergence analysis. Numerically, a linearly implicit Milstein method is employed to ensure the numerical positivity under the condition of h

Suggested Citation

  • Yang, Huizi & Yang, Zhanwen & Ming, Aoyun, 2026. "Numerical analysis of linearly implicit Milstein method for stochastic SEIR models with nonlinear incidence rates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 659-675.
    • Handle: RePEc:eee:matcom:v:241:y:2026:i:pa:p:659-675
    DOI: 10.1016/j.matcom.2025.09.015
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