Spatial heterogeneity and diffusion-driven dynamics of HCV infection: A mathematical modeling framework

Hepatitis C virus (HCV) infection in the body includes not only virus-to-cell infection, but also cell-to-cell infection. This infection will stimulate the body to produce cytotoxic T lymphocyte (CTL) immune response and antibody immune response. In this paper, we study the disease dynamics of two kinds of infection and two kinds of immune models, which include spatial diffusion and heterogeneity of internal environment, and further explore the influence of spatial heterogeneity on the extinction and persistence of hepatitis C virus (HCV). We defined the basic reproduction number, deduced the corresponding expression of the basic reproduction number $R_0$, and proved that the basic reproduction number $R_0$ can be used as the threshold of whether the virus exists or not. That is, if the basic reproduction number $R_0<1$, the disease-free balance is globally stable and HCV is extinct; if the basic reproduction number $R_0>1$, there is at least one local equilibrium, and HCV will persist. Furthermore, we performed numerical simulations to investigate how spatial diffusion and heterogeneity affect disease dynamics. Combining theoretical analysis with numerical simulations, our findings reveal that spatial heterogeneity can increase the risk of viral infection within the host. However, the mobility of infected cells and viruses may serve to diminish these risks.