A non-integer order model for Zika and Dengue co-dynamics with cross-enhancement

Iheonu, N.O.; Nwajeri, U.K.; Omame, A.

doi:10.1016/j.health.2023.100276

Cited by 3 publications

(5 citation statements)

References 49 publications

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“…24,28,32), protecting themselves from pathogens through personal awareness and non-pharmaceutical interventions, namely, quarantine and isolation policy (Figs. 23,27,31). Opposite scenarios when natural immunity wanes at a certain rate.…”

Section: Resultsmentioning

confidence: 99%

“…As a result, according to the considered fractional order model, one gets, Therefore, according to Ref. 31 , it is evident that the solution of the proposed fractional-order model ( 4) is positive.…”

Section: Proofmentioning

confidence: 87%

“…Under the presumption that H(t) is a function on the interval b[0, T] , we can get the integral that corresponds to it in the ABC sense by using the following formula: Definition 4 31 Laplace transformation of the Atangana-Baleanu fractional derivative of fractional-order α > 0 in the sense of Caputo is as follows, where the lower limit is equal to zero:…”

Section: Definitionmentioning

confidence: 99%

“…QT α max , is a contraction, and according to Banach's contraction principle, it has a unique fixed point 31 . This fact completes the proof of the theorem mentioned above.…”

Section: Theoremmentioning

confidence: 99%

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An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

Akter,

Nurunnahar,

Ullah

et al. 2024

Sci Rep

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This study uses imposed control techniques and vaccination game theory to study disease dynamics with transitory or diminishing immunity. Our model uses the ABC fractional-order derivative mechanism to show the effect of non-pharmaceutical interventions such as personal protection or awareness, quarantine, and isolation to simulate the essential control strategies against an infectious disease spread in an infinite and uniformly distributed population. A comprehensive evolutionary game theory study quantified the significant influence of people’s vaccination choices, with government forces participating in vaccination programs to improve obligatory control measures to reduce epidemic spread. This model uses the intervention options described above as a control strategy to reduce disease prevalence in human societies. Again, our simulated results show that a combined control strategy works exquisitely when the disease spreads even faster. A sluggish dissemination rate slows an epidemic outbreak, but modest control techniques can reestablish a disease-free equilibrium. Preventive vaccination regulates the border between the three phases, while personal protection, quarantine, and isolation methods reduce disease transmission in existing places. Thus, successfully combining these three intervention measures reduces epidemic or pandemic size, as represented by line graphs and 3D surface diagrams. For the first time, we use a fractional-order derivate to display the phase-portrayed trajectory graph to show the model’s dynamics if immunity wanes at a specific pace, considering various vaccination cost and effectiveness settings.

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Section: Resultsmentioning

confidence: 99%

Section: Proofmentioning

confidence: 87%

Section: Definitionmentioning

confidence: 99%

“…QT α max , is a contraction, and according to Banach's contraction principle, it has a unique fixed point 31 . This fact completes the proof of the theorem mentioned above.…”

Section: Theoremmentioning

confidence: 99%

See 2 more Smart Citations

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

Akter,

Nurunnahar,

Ullah

et al. 2024

Sci Rep

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“…Mathematical and statistical models have been developed to study the transmission dynamics of anthrax disease and have used several methodological approaches to understand its spread in several countries [8]. Some of these methodological approaches have also been used to study the transmission of Mpox disease by the authors in [9], Zika and Dengue viruses in [10], and most recently, the highly contagious COVID-19 epidemic that was experienced globally in [11]. We will attempt to review some of the articles in this research direction and will state some of the gaps in the literature and our contribution to the modeling of anthrax disease dynamics.…”

Section: Introductionmentioning

confidence: 99%

A Risk-Structured Model for the Transmission Dynamics of Anthrax Disease

Akande,

Akinyemi,

Iheonu

et al. 2024

Mathematics

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Anthrax, a zoonotic disease with serious public health consequences, has been the subject of rigorous mathematical and statistical modeling to better understand its dynamics and to devise effective control techniques. In this study, we propose a novel mathematical risk-structured model for anthrax disease spread that includes both qualitative and quantitative evaluations. Our research focuses on the complex interplay between host–anthrax interactions and zoonotic transmission. Our mathematical approach incorporates bifurcation analysis and stability considerations. We investigate the dynamic behavior of the proposed model under various settings, shedding light on the important parameters that determine anthrax transmission and persistence. The normalized forward sensitivity analysis method is used to determine the parameters that are relevant to reducing Rc and, by extension, disease spread. Through scenario simulation of our model, we identify intervention techniques, such as enlightenment of the populace, that will effectively minimize disease transmission. Our findings provide insights into anthrax epidemiology and emphasize the importance of effective disease management. Bifurcation investigations reveal the existence and stability of numerous equilibria, allowing for a better understanding of the behavior of the system under various scenarios. This study adds to the field of anthrax modeling by providing a foundation for informed decision-making regarding public health measures. The use of a mathematical modeling approach improves our ability to anticipate and control anthrax epidemics, ultimately helping to protect both human and animal populations.

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A mathematical analysis of the corruption dynamics model with optimal control strategy

Gutema,

Wedajo,

Koya

2024

Front. Appl. Math. Stat.

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Corruption is a global problem that affects many countries by destroying economic, social, and political development. Therefore, we have formulated and analyzed a mathematical model to understand better control measures that reduce corruption transmission with optimal control strategies. To verify the validity of this model, we examined a model analysis showing that the solution of the model is positive and bounded. The basic reproduction number R0 was computed by using the next-generation matrix. The formulated model was studied analytically and numerically in the context of corruption dynamics. The stability analysis of the formulated model showed that the corruption-free equilibrium is locally and globally asymptotically stable for R0 < 1, but the corruption-endemic equilibrium is globally asymptotically stable for R0 > 1. Furthermore, the optimal control strategy was expressed through the Pontryagin Maximum Principle by incorporating two control variables. Finally, numerical simulations for the optimal control model were performed using the Runge-Kutta fourth order forward and backward methods. This study showed that applying both mass education and law enforcement is the most efficient strategy to reduce the spread of corruption.

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A non-integer order model for Zika and Dengue co-dynamics with cross-enhancement

Cited by 3 publications

References 49 publications

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

An innovative fractional-order evolutionary game theoretical study of personal protection, quarantine, and isolation policies for combating epidemic diseases

A Risk-Structured Model for the Transmission Dynamics of Anthrax Disease

A mathematical analysis of the corruption dynamics model with optimal control strategy

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