[Question] Estimating COVID cases & deaths in India over the coming months

Does anyone have a good method to estimate the number of COVID cases India is likely to experience in the next couple of months? I realize this is a hard problem but any method I can use to put bounds on how good or how bad it could be would be helpful.

I’m trying to convince some people who work in global health to send the US stockpile of unused and unapproved Astra Zeneca vaccines to the hardest hit parts of India. My naive calculation indicates sending 25,000,000 doses (basically our whole stockpile) would save at least 17,000 lives using fairly conservative assumptions. But that was based on an estimate that 20% of the total population would be infected and a third of those would be infected after the vaccines we send are injected and become effective.

The 20% is based on the rate of US infections and the 1/​3rd is basically a random guess about how many infections there would be left between vaccination and the end of the pandemic.