Quite a few more syntax errors in your code: separate operations are separated by semi-colons, not commas. And you can't do something like 1/etau = 0.05: you need etau = 1/0.05.
Here is a better way to do what you posted:
Clear["Global`*"]
parameters = {betas -> 0.274, mu -> 0.062, gammaa -> 0.29,
alphaa -> 0.4775, etau -> 1/0.05, alphau -> 0.695, qi -> 0.078,
etai -> 1/0.009};
baseR0 = (betas*alphaa)/(gammaa + mu) + (betas*alphau*
gammaa*(1 - qi))/((gammaa + mu)*(etau + mu)) /. parameters
Now, assuming everything is correct, this does what you describe:
In[119]:= Table[
oldParameter = parameters[[parameter, 2]];
newParameter = oldParameter*1.001;
deltaParameter = newParameter - oldParameter;
newR0 = (betas*alphaa)/(gammaa + mu) + (betas*alphau*
gammaa*(1 - qi))/((gammaa + mu)*(etau + mu)) /.
ReplacePart[parameters, {parameter, 2} -> newParameter];
deltaR0 = newR0 - baseR0;
{parameters[[parameter,
1]], (oldParameter/baseR0)*(deltaR0/deltaParameter)}, {parameter,
1, Length[parameters] - 1}]
Out[119]= {{betas, 1.}, {mu, -0.176164}, {gammaa, -0.804172}, {alphaa,
0.980971}, {etau, -0.0189516}, {alphau,
0.0190293}, {qi, -0.00160985}}
As you see though, it doesn't give the same values you posted. So it's possible there is something wrong with either your formula for R0 value, or for the sensitivity.
