Stability of traveling wave solutions for a spatially discrete SIS epidemic model

Hsu, Cheng Hsiung; Lin, Ja-Hon

doi:10.1007/s00033-019-1107-1

Cited by 8 publications

(5 citation statements)

References 19 publications

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“…This conversion enables the utilization of mathematical techniques and algorithms specifically designed for solving boundary value problems. By formulating the problem in terms of both initial and final conditions, the transversality conditions provide a comprehensive depiction of the system dynamics [38]- [39].…”

Section: Optimal Control Strategiesmentioning

confidence: 99%

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Abougarair,

Elwefati

2023

IJRCS

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Developing effective strategies to contain the spread of infectious diseases, particularly in the case of rapidly evolving outbreaks like COVID-19, remains a pressing challenge. The Susceptible-Infected-Recovery (SIR) model, a fundamental tool in epidemiology, offers insights into disease dynamics. The SIR system exhibits complex nonlinear relationships between the input variables (e.g., population, infection rate, recovery rate) and the output variables (e.g., the number of infected individuals over time). We employ Recurrent Neural Networks (RNNs) to model the SIR system due to their ability to capture sequential dependencies and handle time-series data effectively. RNNs, with their ability to model nonlinear functions, can capture these intricate relationships, enabling accurate predictions and understanding of the dynamics of the system. Additionally, we apply the Pontryagin Minimum Principle (PMP) based different control strategies to formulate an optimal control approach aimed at maximizing the recovery rate while minimizing the number of affected individuals and achieving a balance between minimizing costs and satisfying constraints. This can include optimizing vaccination strategies, quarantine measures, treatment allocation, and resource allocation. The findings of this research indicate that the proposed modeling and control approach shows potential for a comprehensive analysis of viral spread, providing valuable insights and strategies for disease management on a global level. By integrating epidemiological modeling with intelligent control techniques, we contribute to the ongoing efforts aimed at combating infectious diseases on a larger scale.

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Section: Optimal Control Strategiesmentioning

confidence: 99%

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Abougarair,

Elwefati

2023

IJRCS

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“…• The relation between the used model and genetic models is given in detail in [19,49] • Representation of the obtained solutions We obtained some novel analytical solutions of the nonlinear FKPP equation and the physical meaning of them is given in the following form: 1 Equations (8), ( 9), ( 12), ( 13), ( 20), ( 22), ( 23), ( 26), (27) are trigonometric solutions. 2 Equations (10), ( 14), ( 24), ( 29), (30) are compacton hyperbolic solutions. 3 Equations ( 11), ( 15), ( 16), ( 16), ( 17), ( 25), (28) are Peakon hyperbolic solutions.…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…It is considered as the first life forms on the Earth and usually lives in the radioactive waste, the deep portions of Earth's crust, soil, water, radioactive waste, and acidic hot springs. Just 27% of bacteria cell can be grown in the laboratory where there are 5 10 30 [ ]bacteria on Earth, so you can imagine the number of bacteria that can be grown in the laboratory. The bacteriology is the scientific name of studying the bacteria and its role in human life [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…Khater method, the modified Khater method (modified auxiliary equation method) and so on [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. The rest of this research paper is ordered in the following order: section 2 applies the modified Khater method [36][37][38][39][40][41][42], and Bspline schemes [43][44][45][46][47] to the nonlinear FKPP equation.…”

Section: Introductionmentioning

confidence: 99%

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Computational and numerical simulations for the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation

Khater

Attia

2020

Phys. Scr.

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This research paper elucidates solitary, compacton, and peakon computational solutions, and numerical solutions of the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation that belongs to the class of reaction–diffusion equation. This equation describes the behavior of genetic models in the increase of microorganisms. Usually, it is used as a biological model to investigate the microbiological densities in bacteria cells as a result of diffusion mechanisms in terms of space-time. The present framework depends on applying the modified Khater method to the FKPP equation to extract the computational solutions then using these solutions to get necessary boundary conditions to implement the numerical B–spline schemes on the suggested equation. The reliability and accuracy of the computational method and solutions are verified by using numerical simulations. For more explanation of the obtained analytical solutions, some sketches are plotted in different types. Also, the comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error.

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“…deduced the threshold of the classical SIS model and verified it experimentally. Hsu and Lin [20] examined the stability of the spatially discrete SIS epidemic model. Wang et al [21] proposed an improved SEIR model and proved its stability.…”

Section: Related Workmentioning

confidence: 99%

SETQR Propagation Model for Social Networks

Zhang

Chen

2019

IEEE Access

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The study of the laws and influencing factors of information dissemination in social networks is critical to analyzing the spread of public opinion, preventing the spread of rumors, and guiding information transmission. This paper addresses the shortcomings of the traditional SEIR model. We establish the SETQR model and use the probability theorem to derive the law of information propagation. Furthermore, the equilibrium point and the basic regeneration number of the SETQR model are obtained using differential dynamics and the regenerative matrix method. The stability of the SETQR model at the equilibrium point is derived theoretically. Finally, experimental verification is conducted. The simulation results indicate that the SETQR model achieves local stability at the equilibrium point, which is consistent with the results of the theoretical analysis. Through further simulation, the effects of time lag, containment, and forgetting mechanisms on the speed of information dissemination and the time required for the network to reach equilibrium are analyzed.INDEX TERMS Basic reproductive number, complex network, infectious disease model, information dissemination, stability.

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Stability of traveling wave solutions for a spatially discrete SIS epidemic model

Cited by 8 publications

References 19 publications

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Identification and Control of Epidemic Disease Based Neural Networks and Optimization Technique

Computational and numerical simulations for the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation

SETQR Propagation Model for Social Networks

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