Abstract
The deterministic stability of a model of Hepatitis C which includes a term defining the effect of immune system is studied on both local and global scales. Random effect is added to the model to investigate the random behavior of the model. The numerical characteristics such as the expectation, variance and confidence interval are calculated for random effects with two different distributions from the results of numerical simulations. In addition, the compliance of the random behavior of the model and the deterministic stability results is examined.
Highlights
Hepatitis C is an infectious liver disease
The results show that the disease-free equilibrium point of the model is locally asymptotically stable if R0 1 and unstable if R0 > 1
A Lyapunov function was constructed for the global stability analysis of the disease free equilibrium
Summary
Hepatitis C is an infectious liver disease. The virus which causes this disease was identified in 1989 but the worldwide presence of the virus shows that it has been active for a much longer period. It should be noted that the use of spatial effects may provide useful results for analyzing Hepatitis C transmission dynamics [13,14,15,16] These models use mathematical tools to guide and enhance studies in medicine, biology and etc. The components of the basic three-component model are uninfected hepatocytes, infected hepatocytes and the virus, which are denoted by T(t), I(t) and V(t), respectively. DV dt 1⁄4 ð1 À pÞpI À cV: The parameters of the model describe the rates of change in the uninfected hepatocytes, infected hepatocytes and virus during treatment. The treatment effects are included in the model with two parameters p and η, which describe the virion production blockage and new infection reduction respectively. If R0 > 1, there exists positive equilibria for the System (1) and one of these T1Ã 1⁄4
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
