Would you mind explaining the maths to me, I have a mathematics degree so you can get reasonably complex. Issue one, I have a 85 year old to care for who I don

Would you mind explaining the maths to me, I have a mathematics degree so you can get reasonably complex. Issue one, I have a 85 year old to care for who I don't want to kill by getting the virus by unknown means and asymptotically giving them virus. When I know contact point there is no unknown period to self isolate for. Issue two, while it's quite, in the minuscule change I got really sick (I am very low chance of complications) it would be better to go to hospital now than kicking out an older person in a few months time. I doubt I will be going to hospital. Issue three, I'd like to contribute to herd immunity by getting a Claytons vaccine, I don't think other's should feel obliged but those who wish to should be allowed. I am aware you may be able to get it twice after a unknown period, there is no evidence this is possible for most people in a short time. If that was true we are very much in trouble. I'm also aware it seems like it can become active again in some people, these seem to be misidentified as catching it twice. I'm aware vaccines are at crazy best a year away. I'm aware treatments are improving. How would you model this?