Modeling viral evolution: a multi-strain dynamical systems approach to mutation and transmission

Abstract

This study presents a mathematical framework for modeling viral evolution using a multi-strain dynamical systems approach that integrates mutation and transmission processes. The model extends classical compartmental structures by incorporating multiple co-circulating strains and allowing transitions between them through mutation. Each strain is characterized by distinct transmission parameters, enabling the analysis of heterogeneous fitness landscapes and evolutionary advantages. The resulting system of nonlinear ordinary differential equations captures key epidemiological dynamics, including strain competition, coexistence, and replacement.The model further incorporates partial cross-immunity to account for the reduced susceptibility of individuals previously exposed to related strains. Analytical techniques are employed to derive equilibrium states and determine their stability, with particular emphasis on the role of reproduction numbers in governing strain invasion and persistence. Numerical simulations are conducted to illustrate the impact of mutation rates and immune interactions on disease progression and strain dominance. Results demonstrate that higher mutation rates can accelerate the emergence of dominant variants, while cross-immunity significantly influences the long-term distribution of strains.Overall, the proposed framework provides a robust tool for understanding the interplay between viral mutation and transmission dynamics, offering valuable insights for predicting evolutionary trends and informing adaptive public health interventions.