A new fractional mathematical model to study the impact of vaccination on COVID-19 outbreaks

This research paper investigates the SIZR model for Zombie infection outbreaks with a time-dependent infection rate. The proposed model is extended to the fractional order using different fractional derivative operators. The solution of the proposed model by numerical schemes, is briefed. Graphical representations provide us with a better understanding of this mathematical model. Lastly, as observed in movies, we conclude that Zombie infection can open to the destruction and collapse of human development and it is imperious to deal with Zombies as early as possible. Otherwise, this will put the civilization in unresting and destructive circumstances.

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“…Here, C ζ η t denotes the fractional Caputo derivative of order η. To find the numerical solution [31], consider…”

Section: Numerical Scheme For the Sizr Model In Frame Of Caputo Deriv...mentioning

confidence: 99%

Fractional SIZR model of Zombie infection

Jafari

Goswami

Dubey

et al. 2023

International Journal of Mathematics and Computer in Engineering

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“…Nowadays, mathematical modeling is considered an effective and important tool for describing the cause and transmission dynamics of many common infectious diseases such as the HIV/AIDS [ 29 , 30 ], COVID-19 [ 27 , 31 , 48 ], tuberculosis (TB) [ 3 , 37 ], Lassa fever [ 4 ], Ebola, syphilis [ 9 ] cancer cells [ 36 ], polio [ 21 ] and many others which are classified in [ 4 ]. In recent years, a fractional-order derivative which is being regarded as an extension of the integer-order derivative has gained a lot of scholars’ attention due to its nonlocal properties and memory effects [ 22 , 41 ].…”

Section: Introductionmentioning

confidence: 99%

A computational technique for the Caputo fractal-fractional diabetes mellitus model without genetic factors

Karaağaç

Owolabi

Pindza

2023

Int. J. Dynam. Control

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The concept of a Caputo fractal-fractional derivative is a new class of non-integer order derivative with a power-law kernel that has many applications in real-life scenarios. This new derivative is applied newly to model the dynamics of diabetes mellitus disease because the operator can be applied to formulate some models which describe the dynamics with memory effects. Diabetes mellitus as one of the leading diseases of our century is a type of disease that is widely observed worldwide and takes the first place in the evolution of many fatal diseases. Diabetes is tagged as a chronic, metabolic disease signalized by elevated levels of blood glucose (or blood sugar), which results over time in serious damage to the heart, blood vessels, eyes, kidneys, and nerves in the body. The present study is devoted to mathematical modeling and analysis of the diabetes mellitus model without genetic factors in the sense of fractional-fractal derivative. At first, the critical points of the diabetes mellitus model are investigated; then Picard’s theorem idea is applied to investigate the existence and uniqueness of the solutions of the model under the fractional-fractal operator. The resulting discretized system of fractal-fractional differential equations is integrated in time with the MATLAB inbuilt Ode45 and Ode15s packages. A step-by-step and easy-to-adapt MATLAB algorithm is also provided for scholars to reproduce. Simulation experiments that revealed the dynamic behavior of the model for different instances of fractal-fractional parameters in the sense of the Caputo operator are displayed in the table and figures. It was observed in the numerical experiments that a decrease in both fractal dimensions and leads to an increase in the number of people living with diabetes mellitus.

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“…Many fractional differential problems either lack closed-form solutions or have analytical answers that are too complicated to be helpful. As a result, many authors, such as [41] , [42] , [43] , [44] , [45] have proposed numerous numerical approximation approaches, including the Newton polynomial interpolation, Lagrange interpolation, Adams-type predictor–corrector iterative scheme, Adams–Moulton Rule and other methods.…”

Section: Introductionmentioning

confidence: 99%