Application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics
type: Item
instance of: scholarly article
title: Application of a new generalized fractional derivative and rank of control measures on cholera transmission dynamics
zbMATH Open document ID: 1486.92212
DOI: 10.1155/2021/2104051
author: Kumama Regassa Cheneke
author: Koya Purnachandra Rao
author: Geremew Kenassa Edessa
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2022-01-19T00:00:00Z
review text: Summary: In this study, the mathematical model of the cholera epidemic is formulated and analyzed to show the impact of \textit{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 \textit{Vibrio cholerae} can be controlled if continuous treatment is applied in reserved freshwater used for drinking purposes so that the intrinsic growth rate of \textit{Vibrio cholerae} in water is less than the natural death of \textit{Vibrio cholerae}. We have applied the stability theory of differential equations and proved that the disease-free equilibrium is asymptotically stable if \(R_0<1\), and the intrinsic growth rate of the \textit{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 \(R_0=1\) and the local stability of endemic equilibrium if \(R_0>1\). 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.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C60
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 7459469
zbMATH Keywords: transmission dynamics
zbMATH Keywords: vibrio cholerae
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/2104051
OpenAlex ID: W3210743358
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description: scientific article; zbMATH DE number 7459469