On a new and generalized fractional model for a real cholera outbreak

Băleanu, Dumitru; Ghassabzade, Fahimeh Akhavan; Nieto, Juan J.; Jajarmi, Amin

doi:10.1016/j.aej.2022.02.054

Cited by 123 publications

(44 citation statements)

References 28 publications

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“…Proof. To show boundedness we apply technique applied in [15,20,21]. Hence, first we consider the fractional derivative of human population dynamics.…”

Section: Theoremmentioning

confidence: 99%

“…where, N � S + I + R. Similar to the works done in [15], the solution of the preceding inequality (7) is given by…”

Section: Theoremmentioning

confidence: 99%

“…Due to sudden outbreak of cholera infection and its huge impact on economic resources, optimal control strategies toward infection is highly recommended [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. On the other hand, fractional derivative is one of the highly applicable di erential calculus to describe both biological and physical phenomena [1,[15][16][17][18][19]. Di erent mathematical models of cholera infection are developed starting from the discovery of infection.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Derivative and Optimal Control Analysis of Cholera Epidemic Model

Cheneke

Koya

Edessa

2022

Journal of Mathematics

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In this study, a cholera model with fractional derivative and optimal control analysis is presented. Numerical simulation analysis shows that increasing the order of fractional derivatives contributes to updating the memory of the population to control the effects of cholera infection through available controlling techniques. On the other hand, the optimal analysis gives an indication of applying controlling infection with available treatment and prevention techniques. It provides a better mechanism to prevent the happening of cholera infection. Moreover, cost-effectiveness evaluation of cholera contamination intervention with feasible three or four combos of manipulate measures hygiene, vaccination, remedy of infectives, and chlorination indicates that hygiene, vaccination, and chlorination are the desired higher mixture to govern in addition propagation of cholera contamination. Numerical simulations are performed with the MATLAB platform and numerical solutions and results are discussed.

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“…Proof. To show boundedness we apply technique applied in [15,20,21]. Hence, first we consider the fractional derivative of human population dynamics.…”

Section: Theoremmentioning

confidence: 99%

“…where, N � S + I + R. Similar to the works done in [15], the solution of the preceding inequality (7) is given by…”

Section: Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractional Derivative and Optimal Control Analysis of Cholera Epidemic Model

Cheneke

Koya

Edessa

2022

Journal of Mathematics

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“…Results show that, in contrast to the previous mathematical formalism, the freedom to choose the kernel allows for the discovery of new properties of the capacitor microphone under investigation. Baleanu et al [13] studied the relative importance of memory on cholera outbreak. The work in [14] presented some applications of a regularized Ψ-Hilfer fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order Ebola-Malaria Coinfection Model with a Focus on Detection and Treatment Rate

Zhang

Addai

Ackora-Prah

et al. 2022

Computational and Mathematical Methods in Medicine

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Coinfection of Ebola virus and malaria is widespread, particularly in impoverished areas where malaria is already ubiquitous. Epidemics of Ebola virus disease arise on a sporadic basis in African nations with a high malaria burden. An observational study discovered that patients in Sierra Leone's Ebola treatment centers were routinely infected with malaria parasites, increasing the risk of death. In this paper, we study Ebola-malaria coinfections under the generalized Mittag-Leffler kernel fractional derivative. The Banach fixed point theorem and the Krasnoselskii type are used to analyse the model's existence and uniqueness. We discuss the model stability using the Hyers-Ulam functional analysis. The numerical scheme for the Ebolamalaria coinfections using Lagrange interpolation is presented. The numerical trajectories show that the prevalence of Ebolamalaria coinfections ranged from low to moderate depending on memory. This means that controlling the disease requires adequate knowledge of the past history of the dynamics of both malaria and Ebola. The graphical dynamics of the detection rate indicate that a variation in the detection rate only affects the following compartments: individuals that are latently infected with the Ebola, Ebola virus afflicted people who went unnoticed, individuals who have been infected with the Ebola virus and have been diagnosed with the disease, and persons undergoing Ebola virus therapy.

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“…We will look at the stability and existence of Hopf bifurcation in fractional-order complex-valued neural networks in [4] , [5] , [6] . Investigate the asymptotic behaviour of immunogenic tumour dynamics using a new fractional model built using the general fractional operators approach [7] , [33] , [34] . Using another fractional order derivative constructed as a kernel based on the generalized MITTAG–LEFFLER function, the predatory model is generated in [35] , [36] , [37] .…”

Section: Introductionmentioning

confidence: 99%