Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination

Li, Fēi; Meng, Xinzhu; Wang, Xinzeng

doi:10.1155/2018/7873902

Cited by 38 publications

(27 citation statements)

References 53 publications

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“…Then direct computation leads to R 2 (t) T = 0.2573 > 0. From Theorem 3.2, we can see that system (2) has at least one positive T-periodic solution (see Fig. 2).…”

Section: Conclusion and Numerical Simulationsmentioning

confidence: 90%

“…Then the dynamic behaviors of the two models are studied. Firstly, for system (2), there are the following properties:…”

Section: Conclusion and Numerical Simulationsmentioning

confidence: 99%

“…In the natural world, various systems are inevitably affected by the random factors [1][2][3]. Stochastic differential equations are important tools for studying random phenomena (see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…where A(t), d(t), β(t), δ(t), γ (t), α(t) and σ i (t) stand for the continuous positive periodic functions of period T, i = 1, 2, 3. In this paper, we intend to prove the existence of nontrivial positive T-periodic solutions under sufficient conditions of system (2).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

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In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtained firstly. Then we show that the stochastic system has at least one nontrivial positive T-periodic solution under some conditions. For the model that are both disturbed by the white noise and telephone noise, we construct a suitable Lyapunov functions to verify the existence of a unique ergodic stationary distribution. Meanwhile, the sufficient condition for the extinction of the disease is also established. Finally, examples are introduced to illustrate the theoretical analysis. MSC: 60H10; 65C30; 91B70

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“…Then direct computation leads to R 2 (t) T = 0.2573 > 0. From Theorem 3.2, we can see that system (2) has at least one positive T-periodic solution (see Fig. 2).…”

Section: Conclusion and Numerical Simulationsmentioning

confidence: 90%

“…Then the dynamic behaviors of the two models are studied. Firstly, for system (2), there are the following properties:…”

Section: Conclusion and Numerical Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics analysis of stochastic epidemic models with standard incidence

et al. 2019

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“…Many population models with random interference have been investigated [55][56][57][58][59][60]. Recently, Zhao et al [61] and Xu et al [62] considered the break-even concentration in a single-species stochastic chemostat model.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Chi

Zhao

2018

Adv Differ Equ

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In this paper, we propose a multi-nutrient and single microorganism chemostat model with stochastic effect and impulsive toxicant input. Firstly, for the system neglecting stochastic effect, we investigate the global dynamics including the existence and global asymptotic stability of 'microorganism-extinction' periodic solution, as well as the permanence of the system. Then, for the stochastic differential system with impulsive effect, we discuss the persistence and extinction of microorganisms with stochastic effect in a polluted environment. Our results indicate that the stochastic disturbance can lead to microbial extinction. Moreover, the concentration of toxicant will also affect the survival of microorganisms. Finally, numerical simulations are carried out to illustrate our theoretical results. MSC: 60H10; 65C30; 91B70

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Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

Macías‐Díaz

Ahmed

Jawaz

et al. 2020

Math Methods in App Sciences

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In this work, we propose a time‐delayed reaction–diffusion model to describe the propagation of infectious viral diseases like COVID‐19. The model is a two‐dimensional system of partial differential equations that describes the interactions between disjoint groups of a human population. More precisely, we assume that the population is conformed by individuals who are susceptible to the virus, subjects who have been exposed to the virus, members who are infected and show symptoms, asymptomatic infected individuals, and recovered subjects. Various realistic assumptions are imposed upon the model, including the consideration of a time‐delay parameter which takes into account the effects of social distancing and lockdown. We obtain the equilibrium points of the model and analyze them for stability. Moreover, we examine the bifurcation of the system in terms of one of the parameters of the model. To simulate numerically this mathematical model, we propose a time‐splitting nonlocal finite‐difference scheme. The properties of the model are thoroughly established, including its capability to preserve the positivity of solutions, its consistency, and its stability. Some numerical experiments are provided for illustration purposes.

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Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination

Cited by 38 publications

References 53 publications

Dynamics analysis of stochastic epidemic models with standard incidence

Dynamics analysis of stochastic epidemic models with standard incidence

Dynamical analysis of multi-nutrient and single microorganism chemostat model in a polluted environment

Design and analysis of a discrete method for a time‐delayed reaction–diffusion epidemic model

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