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

ABSTRACT

Spreading of viral infection in the tissues such as lymph nodes or spleen depends on virus multiplication in the host cells, their transport and on the immune response. Reaction–diffusion systems of equations with delays in proliferation and death terms of the immune cells represent an appropriate model to study this process. The properties of the immune response and the initial viral load determine the regimes of infection spreading. In the proposed model, the proliferation rate of the immune cells is represented by a bell-shaped function of the virus concentration which increases for small concentrations and decreases if the concentration is sufficiently high. Here we use such a model system to show that an infection can be completely eliminated or it can remain present together with a decreased concentration of immune cells. Finally, immune cells can be completely exhausted leading to a high virus concentration in the tissue. In addition, we predicted two novel regimes of infection dynamics not observed before. Infection propagation in the tissue can occur as a superposition of two travelling waves: first wave propagates as a low level infection front followed by a high level infection front with a smaller speed of propagation. Both of the travelling waves can have a positive or a negative speed corresponding to infection advancement or retreat. These regimes can be accompanied by instabilities and the emergence of complex spatiotemporal patterns.

Graphical Abstract

Schematic representation of the processes underlying the population dynamics of virus infection spread and the antiviral immune response.

KEYWORDS:

• Infection spreading
• tissue
• immune response
• mathematical model
• reaction–diffusion equations
• time-delay

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Russian Science Foundation [grant number 15-11-00029].