Stochastic differential equations model for the interaction of HCV with liver cells

Abstract

The main objective of this paper is to study the dynamic behavior of the hepatitis C virus to control the spread of this disease. The study was conducted by creating a new stochastic mathematical model. Three equilibriums specific to this system are discussed, namely, disease-free equilibrium, equilibrium in the absence of an antibody response, and equilibrium when immune response CTLs are zero. We also showed conditions that must be met for the injured person to recover by searching for the basic reproduction number. If it means that the liver will get rid of the virus and heal the infected person. while in this case, the infection grows and the disease can invade all liver cells. These results have also been demonstrated by computer simulations.

Keywords

• Mathematical modeling of HCV
• Basic reproduction number
• Immune responses CTLs
• Stochastic model
• Hepatitis C virus