Dynamics of a stochastic periodic SIRS model with time delay

Shi, Xiangyun; Cao, Yimeng

doi:10.1142/s1793524520500722

Cited by 8 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, some interesting topics deserve further investigation. We can explore the effects of delay [ 36 ] or impulse [ 30 ] on periodic model ( 1.4 ), and may study model ( 1.6 ) driven by Lévy jumps [ 29 ]. We leave these issues for future consideration.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, temperature changes, humidity and media coverage inevitably affect the spread of epidemic. To better explain these phenomena, many researchers have included stochastic perturbations in the process of epidemic modelling and achieved numerous good results [26][27][28][29][30][31][32][33][34][35][36]. Keeping in mind such an idea, Shangguan and Liu et al [37] recently incorporated white noises into model (1.2) and assumed that stochastic perturbations on the individuals are proportional to S(t), E(t), I (t), and derived a new stochastic version as follows…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine

Shangguan

Liu

Wang

et al. 2021

J. Appl. Math. Comput.

View full text Add to dashboard Cite

Two types of stochastic epidemic models are formulated, in which both infectivity in the latent period and household quarantine on the susceptible are incorporated. With the help of Lyapunov functions and Has’minskii’s theory, we derive that, for the nonautonomous periodic version with white noises, it owns a positive periodic solution. For the other version with white and telephone noises, we construct stochastic Lyapunov function with regime switching to present easily verifiable sufficient criteria for the existence of ergodic stationary distribution. Also, we introduce a series of numerical simulations to support our analytical findings. At last, a brief discussion of our theoretical results shows that the stochastic perturbations and household quarantine measures can significantly affect both periodicity and stationary distribution.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine

Shangguan

Liu

Wang

et al. 2021

J. Appl. Math. Comput.

View full text Add to dashboard Cite

show abstract

“…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%

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

Zhou

Shi

Zhou

2023

Axioms

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Recent high-profile outbreaks, like those caused by Ebola, Zika, Pandemic influenza, Middle East Respiratory Syndrome (MERS), and COVID-19, have highlighted the global importance of infectious diseases and the need for coordinated efforts to prevent outbreaks. Fractional order models for influenza, dengue fever, malaria, and tuberculosis, for example [19]- [29]. The COVID-19 pandemic has already spread throughout the world and the people are aware of the disease and they are using precautions against the pandemic.…”

Section: Introductionmentioning

confidence: 99%

A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

Al‐Zahrani¹,

Elsmih²,

Al-Zahrani³

et al. 2022

MJMS

View full text Add to dashboard Cite

In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.

show abstract

Dynamics of a stochastic periodic SIRS model with time delay

Cited by 8 publications

References 20 publications

Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine

Periodicity and stationary distribution of two novel stochastic epidemic models with infectivity in the latent period and household quarantine

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

A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis

Contact Info

Product

Resources

About