"Evolution into chaos - implications of the trade-off between transmissibility and immune evasion"Sayyar, GolsaThe prediction of viral evolution poses a substantial challenge and represents a paramount public health imperative. In response to this challenge, we develop a pioneering model for viral evolution that integrates considerations of the trade-off between immunity evasion and transmissibility. Our findings demonstrate that when the pathogen exhibits high transmissibility, evolution tends to favor immune evasion, whereas lower transmissibility favors heightened transmission rates. Moreover, we illustrate the long-term evolutionary patterns following the emergence of new strains with maximum invasion fitness modeled by a difference equation. We provide sufficient criteria for when evolution converges, and subsequent strains exhibit similar transmissibility. Furthermore, we identify scenarios characterized by a biennial pattern in subsequent strains, indicating a sequence wherein a highly transmissible strain is succeeded by a less immune-evasive strain, and vice versa. This cyclic pattern recurs iteratively. Visualization through bifurcation diagrams illustrates our analytical findings, elucidating rich dynamic phenomena encompassing the existence of various periodic solutions, extending to chaotic behavior. This comprehensive analysis provides valuable insights into the complexities of viral evolution in the light of the trade-off between immunity evasion and transmissibility. |
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