Dynamical analysis of a fractional-order foot-and-mouth disease model

Gashirai, Tinashe B.; Hove-Musekwa, Senelani D.; Mushayabasa, Steady

doi:10.1007/s40096-020-00372-3

Cited by 8 publications

(5 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Computational and Mathematical Methods in Medicine fractional-order calculus has been widely and extensively used by several researchers recently, to investigate the role of memory effects in different diseases [29][30][31][32][33]. The frac-tional derivative has several definitions such as those derived from Riemann-Liouville, Caputo, Liouville, Weyl, Riesz, Grünwald-Litnikov, Marchaud and Hifler, Caputo-Fabrizio-Caputo, Atanga-Baleanu, Atanga-beta derivative, M -fractional derivative, conformable derivative, Atangana-Koca, Atanga-Gomez, and variable-order and fractalfractional idea [34,35].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

Helikumi

Eustace

Mushayabasa

2022

Computational and Mathematical Methods in Medicine

Self Cite

View full text Add to dashboard Cite

In this paper, a nonlinear fractional-order chikungunya disease model that incorporates asymptomatic infectious individuals is proposed and analyzed. The main interest of this work is to investigate the role of memory effects on the dynamics of chikungunya. Qualitative analysis of the model’s equilibria showed that there exists a threshold quantity which governs persistence and extinction of the disease. Model parameters were estimated based on the 2015 weekly reported cases in Colombia. The Adams-Bashforth-Moulton method was used to numerically solve the proposed model. We investigated the role of asymptomatic infectious patients on short- and long-term dynamics of the diseases. We also determined threshold levels for the efficacy of preventative strategies that results in effective management of the disease. We believe that our model can provide invaluable insights for public health authorities to predict the effect of chikungunya transmission and analyze its underlying factors and to guide new control efforts.

show abstract

Section: Introductionmentioning

confidence: 99%

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

Helikumi

Eustace

Mushayabasa

2022

Computational and Mathematical Methods in Medicine

Self Cite

View full text Add to dashboard Cite

show abstract

“…A nonlinear fractional-order model was proposed by [137] as a way to explain and grasp the foot-and-mouth outbreaks. A fractional-order model for the spread and treatment of foot-and-mouth disease is presented and examined in [138]. Fractional order mathematical model to explain how the hand, foot, and mouth illness spreads [139].…”

Section: Contribution Of Fractional On Epidemic Modelmentioning

confidence: 99%

Untitled

2023

Progr. Fract. Differ. Appl.

View full text Add to dashboard Cite

Both mathematics and science are important for one another and have a close relationship. It is impossible to dispute the significance of mathematics in a number of scientific disciplines, including electrical engineering, physics, biology, and medicine. Due to a number of applications of mathematical biology in the twenty-first century, researchers have taken a special interest in this field. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. New fractional operators, the infectious disease model has been studied in this paper. By using different numerical techniques and the time fractional parameters, the mechanical characteristics of the fractional order model are identified. The uniqueness and existence have been established. The model's local and global stability analysis has been found. In order to justify the theoretical results, numerical simulations are carried out for the presented method in the range of fractional order to show the implications of fractional and fractal orders. We applied very effective numerical technique to obtain the solutions of the model and simulations. Also, we present conditions of existence for a solution to the purposed epidemic model and to calculate the reproduction number in certain state conditions of the analyzed dynamic system. Infectious disease fractional order model is offered for analysis with simulations in order to determine the possible efficacy of disease transmission in the Community. The Fractal fractional operator is employed to study the dynamical transmission of diseases effect on society which is helpful for analysis, decision making, and disease control. Are treated with the Banach contraction principle. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples. Finally, numerical simulations that demonstrate the impact of fractional parameters on our found solutions are built to study the impact of the system parameter on the disease's spread. In conclusion, fractional operators in mathematical models can help decision-makers make better choices regarding the course of action to take in an epidemic situation. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling.

show abstract

“…A fractional order model, incorporating constant and optimum controls, was constructed in [11] to understand the transmission dynamics of HFMD. The authors in [12] constructed a fractional order model to investigate the dynamics of HFMD that included vaccination and quarantine strategies for disease intervention. They used the fundamental reproduction number to assess the stability of the model.…”

Section: Introductionmentioning

confidence: 99%

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Mohandoss,

Chandrasekar,

Meetei

et al. 2024

Axioms

View full text Add to dashboard Cite

This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease.

show abstract

Dynamical analysis of a fractional-order foot-and-mouth disease model

Cited by 8 publications

References 43 publications

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

Dynamics of a Fractional-Order Chikungunya Model with Asymptomatic Infectious Class

Untitled

Fractional Order Mathematical Modelling of HFMD Transmission via Caputo Derivative

Contact Info

Product

Resources

About