RETRACTED ARTICLE: Fractional-order scheme for bovine babesiosis disease and tick populations

Abstract

This article shows epidemic model, earlier suggested in ordinary differential equation philosophy, can be extended to fractional order on a reliable agenda of biological comportment. A set of domains for the model wherein allvariables are limited is established. Furthermore, the stability and existence of steadiness points are studied. We present the evidence that the endemic equilibrium (EE) point is locally asymptotically stable when reproduction number R 0 > 1. This outcome is attained via the linearization statement for fractional differential equations (FDEs). The worldwide asymptotic stability of a disease-free point, when R 0 < 1, is also verified by comparison theory for fractional differential equations. The numeric replications for diverse consequences are carried out, and data attained are in good agreement with theoretical outcomes, displaying a vital perception about the use of the set of fractional coupled differential equations to model babesiosis disease and tick populations.

A discrete epidemic model for bovine Babesiosis disease and tick populations

“…Besides, based on our work in [6], Carvalho et al [8] presented a new version of our classical model changing the ordinary derivative by fractional Caputo derivate. Likewise, in [9], authors study a fractional-order scheme model on the disease. Our continuous model in [6] has also served as a basis to set out and study similar models, including other factors such as a two-stage in the cattle class in [10] or the effect of seasonal changes in [11].…”

A reliable numerical analysis for stochastic dengue epidemic model with incubation period of virus

“…It is well known that nonlinear initial value problems (IVPs) do not always possess analytical solutions. The available classical explicit finite-difference schemes, such as Runge-Kutta and Euler methods, can bring about misleading chaos and deceitful oscillations for certain intensities of the discretization parameters [7][8][9][10][11]. Due to these reasons and some other scheme-dependent numerical instabilities such methods prove to be less privileged options.…”

Comparison of fractional order techniques for measles dynamics

“…Moreover, non-integer calculus displays a vivacious part of superdiffusive and subdiffusive measures, which make it an obliging instrument in the learning of syndrome transmission [6]. As integer order differential equations cannot authoritatively depict the exploratory and field estimation information, as an alternative approach fractional order differential equations mockups are at the moment being widely applied [20]. The fractional modeling is a beneficial approach which has been practiced to understand the comportment of syndromes; the non-integer derivative is a generalization of the ordinary derivative.…”

“…A significant role of modeling enterprises is that it can alert us to the paucities in our up-to-date understanding of the epidemiology of numerous infectious ailments, and propose critical queries for analysis and data that need to be collected. Lately, it has been applied to analyze dengue internal transmission model, bovine babesiosis disease and a tick population model, a HIV/AIDS epidemic model and the Lengyel-Epstein chemical reaction model [6,7,20,21]. Although the operating of the non-integer approach is more complex than the out-dated one, there are numerical approaches for cracking systems of DEs which are nonlinear.…”