Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Abstract

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

Modelling the dynamics of virus infection and immune response in space and time

“…Taking it into account by formulation a reaction-diffusion model, we observe the existence of multiple steady-states and possible transition between the different equilibria. Similar to the study based on a single PDE model [6], behavior of the system is determined by the characteristics of antiviral immune response and by the initial viral load.…”

“…introduced and studied in [6]. As it is mentioned in the introduction, there are three main regimes of the infection spreading in this case: with low level infection level behind the infection front, with high level infection level, and with low level followed by high level infection.…”

“…Existence of such solution is known for the case without delay (µ = 0) [18] and for a single equation with delay (see [6] and the references therein). We expect that the existence result remains valid for the system of two equations with delay since the methods based on maximum principle remain applicable here.…”

“…In particular, the computational models of antiviral immune response can provide insights into the regulation of the dynamics processes underlying various patterns in disease progression. Except for few studies, mathematical models of the immune response against virus infections conventionally consider the infected whole organism as a single homogenous compartment [5,6]. Thus they do not take into account that the dynamics of infection spread differs between tissues, organs and blood.…”

“…In our previous work [6] we studied the spread of a viral infection in tissue with a single reaction-diffusion equation for the virus concentration. The concentration of the immune cells was considered as a function of the infection level.…”