The evolutionary battle: data-driven analysis of SARS-CoV-2 virulence

Combining perspectives of infectious disease dynamics and evolutionary adaptive dynamics, we reveal the evolving patterns of SARS-CoV-2 virulence with the use of data-driven analysis from 22 January 2020 to 21 October 2022 and focus primarily on the Wild-type virus, D614G, Alpha, Delta, Omicron and XBB. We discuss conditions between transmission rate (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>) and the sum of natural death rate (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>), mortality rate due to disease (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mtext>,</mml:mtext></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>), and recovery rate (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>γ</mml:mi></mml:mrow></mml:math>) for virus substitution and coexistence. (i) When <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mo><</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mrow><mml:mtext>,</mml:mtext></mml:math> mutant <i>y</i> replaces the resident virus <i>x</i>; (ii) when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mi>β</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mo>+</mml:mo><mml:mi>α</mml:mi><mml:mo>(</mml:mo><mml:mi>y</mml:mi><mml:mo>)</mml:mo><mml:mo>+</mml:mo><mml:mi>γ</mml:mi></mml:mrow></mml:mfrac></mml:mrow></mml:mrow><mml:mtext>,</mml:mtext></mml:math> the mutant coexists with the resident virus and they are homogeneous virus. Further we adopt a segmented classification method to find that the transmission rate is gradually increasing and the mortality rate due to disease shows a significant increase at first, with the increasing virulence of the virus, there is a trend of gradual decline in the later period of the epidemic. Additionally, it turns out that reducing personnel mobility is conducive to the retention of virulent viruses and the symptoms of the patients tend to abate. To investigate the impact of dynamic changes in infectious disease systems links to SARS-CoV-2 on the evolution of its virulence over time scales, the coupling nesting of evolutionary dynamics and transmission dynamics is carried out. It suggests the results of the adaptive evolution of the virus have been verified and the increased speed of evolutionary adaptation shorts the time for viruses to peak.