RESUMO
In this study, a physical system called the blood ethanol concentration model has been investigated in its fractional (non-integer) order version. The three most commonly used fractional operators with singular (Caputo) and non-singular (Atangana-Baleanu fractional derivative in the Caputo sense-ABC and the Caputo-Fabrizio-CF) kernels have been used to fractionalize the model, whereas during the process of fractionalization, the dimensional consistency for each of the equations in the model has been maintained. The Laplace transform technique is used to determine the exact solution of the model in all three cases, whereas its parameters are fitted through the least-squares error minimization technique. It is shown that the fractional versions of the model based upon the Caputo and ABC operators estimate the real data comparatively better than the original integer order model, whereas the CF yields the results equivalent to the results obtained from the integer-order model. The computation of the sum of squared residuals is carried out to show the performance of the models along with some graphical illustrations.
Assuntos
Concentração Alcoólica no Sangue , Humanos , Modelos BiológicosRESUMO
In the present study, the fractional version with respect to the Atangana-Baleanu fractional derivative operator in the caputo sense (ABC) of the two-strain epidemic mathematical model involving two vaccinations has extensively been analyzed. Furthermore, using the fixed-point theory, it has been shown that the solution of the proposed fractional version of the mathematical model does not only exist but is also the unique solution under some conditions. The original mathematical model consists of six first order nonlinear ordinary differential equations, thereby requiring a numerical treatment for getting physical interpretations. Likewise, its fractional version is not possible to be solved by any existing analytical method. Therefore, in order to get the observations regarding the output of the model, it has been solved using a newly developed convergent numerical method based on the Atangana-Baleanu fractional derivative operator in the caputo sense. To believe upon the results obtained, the fractional order α has been allowed to vary between ( 0 , 1 ] , whereupon the physical observations match with those obtained in the classical case, but the fractional model has persisted all the memory effects making the model much more suitable when presented in the structure of fractional order derivatives for ABC. Finally, the fractional forward Euler method in the classical caputo sense has been used to illustrate the better performance of the numerical method obtained via the Atangana-Baleanu fractional derivative operator in the caputo sense.
Assuntos
Modelos Teóricos , Orthomyxoviridae , Vacinação , Doenças Transmissíveis , Epidemias , HumanosRESUMO
Background: Gastroparesis is a serious condition that can be caused by diabetes, surgery or infection, or can be idiopathic. When there is no mechanical obstruction, gastroparesis is characterized by delayed stomach emptying. Itopride, a prokinetic drug, inhibits acetylcholinesterase activity in addition to antagonizing dopamine D2 receptors. Methods: This prospective, multicentre study is based on real-world data from 988 patients with a diagnosis of diabetic gastroparesis for index (PAGI-SYM2) evaluation at baseline and week 4 of treatment for upper gastrointestinal disorder symptoms. Results: Upper gastrointestinal symptom severity scores improved significantly after 4 weeks of treatment (p<0.001), with significant improvement across all categories of gastroparesis (very mild (37-58.6%), mild degree (24.6-31.6%), moderate (29.3-7.3%) and severe (8.8-2.6%). Conclusion: Itopride SR (Nogerd SR) in a 150 mg once-daily dose showed promising results in reducing the severity of upper gastrointestinal disorder symptoms associated with diabetic gastroparesis. Both statistical and clinical effectiveness were observed. Moreover, the treatment demonstrated a favourable tolerability profile, with a low incidence of adverse effects.
RESUMO
This paper proposes a three-step iterative technique for solving nonlinear equations from medical science. We designed the proposed technique by blending the well-known Newton's method with an existing two-step technique. The method needs only five evaluations per iteration: three for the given function and two for its first derivatives. As a result, the novel approach converges faster than many existing techniques. We investigated several models of applied medical science in both scalar and vector versions, including population growth, blood rheology, and neurophysiology. Finally, some complex-valued polynomials are shown as polynomiographs to visualize the convergence zones.