Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate
The article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain a significant criterion R0S which relies on environmental noises. By means of Lyapunov function approach, we show that there is a...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2022/5574983 |
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| _version_ | 1832560858679476224 |
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| author | Chun Lu |
| author_facet | Chun Lu |
| author_sort | Chun Lu |
| collection | DOAJ |
| description | The article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain a significant criterion R0S which relies on environmental noises. By means of Lyapunov function approach, we show that there is a stationary distribution if R0S>1. Its condition implies that when white noise is small, in the stochastic model, there exists a stochastic positive equilibrium state without changing the basic properties of its corresponding deterministic model. Secondly, we derive sufficient criteria for extinction of the disease. Finally, we propose a definition of the solution to an impulsive stochastic functional differential equation with Markovian switching (ISFDM). |
| format | Article |
| id | doaj-art-39cf9dbfa1b540569cd213aefd1faaf3 |
| institution | Kabale University |
| issn | 2314-8888 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-39cf9dbfa1b540569cd213aefd1faaf32025-02-03T01:26:34ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5574983Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence RateChun Lu0Department of MathematicsThe article researches a stochastic hepatitis B epidemic model with saturated incidence rate, which is perturbed by both white noise and colored noise. Firstly, we obtain a significant criterion R0S which relies on environmental noises. By means of Lyapunov function approach, we show that there is a stationary distribution if R0S>1. Its condition implies that when white noise is small, in the stochastic model, there exists a stochastic positive equilibrium state without changing the basic properties of its corresponding deterministic model. Secondly, we derive sufficient criteria for extinction of the disease. Finally, we propose a definition of the solution to an impulsive stochastic functional differential equation with Markovian switching (ISFDM).http://dx.doi.org/10.1155/2022/5574983 |
| spellingShingle | Chun Lu Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate Journal of Function Spaces |
| title | Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate |
| title_full | Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate |
| title_fullStr | Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate |
| title_full_unstemmed | Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate |
| title_short | Dynamical Behavior of Stochastic Markov Switching Hepatitis B Epidemic Model with Saturated Incidence Rate |
| title_sort | dynamical behavior of stochastic markov switching hepatitis b epidemic model with saturated incidence rate |
| url | http://dx.doi.org/10.1155/2022/5574983 |
| work_keys_str_mv | AT chunlu dynamicalbehaviorofstochasticmarkovswitchinghepatitisbepidemicmodelwithsaturatedincidencerate |