Whats the probability of not getting a disease today where. t = transmition rate given contact with infected individual r = % of population infected c = number of contacts today
is it A) (1-rt)^c i.e. I meet c people , for each person the chance is transmitionRate * chance they have disease.
B) (1- t)^cr i.e. I'm likely to meet cr infected people , each meeting has a probability of t to transfer the disease.
Both seem valid, have similar but not identical results. e.g. if r=0.01 , c =100, t =0.5. the results are A~0.6 B=0.5. B seems accurate if I imagine the entire population = 100, then the actual result = 0.5.
Whats the difference/breakdown in the logic ?