Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics

In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cho...

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Autores principales:	Kumama Regassa Cheneke, Koya Purnachandra Rao, Geremew Kenassa Edessa
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d483cb5e35864384b78867ccc8da94f1
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spelling	oai:doaj.org-article:d483cb5e35864384b78867ccc8da94f12021-11-15T01:19:45ZApplication of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics1687-042510.1155/2021/2104051https://doaj.org/article/d483cb5e35864384b78867ccc8da94f12021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/2104051https://doaj.org/toc/1687-0425In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if R0<1, and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point R0=1 and the local stability of endemic equilibrium if R0>1. Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.Kumama Regassa ChenekeKoya Purnachandra RaoGeremew Kenassa EdessaHindawi LimitedarticleMathematicsQA1-939ENInternational Journal of Mathematics and Mathematical Sciences, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Kumama Regassa Cheneke Koya Purnachandra Rao Geremew Kenassa Edessa Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
description	In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of Vibrio cholerae in reserved freshwater. Moreover, the results obtained from applying the new fractional derivative method show that, as the order of the fractional derivative increases, cholera-preventing behaviors also increase. Also, the finding of our study shows that the dynamics of Vibrio cholerae can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of Vibrio cholerae in water is less than the natural death of Vibrio cholerae. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if R0<1, and the intrinsic growth rate of the Vibrio cholerae bacterium population is less than its natural death rate. The center manifold theory is applied to show the existence of forward bifurcation at the point R0=1 and the local stability of endemic equilibrium if R0>1. Furthermore, the performed numerical simulation results show that, as the rank of control measures applied increases from no control, weak control, and strong control measures, the recovered individuals are 55.02, 67.47, and 674.7, respectively. Numerical simulations are plotted using MATLAB software package.
format	article
author	Kumama Regassa Cheneke Koya Purnachandra Rao Geremew Kenassa Edessa
author_facet	Kumama Regassa Cheneke Koya Purnachandra Rao Geremew Kenassa Edessa
author_sort	Kumama Regassa Cheneke
title	Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
title_short	Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
title_full	Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
title_fullStr	Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
title_full_unstemmed	Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics
title_sort	application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/d483cb5e35864384b78867ccc8da94f1
work_keys_str_mv	AT kumamaregassacheneke applicationofanewgeneralizedfractionalderivativeandrankofcontrolmeasuresoncholeratransmissiondynamics AT koyapurnachandrarao applicationofanewgeneralizedfractionalderivativeandrankofcontrolmeasuresoncholeratransmissiondynamics AT geremewkenassaedessa applicationofanewgeneralizedfractionalderivativeandrankofcontrolmeasuresoncholeratransmissiondynamics
_version_	1718428950838902784

Application of a New Generalized Fractional Derivative and Rank of Control Measures on Cholera Transmission Dynamics

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