Dynamics for a stochastic delayed SIRS epidemic model

Shi, Xiangyun; Cao, Yimeng; Zhou, Xueyong

doi:10.15388/namc.2020.25.17804

Cited by 6 publications

(5 citation statements)

References 23 publications

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“…Impulsive diferential equation is a basic tool to study process state transition and has important applications in life science. Compared to diferential equations without pulses, impulsive diferential equations can more truly and accurately refect the motion laws of nature and scientifc felds, so they are widely used in the research of population dynamic systems, infectious disease dynamic models, microbial models, medical chemotherapy, and neural network systems [1][2][3][4][5][6][7]. In the history of human development, infectious disease is a major pain point afecting human health and life span.…”

Section: Introductionmentioning

confidence: 99%

Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems

Li,

Guo,

Wang

2024

Journal of Mathematics

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Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.

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Section: Introductionmentioning

confidence: 99%

Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems

Li,

Guo,

Wang

2024

Journal of Mathematics

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“…This has led to the introduction of perturbation into deterministic models. Thus, numerous researchers have explored stochastic infectious disease models [17][18][19]. For instance, the authors of [17] examined a stochastic delayed SIRS epidemic model with seasonal variation, defining the system's stochastic threshold and observing that the periodic solution's oscillation intensity is dependent on the noise intensity.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, numerous researchers have explored stochastic infectious disease models [17][18][19]. For instance, the authors of [17] examined a stochastic delayed SIRS epidemic model with seasonal variation, defining the system's stochastic threshold and observing that the periodic solution's oscillation intensity is dependent on the noise intensity. In [18], a stochastic cholera model with a saturated recovery rate was discussed, showing that high levels of noise could result in disease extinction.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of a Stochastic Delayed SEIRS Epidemic Model with Lévy Jumps and the Impact of Public Health Education

Zhou

Shi

Zhou

2023

Axioms

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This study presents a class of the stochastic time-delayed susceptible–educated–infective–recovered–susceptible (SEIRS) epidemic model incorporating both public health education and Lévy jumps. We prove that the system has a unique global positive solution. We also provide derived conditions sufficient for both extinction and persistence in the mean. The verification of the findings and conclusions is performed through parameter sensitivity analysis and numerical simulations. This study concludes that public health education, stochastic noises, vaccination, increased disease recovery levels, and reduced patient contact significantly contribute significantly to disease prevention and control.

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“…In reality, infectious diseases are always influenced by environmental noise, which makes the related parameters (such as contact rate, mortality rate, and recovery rate) show random fluctuations. us, it is more realistic to research the dynamic behaviors of stochastic epidemic model (see [17][18][19][20][21][22][23]). At present, a lot of academics have studied stochastic epidemic models with media coverage and obtained some results (see [14,16,24]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis for a Stochastic SIRI Model Incorporating Media Coverage

Wang

Liu

2022

Mathematical Problems in Engineering

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We investigate a stochastic SIRI model incorporating media coverage. Firstly, existence and uniqueness of global positive solution of the model are established. By using the Hasminskii theory, we study stationary distribution of the model. Then, we prove extinction of the disease. Moreover, the asymptotic properties of solutions are studied by using Lyapunov method. Finally, numerical simulations are presented. In addition, it shows that media coverage can strain the spread of infectious diseases.

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Dynamics for a stochastic delayed SIRS epidemic model

Cited by 6 publications

References 23 publications

Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems

Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems

Dynamic Analysis of a Stochastic Delayed SEIRS Epidemic Model with Lévy Jumps and the Impact of Public Health Education

Dynamics Analysis for a Stochastic SIRI Model Incorporating Media Coverage

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