A study of the fractional‐order mathematical model of diabetes and its resulting complications

Abstract

Diabetes is a worldwide problem that affects one of every 11 persons nowadays. The IDF Diabetes Atlas (Eighth edition, 2017) states that approximately 415 million people in the world are living with the disease and that this number will rise to 629 million by the year 2045. It is a very serious problem of the world. A major part of the world population is affected by this disease and its resulting complications. In this paper, we propose to investigate a fractional-order model of diabetes and its resulting complications. The mathematical model's parameters define the population of diabetic patients and those who are diabetic with complications at a given time t. We have also discussed the existence, uniqueness, and stability of the fractional-order model, which we consider here. We make use of the homotopy decomposition method (HDM) in order to solve the problem. KEYWORDSdiabetes and its resulting complications, existence, fractional calculus, fractional-order modeling, homotopy decomposition method (HDM), uniqueness and stability

Numerical Simulation of the Fractal-Fractional Ebola Virus

“…These integrals are evaluated directly and the numerical solutions of (5)- (8) involving the FFP derivative are given by…”

“…We turn now to the current onslaught of the Corona virus, which is referred to as COVID-19 (see, for details, [4][5][6]). As in the case of the Corona virus, the Ebola virus can be transmitted to others by contact with infected body fluids, through broken skin, or through the mucous membranes of the eyes, nose and mouth, but the Ebola virus can also be transmitted through sexual contact with a person who has the virus or has recovered from it (see, for details, [7]; see also the recently-published works [8][9][10][11] for the fractional-order modeling of various other diseases and other biological situations).…”

Global Stability for Novel Complicated SIR Epidemic Models with the Nonlinear Recovery Rate and Transfer from Being Infectious to Being Susceptible to Analyze the Transmission of COVID-19

“…In 1927, Kermack and McKendrick were the first to develop the susceptibleinfective-recovered (SIR) model, where the total population is divided into three classes: susceptible, infective, and recov-ered [4]. After that, variant of SIR compartmental models were developed, some of them outlined in [5][6][7][8]. Here, we consider a complex SIR epidemic model with nonstandard nonlinear incidence and recovery rates.…”

An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus

“…Generally speaking, the Ebola virus can infect humans in one of the following ways: Direct contact with humans, blood, body fluids, animal tissues, and through direct contact with body fluids of a sick person or a person who died from the Ebola virus disease. As the current onslaught of the Corona virus, which is referred to as COVID-19 (see, for details, [1] , [27] and [29] ), the Ebola virus is transmitted to other patients or the virus can pass through broken skin or mucous membranes in the eyes, nose and mouth when a person comes into contact with infected body fluids (or contaminated objects), but the Ebola virus is also transmitted through sexual contact with someone who has the virus or who has recovered from it (see [7] ; see also the recently-published works [36] and [37] for the fractional-order modeling of other diseases).…”