A novel fractional order model of SARS-CoV-2 and Cholera disease with real data

Özköse, Fatma; Habbireeh, Rafla; Şenel, M. Tamer

doi:10.1016/j.cam.2022.114969

“…Significant advancements have been achieved across various domains including oscillation, control systems, diffusion and transport theory, biological organization, organic chemical industry, and medicine [13][14][15][16][17][18][19][20]. The use of fractional derivative models addresses a critical limitation where classical integer differential model theories fail to align well with experimental results; instead yielding relatively better outcomes with fewer parameters.…”

Section: 、Introductionmentioning

confidence: 99%

Main sub-harmonic joint resonance of fractional quintic van der Pol-Duffing oscillator

Ren,

Chen,

Wang

et al. 2024

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0

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The main sub-harmonic joint resonance of the van der Pol-Duffing system with a quintic oscillator under dual-frequency excitation is investigated in this paper. The study examines the conditions for chaos and vibration resonance under different parameters. An approximate analytical solution for the principal sub-harmonic joint resonance of the system under dual-frequency excitation is obtained using the multi-scale method, while the Melnikov method provides necessary conditions for chaos in the system. Furthermore, based on the fast and slow variable separation method, vibration resonance of the system under various conditions is determined. Numerical simulations explore amplitude-frequency characteristics of total response at different excitation frequencies through analytical and simulation methods, with consistency between numerical and analytical results verified by plotting amplitude-frequency characteristic curves. Additionally, an analysis is conducted to investigate how fractional order, fractional differential coefficient, and cubic stiffness affect co-amplitude-frequency curves of the van der Pol-Duffing oscillator. The analysis reveals that a jump phenomenon exists in co-amplitude-harmonic resonance of this oscillator; moreover, changes in different parameters can alter both jump points and cause disappearance of such phenomena. Sub-critical fork bifurcation behavior as well as supercritical fork bifurcation behavior are studied along with vibration resonance caused by parameter variations. Results indicate that sub-critical fork bifurcation arises from changes in excitation term coefficient while supercritical fork bifurcation occurs due to fractional order variations. Furthermore, when different fractional order values are considered, there will be changes in resonance location, response amplitude gain, and vibration resonance mode within the system. The implementation of this measure enhances our comprehension of the vibration characteristics of the system, thereby refining the accuracy of the model and bolstering the stability of the system. Additionally, it serves as a preventive measure against resonance issues, which are particularly critical for mitigating the hazards associated with system resonance triggered by supercritical fork bifurcations. These hazards encompass potential structural damage and equipment failure.

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“…Hezam [26] proposed and analyzed an optimal control model for COVID-19 and cholera using the integer order derivative. Also, the authors [40] have studied and analyzed a model for SARS-CoV-2 and cholera using real data from Congo.…”

Section: Introductionmentioning

confidence: 99%

Analysis of a non-integer order compartmental model for cholera and COVID-19 incorporating human and environmental transmissions

Usman,

Abbas,

Omame

2023

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Fractional differential operators have increasingly gained wider applications in epidemiological modelling due to their ability to capture memory effect in their definitions; an attribute which lacks in the concept of classical integer derivatives. In this paper, employing the Caputo fractional operator with singular kernel, the co-dynamical model for cholera and COVID-19 diseases is proposed and analyzed, incorporating both direct and indirect transmission routes for cholera. The necessary conditions for existence of the unique solution of the proposed model are studied. Using the results from fixed point theory, Ulam-Hyers stability analysis of the system is performed. The model is fitted to real data from Pakistan and the optimized order of the fractional derivative for which the system fits well to data is obtained. Other numerical assessments of the model are also executed. Phase portraits of the infected classes with different initial conditions and various order of the fractional derivative are obtained in the cases when the reproduction number  0 < 1 and  0 > 1 . It is observed that the trajectories for the infected compartments tend towards the infection-free steady state when  0 < 1 and the endemic steady state when  0 > 1 irrespective of the initial conditions and the order of the fractional derivative. Increment in the COVID-19 vaccine efficacy, keeping the vaccination rate fixed at δ 1 ω = 0.8 , resulted in a decline in the COVID-19 disease. Also, increasing the COVID-19 vaccination rate, keeping the vaccine efficacy for COVID-19 fixed at ϕ c ω = 0.85 , led to a decline in the COVID-19 associated reproduction number. The simulations also pointed out the impact of COVID-19 and cholera vaccinations, direct and indirect transmissions of cholera.

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“…Özköse et al [20] presented a novel approach to utilizing a fractional-order model, investigating the Congo's COVID-19 and cholera outbreaks. Naik et al [21] investigate the critical normal form coefficients for the one-parameter and two-parameter bifurcations of a discrete-time Bazykin-Berezovskaya prey-predator model.…”

Section: Introductionmentioning

confidence: 99%

Long-Term Side Effects: A Mathematical Modeling of COVID-19 and Stroke with Real Data

Özköse

2023

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The post-effects of COVID-19 have begun to emerge in the long term in society. Stroke has become one of the most common side effects in the post-COVID community. In this study, to examine the relationship between COVID-19 and stroke, a fractional-order mathematical model has been constructed by considering the fear effect of being infected. The model’s positivity and boundedness have been proved, and stability has been examined for disease-free and co-existing equilibrium points to demonstrate the biological meaningfulness of the model. Subsequently, the basic reproduction number (the virus transmission potential (R0)) has been calculated. Next, the sensitivity analysis of the parameters according to R0 has been considered. Moreover, the values of the model parameters have been calculated using the parameter estimation method with real data originating from the United Kingdom. Furthermore, to underscore the benefits of fractional-order differential equations (FODEs), analyses demonstrating their relevance in memory trace and hereditary characteristics have been provided. Finally, numerical simulations have been highlighted to validate our theoretical findings and explore the system’s dynamic behavior. From the findings, we have seen that if the screening rate in the population is increased, more cases can be detected, and stroke development can be prevented. We also have concluded that if the fear in the population is removed, the infection will spread further, and the number of people suffering from a stroke may increase.

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A novel fractional order model of SARS-CoV-2 and Cholera disease with real data

Cited by 13 publications

References 34 publications

Main sub-harmonic joint resonance of fractional quintic van der Pol-Duffing oscillator

Main sub-harmonic joint resonance of fractional quintic van der Pol-Duffing oscillator

Analysis of a non-integer order compartmental model for cholera and COVID-19 incorporating human and environmental transmissions

Long-Term Side Effects: A Mathematical Modeling of COVID-19 and Stroke with Real Data

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