# Stochastic Modeling and Simulation of Viral Evolution

## Abstract

RNA viruses comprise vast populations of closely related, but highly genetically diverse, entities known as *quasispecies*. Understanding the mechanisms by which this extreme diversity is generated and maintained is fundamental when approaching viral persistence and pathobiology in infected hosts. In this paper, we access quasispecies theory through a mathematical model based on the theory of multitype branching processes, to better understand the roles of mechanisms resulting in viral diversity, persistence and extinction. We accomplish this understanding by a combination of computational simulations and the theoretical analysis of the model. In order to perform the simulations, we have implemented the mathematical model into a computational platform capable of running simulations and presenting the results in a graphical format in real time. Among other things, we show that the establishment of virus populations may display four distinct regimes from its introduction into new hosts until achieving equilibrium or undergoing extinction. Also, we were able to simulate different *fitness distributions* representing distinct environments within a host which could either be favorable or hostile to the viral success. We addressed the most used mechanisms for explaining the extinction of RNA virus populations called *lethal mutagenesis* and *mutational meltdown*. We were able to demonstrate a correspondence between these two mechanisms implying the existence of a unifying principle leading to the extinction of RNA viruses.

## Keywords

Viral evolution Quasispecies theory Branching process Lethal mutagenesis Mutational meltdown Stochastic simulation## Notes

### Acknowledgements

LG acknowledges the support of FAPESP through the Grant Number 14/13382-1. BG and DC received financial support from CAPES.

### Author Contributions

LG and DC contributed equally to this work. LMRJ and FA contributed equally to this work. Conceived the model and formulated the underlying theory: LMJR and FA. Implemented the software: LG, DC and BG. Simulated the model and analyzed the output: LG and DC. Wrote the paper: LMRJ and FA.

## Supplementary material

## References

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