Random walk: Expected position 0 What would be the expected distance from the origin after making k = 10 steps I What is the probability that the walker ends up at origin? 5 steps in the positive X direction 0 How many ways can the walker end up \"I unit away from the origin...? Ir '1 n 1 III -' 1 n - 1 n 1 . .:-"; .. I, ] .. I: 4'] ._.. I. I . .. . \"'I - + 3 1'I._1o_; + 2 ' .1 [8) + 2 (a) + 2 (4.} + + 2 '+ l3} --_3 ' If] Recall Combinatorics! Remember n! (factorial) 1 x 2 x 3... x (n-1} x n Remember (:3) (n cheese k) - given n objects, how many ways are there to pick k {without repetition)? _ n] '_. It] (in. k. j]! Mathematical Modeling of Epidemics . Susceptibles Infectives Removals (SIR) model . Susceptibles Exposed Infectives Removals (SEIR) . Susceptibles Infectives Susceptibles (SIS) 2500 Susceptible Susceptibles as Infected Recoverd -......- S = -asI 2000 dt 1500 dI -=+asI -61 Population Infectives dt 1000 I dR 500 -=+61 dt 20 30 40 50 70 Time Steps Removed R Let a be the transmission rate based on contact rate and infectivity Let ybe the rate of infectives becoming non-infectious