Fractional order differential equations for chronic liver cirrhosis with frequent hospitalization

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.