Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease

Addai, Emmanuel; Zhang, Lingling; Preko, Ama Kyerewaa; Asamoah, Joshua Kiddy K.

doi:10.1016/j.health.2022.100114

Cited by 21 publications

(10 citation statements)

References 45 publications

(40 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we review several key definitions, lemmas, and concepts that are necessary to understand the suggested model. Definition 2.1 Let f ∈ Q 1 (p, q), q > p, and α * ∈ (0, 1) (17), (40). Then, the Caputo-Fabrizio fractional-order derivative can be defined as…”

Section: Preliminariesmentioning

confidence: 99%

“…Considering the characteristics of exponential decay, the Caputo-Fabrizio fractional-order operator has been preferred over Atangana-Beleanu beta derivatives and a few other operators in the field of mathematical biology with more information (17-19, 24, 36-39). For instance, in Addai et al (40), the authors studied a novel model of COVID-19 incorporating Alzheimer's disease using the Caputo-Fabrizio fractional-order operator. The results of the aforementioned study revealed that the two diseases have a link and the authors also concluded that the fractional operator is related to the rate of infection.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Ngungu

Addai

Adeniji

et al. 2023

Front. Public Health

Self Cite

View full text Add to dashboard Cite

In this study, a mathematical model for studying the dynamics of monkeypox virus transmission with non-pharmaceutical intervention is created, examined, and simulated using real-time data. Positiveness, invariance, and boundedness of the solutions are thus examined as fundamental features of mathematical models. The equilibrium points and the prerequisites for their stability are achieved. The basic reproduction number and thus the virus transmission coefficient ℜ0 were determined and quantitatively used to study the global stability of the model's steady state. Furthermore, this study considered the sensitivity analysis of the parameters according to ℜ0. The most sensitive variables that are important for infection control are determined using the normalized forward sensitivity index. Data from the United Kingdom collected between May and August 2022, which also aid in demonstrating the usefulness and practical application of the model to the spread of the disease in the United Kingdom, were used. In addition, using the Caputo–Fabrizio operator, Krasnoselskii's fixed point theorem has been used to analyze the existence and uniqueness of the solutions to the suggested model. The numerical simulations are presented to assess the system dynamic behavior. More vulnerability was observed when monkeypox virus cases first appeared recently as a result of numerical calculations. We advise the policymakers to consider these elements to control monkeypox transmission. Based on these findings, we hypothesized that another control parameter could be the memory index or fractional order.

show abstract

Section: Preliminariesmentioning

confidence: 99%

mentioning

confidence: 99%

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Ngungu

Addai

Adeniji

et al. 2023

Front. Public Health

Self Cite

View full text Add to dashboard Cite

show abstract

“…Some scholar investigate the impact of self-isolation, quarantine, and contact tracing on the stopping and control of the COVID-19 pandemic using data from the New York population [25] . On the other hand, fractional differential equations play a fundamental role in the distribution of the COVID-19 pandemic [26] , [27] , so there are numerous methods to solve them [28] , [29] , [30] , [31] .…”

Section: Introductionmentioning

confidence: 99%

Analysis, predicting, and controlling the COVID-19 pandemic in Iraq through SIR model

Khalaf¹,

Flayyih²

2023

Results in Control and Optimization

View full text Add to dashboard Cite

“…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

View full text Add to dashboard Cite

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.

show abstract

Fractional order epidemiological model of SARS-CoV-2 dynamism involving Alzheimer’s disease

Cited by 21 publications

References 45 publications

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Mathematical epidemiological modeling and analysis of monkeypox dynamism with non-pharmaceutical intervention using real data from United Kingdom

Analysis, predicting, and controlling the COVID-19 pandemic in Iraq through SIR model

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

Contact Info

Product

Resources

About