Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period
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....
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MDPI AG
2025-07-01
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| Online Access: | https://www.mdpi.com/2075-1680/14/7/535 |
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| author | Mei Li Jing Zhang |
| author_facet | Mei Li Jing Zhang |
| author_sort | Mei Li |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c027feca89e541189cc8ae4a04e35c74 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c027feca89e541189cc8ae4a04e35c742025-08-20T03:58:30ZengMDPI AGAxioms2075-16802025-07-0114753510.3390/axioms14070535Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation PeriodMei Li0Jing Zhang1School of Mathematics and Statistics, Hainan Normal University, Haikou 571158, ChinaSchool of Mathematics and Statistics, Hainan Normal University, Haikou 571158, ChinaThis 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.https://www.mdpi.com/2075-1680/14/7/535stochastic SEIR modelsemi-parametricnonlinear incidence ratelyapunov analysisperiodicityergodic stationary distribution |
| spellingShingle | Mei Li Jing Zhang Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period Axioms stochastic SEIR model semi-parametric nonlinear incidence rate lyapunov analysis periodicity ergodic stationary distribution |
| title | Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period |
| title_full | Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period |
| title_fullStr | Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period |
| title_full_unstemmed | Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period |
| title_short | Dynamical Behaviors of a Stochastic Semi-Parametric SEIR Model with Infectivity in the Incubation Period |
| title_sort | dynamical behaviors of a stochastic semi parametric seir model with infectivity in the incubation period |
| topic | stochastic SEIR model semi-parametric nonlinear incidence rate lyapunov analysis periodicity ergodic stationary distribution |
| url | https://www.mdpi.com/2075-1680/14/7/535 |
| work_keys_str_mv | AT meili dynamicalbehaviorsofastochasticsemiparametricseirmodelwithinfectivityintheincubationperiod AT jingzhang dynamicalbehaviorsofastochasticsemiparametricseirmodelwithinfectivityintheincubationperiod |