Strengths:
A novel model developed to investigate COVID-19 transmission.
Suggestions:
It can be important to estimate the initial value \(I_0\) since it can have considerable effect on the dynamics.
Likelihood should not be reported to 4 decimal places. 1 or 2 is sufficient.
The measurement model for the SEIQR model is curious. Cases are an instantaneous measurement of Q, so individuals in Q can be counted in many measurement intervals (or none at all, if they move quickly out of Q). Generally, one needs an accumulator variable to make a reasonable measurement model.
Conclusion: “The log likelihood value of the SEIQR model is the lowest” is a typo, and should read “highest”
It would be useful to have ARMA or iid benchmarks. The SIR and SEIR log likelihoods are very low, perhaps suggesting a problem with the model.
One problem may be in the measurement models, which have only binomial variability. There is also no process over-dispersion. In the absence of a benchmark likelihood, it is hard to say whether these are fatal flaws.
SEIQR has been used in a previous STATS/DATASCI 531 project (https://ionides.github.io/531w20/final_project/Project37/final.html), but here the development seems to be independently derived from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8053363/
The initializer does not quite satisfy the constrain of summing to \(N\).
In the implementation of the measurement model, the authors manually override the loglikelihood as -1000 whenever the loglikelihood is numerically evaluated as infinite. This requires care since it could hide other problems.
The local search suggests a initial susceptible rate \(\eta\) from roughly 0.94 to 0.96. The authors also stats that the best initial guess of parameters is with \(\eta = 0.95\). However, in the global search, the authors used a range of 0.4 to 0.6 for the parameter \(\eta\).
Where possible, numbers should not be hard-coded in the Rmd document. Rather, they should be referenced using
`r my_variable`