Dynamic Analysis of a Delayed Fractional Infectious Disease Model with Saturated Incidence

Ding, Peng; Wang, Zhen

doi:10.3390/fractalfract6030138

Cited by 2 publications

(1 citation statement)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The reproduction number of a fractional dynamical system can be found using the next-generation matrix method [29,32]. So, the reproduction number of the model ( 7)-( 10) can be computed using the next-generation matrix method and is given by the spectral radius of ðDFÞðDVÞ −1 [33], that is,…”

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%

A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative

Melkamu

Mebrate

2022

Journal of Applied Mathematics

View full text Add to dashboard Cite

In this paper, we propose a Caputo–Fabrizio fractional derivative mathematical model consisting of smoker, people exposed to secondhand smoker, people exposed to thirdhand smoker, and quitters. Secondhand smoke exposure consists of an unintentional inhalation of smoke that occurs close to people smoking and/or in indoor environments where tobacco was recently used, and thirdhand smoke consists of pollutants that remain on surfaces and in dust after tobacco has been smoked, are reemitted into the gas phase, or react with other compounds in the environment to form secondary pollutants. The solution of the proposed model, which is carried out using a fixed-point theorem and an iterative method, exists and is unique. Furthermore, the model is biologically meaningful, that is, positive and bounded. The reproduction number R 0 is determined from the model. If R 0 < 1 , the smoking-free equilibrium point is asymptotically stable, and if R 0 > 1 , the smoking-free equilibrium point is unstable. The results confirm that the smoking-free equilibrium point becomes increasingly stable as the fractional order is increased. Numerical simulations are performed using a three-step Adams-Moulton predictor-corrector method for a range of fractional orders to show the effects of varying the fractional order and to support the theoretical results.

show abstract

Section: Journal Of Applied Mathematicsmentioning

confidence: 99%