Dataset Information

Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization.

ABSTRACT:

Objective

Liver cirrhosis, which is considered as the terminal stage of liver diseases, has become life-threatening among non-communicable diseases in the world. Viral hepatitis (hepatitis B and C) is the major risk factor for the development and progression of chronic liver cirrhosis. The asymptomatic stage of cirrhosis is considered as the compensated cirrhosis whereas the symptomatic stage is considered as decompensated cirrhosis. The latter stage is characterized by complex disorder affecting multiple systems of liver organ with frequent hospitalization. In this paper, we formulate system of fractional differential equations of chronic liver cirrhosis with frequent hospitalization to investigate the dynamics of the disease. The fundamental properties including the existence of positive solutions, positively invariant set, and biological feasibility are discussed. We used generalized mean value theorem to establish the existence of positive solutions. The Adams-type predictor-evaluate-corrector-evaluate approach is used to present the numerical scheme the fractional erder model.

Results

Using the numerical scheme, we simulate the solutions of the fractional order model. The numerical simulations are carried out using MATLAB software to illustrate the analytic findings. The analysis reveals that the number of decompensated cirrhosis individuals decreases when the progression rate and the disease's past states are considered.

SUBMITTER: Dano LB

PROVIDER: S-EPMC9588237 | biostudies-literature | 2022 Oct

REPOSITORIES: biostudies-literature

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Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization.

Dano Lemesa Bedjisa LB Rao Koya Purnachandra KP Keno Temesgen Duressa TD

BMC research notes 20221022 1

<h4>Objective</h4>Liver cirrhosis, which is considered as the terminal stage of liver diseases, has become life-threatening among non-communicable diseases in the world. Viral hepatitis (hepatitis B and C) is the major risk factor for the development and progression of chronic liver cirrhosis. The asymptomatic stage of cirrhosis is considered as the compensated cirrhosis whereas the symptomatic stage is considered as decompensated cirrhosis. The latter stage is characterized by complex disorder ...[more]

PMID: 36273195

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Project description:HCV infection is a leading cause of chronic liver disease with long-term complications-extensive fibrosis, cirrhosis, and hepatocellular carcinoma. The objective of this study is to perform cost analysis of therapy of patients with chronic HCV-related cirrhosis hospitalized in the University Hospital "Queen Joanna-ISUL" for 3-year period (2012-2014).It is a prospective, real life observational study of 297 patients with chronic HCV infection and cirrhosis monitored in the University Hospital "Queen Joanna-ISUL" for 3-year period. Data on demographic, clinical characteristics, and health-care resources utilization (hospitalizations, highly specialized interventions, and pharmacotherapy) were collected. Micro-costing approach was applied to evaluate the total direct medical costs. The points of view are that of the National Health Insurance Fund (NHIF), hospital and the patients. Collected cost data are from the NHIF and hospitals tariffs, patients, and from the positive dug list for medicines prices. Descriptive statistics, chi-squared test, Kruskal-Wallis, and Friedman tests were used for statistical processing.76% of patients were male. 93% were diagnosed in grade Child-Pugh A and B. 97% reported complications, and almost all developed esophageal varices. During the 3 years observational period, patients did not change the critical clinical values for Child-Pugh status and therefore the group was considered as homogenous. 847 hospitalizations were recorded for 3 years period with average length of stay 17 days. The mortality rate of 6.90% was extremely high. The total direct medical costs for the observed cohort of patients for 3-year period accounted for 1,290,533 BGN (€659,839) with an average cost per patient 4,577 BGN (€2,340). Statistically significant correlation was observed between the total cost per patient from the different payers' perspective and the Child-Pugh cirrhosis score.HCV-related cirrhosis is resource demanding and sets high direct medical costs as it is related with increased hospitalizations and complications acquiring additional treatment.

Project description:Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Dataset Information

Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization.

Objective

Results

Publications

Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization.

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