# [Question] Help me with bayesian thinking re:coronavirus?

If I have a fever, what is the like­li­hood that I have a coro­n­avirus in­fec­tion? I’m ac­tu­ally less in­ter­ested in the an­swer than in the un­der­ly­ing thought pro­cess, so feel free to in­sert vari­ables where re­li­able num­bers are hard to find.

I’m just hav­ing trou­ble think­ing clearly about this. Do I start with the prevalence of coro­n­avirus and ad­just that base rate by say­ing if I have a fever, the prob­a­bil­ity goes up be­cause 99% of coro­n­avirus cases have a fever? I guess I could also start with the % of fev­ers that are due to res­pi­ra­tory con­di­tions as my base rate. And then com­pare the pro­por­tion of res­pi­ra­tory-re­lated fev­ers from coro­n­avirus to other causes?

I’m hav­ing trou­ble be­cause I re­al­ize that lots of com­mon non-coro­n­avirus con­di­tions cause a fever, and that if I have a fever, the prob­a­bil­ity I have coro­n­avirus has in­creased, but I can’t figure out how to clearly con­vert the rele­vant in­for­ma­tion into a se­ries of math­e­mat­i­cal state­ments. This feels like a very prac­ti­cal ex­er­cise of bayesian think­ing, so I would love to see how peo­ple who are more fluent than I am with this kind of rea­son­ing would ap­proach this prob­lem.

Thanks!

• To an­swer prop­erly you need to know the prevalence of fever of any kind. In par­tic­u­lar, you might use the num­ber of days with fever per year you had last year /​ 365, for ex­am­ple. If you liter­ally never get a fever for years, I’d worry more then if you did.

P(19coro | fever) = P(fever| 19coro, about 0.5??) * P(19coro, per­haps 0.001??) /​ P(fever)

• Just for clar­ifi­ca­tion P(fever) must in­clude fever which comes from 19coro.

• Yes, true. The ex­act num­bers are very un­cer­tain, but the qual­i­ta­tive point re­mains that some­one who feels fever many days per win­ter has less chance of a similar day with fever be­ing from covid than some­one with a fever to­day who has had no fever for over a year.