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Supplementary Material: 
\[OpenCurlyDoubleQuote]On the Evolutionary Epidemiology of SARS-CoV-2\
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Cell["\<\
Troy Day, Sylvain Gandon, S\[EAcute]bastien Lion, & Sarah P. Otto
June 5, 2020\
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Analysis of model with genetic variation (wildtype and mutant subtypes)\
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In addition, the fact that the characteristic polynomial is zero guarantees \
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This gives us an equivalent way to write the selection coefficient on the \
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Cell["\<\
S vE (uA \[CapitalDelta]\[Beta]A+ uI \[CapitalDelta]\[Beta]I + uP \
\[CapitalDelta]\[Beta]P)-uI vI \[CapitalDelta]\[Alpha]+uE ((1-f)vP+f vA-vE) \
\[CapitalDelta]\[Kappa]E+uE (vA-vP) \[CapitalDelta]f \[Kappa]E-uI vI \
\[CapitalDelta]\[Kappa]I-uP (vP-vI) \[CapitalDelta]\[Kappa]P-uA vA \
\[CapitalDelta]\[Kappa]A

This way of calculating selection makes it clearer what selection acts upon \
when a disease is spreading (\[Lambda]>0):

\t* Always favors increased transmission [\[CapitalDelta]\[Beta]A, \
\[CapitalDelta]\[Beta]P, \[CapitalDelta]\[Beta]I]
\t* Always favors lower virulence [\[CapitalDelta]\[Alpha]] and slower \
recovery [\[CapitalDelta]\[Kappa]I] 
\t* Always favors faster progression from E -> A/P [\[CapitalDelta]\[Kappa]E] \
because (1-f)vP+f vA>vE [see Note 1]
\t* Favors slower progression from P -> I [\[CapitalDelta]\[Kappa]P] if vP > \
vI [always true if \[Beta]I \[LessEqual] \[Beta]P (1+1/(D\[Lambda]) - see \
Note 2]
\t* Favors more asymptomatics individuals [\[CapitalDelta]f] only if vA>vP \
[true only with high enough \[Beta]A - see Note 3]
\t* Never favors faster progression from A -> R [\[CapitalDelta]\[Kappa]Am]\
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[Note 1] In a spreading disease, (1-f)vP+f vA is always greater than vE \
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[Note 2] vP is greater than vI as long as \[Beta]I \[LessEqual] \[Beta]P (1+(\
\[Alpha]+\[Gamma])/(\[Lambda])) because infected individuals have less time \
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Figure 3h: Evolution of virulence \[Alpha], control measures\
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If we increase the pleiotropic effect on the length of the pre-symptomatic \
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Figure 3b: Evolution of asymptomatic fraction f,  no control measures\
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Cell["\<\
Figure 3h: Evolution of virulence \[Alpha], control measures\
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Figure 3e: Evolution of transmission \[Beta], control measures\
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Cell["\<\
Figure 3g: Evolution of pre-symptomatic phase \[Kappa], control measures\
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