I have a dataset that contains weekly counts from 2019 to 2021. What I want to do is to compare the weekly count for a given week in 2020 to the count for the same week in 2019, and similarly compare the count in 2021 to that of the same week in 2019. The data looks like this:

set.seed(123)
df <- data.frame(count = sample(1:300, 156, replace = TRUE),
                 week = rep(seq(1, 52, by = 1), 3),
                 year = rep(2019:2021, each = 52)) 

In my real data, there is significant overdispersion, so I figured a negative binomial model may be best suited. I have run the following:

library(MASS)
nb <- glm.nb(count ~ factor(year)+factor(week), data = df)
summary(nb)

> summary(nb)

Call:
glm.nb(formula = count ~ factor(year) + factor(week), data = df, 
    init.theta = 2.193368056, link = log)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-3.5012  -0.7180  -0.0207   0.4896   1.6763  

Coefficients:
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)       5.180832   0.399664  12.963  < 2e-16 ***
factor(year)2020  0.077185   0.133587   0.578 0.563404    
factor(year)2021  0.037590   0.133609   0.281 0.778448    
factor(week)2    -0.642313   0.556042  -1.155 0.248028    
factor(week)3     0.084091   0.554446   0.152 0.879451    
factor(week)4     0.228528   0.554245   0.412 0.680103    
factor(week)5    -0.275901   0.555095  -0.497 0.619165    
factor(week)6     0.181420   0.554308   0.327 0.743448    
factor(week)7    -0.331875   0.555218  -0.598 0.550015    
factor(week)8    -0.018194   0.554608  -0.033 0.973829    
factor(week)9    -0.093659   0.554737  -0.169 0.865926    
factor(week)10   -0.260570   0.555062  -0.469 0.638753    
factor(week)11   -0.165835   0.554871  -0.299 0.765038    
factor(week)12   -0.003480   0.554583  -0.006 0.994993    
factor(week)13    0.045328   0.554506   0.082 0.934850    
factor(week)14   -0.420895   0.555429  -0.758 0.448581    
factor(week)15   -0.288260   0.555121  -0.519 0.603570    
factor(week)16   -1.719551   0.561984  -3.060 0.002215 ** 
factor(week)17   -0.339217   0.555235  -0.611 0.541237    
factor(week)18   -0.770541   0.556464  -1.385 0.166141    
factor(week)19   -0.088333   0.554728  -0.159 0.873483    
factor(week)20   -0.595712   0.555901  -1.072 0.283893    
factor(week)21   -2.010330   0.565001  -3.558 0.000374 ***
factor(week)22   -0.075819   0.554706  -0.137 0.891282    
factor(week)23    0.298783   0.554157   0.539 0.589772    
factor(week)24    0.114664   0.554401   0.207 0.836147    
factor(week)25    0.089396   0.554439   0.161 0.871907    
factor(week)26   -0.396060   0.555368  -0.713 0.475754    
factor(week)27   -0.261789   0.555065  -0.472 0.637186    
factor(week)28   -0.090157   0.554731  -0.163 0.870894    
factor(week)29    0.210589   0.554269   0.380 0.703990    
factor(week)30   -0.537967   0.555736  -0.968 0.333032    
factor(week)31   -0.401567   0.555381  -0.723 0.469651    
factor(week)32    0.108651   0.554410   0.196 0.844630    
factor(week)33   -0.732234   0.556332  -1.316 0.188113    
factor(week)34   -0.589688   0.555884  -1.061 0.288775    
factor(week)35   -0.437695   0.555471  -0.788 0.430714    
factor(week)36   -0.402218   0.555383  -0.724 0.468933    
factor(week)37   -0.076802   0.554708  -0.138 0.889881    
factor(week)38   -0.151350   0.554844  -0.273 0.785022    
factor(week)39    0.272593   0.554189   0.492 0.622806    
factor(week)40   -0.119806   0.554785  -0.216 0.829027    
factor(week)41   -1.184984   0.558260  -2.123 0.033784 *  
factor(week)42   -0.153762   0.554848  -0.277 0.781685    
factor(week)43   -0.068443   0.554693  -0.123 0.901799    
factor(week)44   -0.721053   0.556294  -1.296 0.194916    
factor(week)45    0.102378   0.554419   0.185 0.853497    
factor(week)46   -0.009142   0.554593  -0.016 0.986848    
factor(week)47   -0.284169   0.555112  -0.512 0.608712    
factor(week)48   -0.133066   0.554809  -0.240 0.810454    
factor(week)49   -0.705118   0.556242  -1.268 0.204924    
factor(week)50   -0.080921   0.554715  -0.146 0.884017    
factor(week)51    0.152016   0.554348   0.274 0.783912    
factor(week)52   -0.503605   0.555642  -0.906 0.364752    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(2.1934) family taken to be 1)

    Null deviance: 221.83  on 155  degrees of freedom
Residual deviance: 169.71  on 102  degrees of freedom
AIC: 1923.7

Number of Fisher Scoring iterations: 1


              Theta:  2.193 
          Std. Err.:  0.243 

 2 x log-likelihood:  -1813.701 

The reference category for factor(year) is 2019, which is what I want it to be. However, I am struggling with the interpretation of the coefficients (and also IRR) for week with week 1 being the reference category.

Is there a better way to do this, in order to achieve the week/year comparison? My main goal is to plot weekly IRR for 2020 and 2021, relative to 2019.