Probing a Stochastic Epidemic Hepatitis C Virus Model with a Chronically Infected Treated Population

Area of Science:

• Epidemiology
• Mathematical Biology
• Virology

Background:

• Hepatitis C virus (HCV) poses a significant global health threat.
• Previous mathematical models for HCV transmission primarily used deterministic approaches, neglecting stochastic factors.
• Stochasticity is crucial in understanding disease pathology and epidemiological dynamics.

Purpose of the Study:

• To investigate a stochastic epidemic model for hepatitis C virus (HCV) transmission dynamics.
• To incorporate environmental influences via stochastic perturbations into the HCV model.
• To analyze the conditions for the extinction and persistence of HCV within the population.

Main Methods:

• Development of a five-state stochastic epidemic model (susceptible, acute, chronic, recovered/removed, treated).
• Mathematical analysis to prove the existence of a unique global positive solution.
• Construction of a Lyapunov function to determine conditions for an ergodic stationary distribution.

Main Results:

• The stochastic HCV model is shown to have a unique global positive solution.
• Sufficient conditions for the extinction of the hepatotropic RNA virus are established.
• Conditions for the existence of an ergodic stationary distribution for the stochastic HCV model were derived.

Conclusions:

• The study confirms the existence and uniqueness of solutions and conditions for HCV extinction and persistence.
• Numerical simulations demonstrate that key parameters significantly impact HCV transmission dynamics.
• The findings validate the theoretical conclusions and highlight the importance of stochasticity in HCV modeling.