# Russian mathematician proposes a model describing virus mutations

The interaction of a virus with the human body is a very complex phenomenon that can be reduced to two processes:

the virus multiplies in host cells and the bodyresists infection through an immune response. A closer look at viral infection reveals that viruses compete for host cells, are altered by antiviral drugs, and mutate during replication. They can develop at a very high rate by modifying old or acquiring new RNA or DNA sequences. These and many other factors make it difficult for biologists to predict the evolutionary dynamics of the virus, to anticipate the emergence of new strains, and to assess their potential levels of resistance.

Vitaly Volpert's team, mathematician from RUDN University,proposed a mathematical model describing the evolution and diversification of quasispecies of viruses. The model shows the dynamic interaction between replication, mutation and virus elimination. The results of the work can be used to predict the appearance of viral strains that are able to avoid immune recognition and resist antiviral drugs.

To keep things simple, the model shows us thatexisting strains are evolving to reduce competition between viruses, weaken the clearance of the virus by the immune response, and become less sensitive to drugs. This trend is leading to the emergence of drug resistant strains /

### Vitali Volpert, mathematician from RUDN University

Working together with his colleagues, the scientist describeda virus strain as a localized solution centered around a given genotype. The emergence of new strains corresponds to a periodic wave propagating in the space of genotypes. The emergence of new peaks in the propagation of waves coincides with the emergence of new strains of viruses. The team described the conditions for the occurrence of periodic traveling waves and their dynamics by analyzing the stability of spatially uniform stationary solutions.

The model is represented by the nonlocal equationdiffusion reactions for virus density. The equation has two integral terms that correspond to the nonlocal effects of the interaction of the virus with host cells and immune cells.

The new model is qualitative and applicable to variousviral infections. However, in order to better describe the dynamics of quasispecies of viruses, it is necessary to know their individual characteristics, such as the nature of their mutations, interaction with the immune system, and response to antiviral drugs.

“Using our model, you can developvarious methods of preventing the spread of viral infections through the tissues of the body and the emergence of new strains, that is, the spread of genotypes in the space. However, in order for these approaches to have practical implementation, they must be combined with experimental and clinical data, ”explains Vitaly Volpert.

The model has a number of limitations, since it is basedon several simplifications. Namely, it does not take into account the existence of many immune cells and cytokines (small informative peptide molecules) that are involved in the immune response, or the complex processes of intracellular regulation and replication of the virus. However, these limitations help scientists identify some common evolutionary features of quasispecies viruses that would be difficult to identify in a more complex model. The work of the team of scientists can be used as a basis for further investigations.