Certainly not GARCH models, mainly build for financial time series

GARCH is not so good as the Error term of COVID cases may or may not be serially correlated. (you need to check the pattern of the data to check the suitability of GARCH)

ARIMA is seems to be good here as the event could be fairly independent.

Wow. Did you pick a hard topic. 1) What do we know about the lifecycle of the dependent variable? Historically, coronavirus contagions follow an F/Chi-squared/Rayleigh type distribution, in a closed system. And that is true whether it is a small system or a large system. 2) What did previous researchers do wrong for covid? Have you read Neil Ferguson's original paper? He made numerous errors which you should not duplicate. Not only were all his parameters wrong, but all of his scenarios were wrong too. When I say "wrong", I don't mean he missed his forecast by 1%. I mean, he missed his forecast by over 90%. He claimed there would be 2.2 million deaths in the four months of flu season for just the US. There were far less than 100,000 "deaths" during that time. I put death in quotes, because that is the next problem. 3) Then there are the dual issues of measurement error and changing of standards. In March of 2020, the CDC changed the way coronaviruses were 'handled' on death certificates in the US. In the past, coronaviruses were never the official "cause of death". Ultimately, what this meant is that people who had stage 4 cancer and were already at death's door, but also had 1 symptom of covid, then they were 'coded' as covid-positive (corrupts your covid-test data, because we don't know for sure that they even had the virus in their body) and then when they died, they were 'coded' as a covid-death (corrupts your covid-deaths data because the real cause of death was cancer, not covid). Now we can look back and see that cancer deaths went down significantly and covid deaths went up. Meanwhile the total number of deaths (from any cause) went down. Obviously all of these factors will change depending upon what country you are studying. But I have observed similar factors across most countries dealing with covid19. This is problematic, because your objective should be to "model" reality. But if the data for "reality" has been significantly corrupted, then how will you know when your model is "doing a good job"? I recommend that you go back and study the literature from the SARS virus. circa 2003. There were several great papers that studied how the virus was contracted, how the uniform diagnosis was made for each case and how each country modelled the case counts.