Comparison of Virus Spread Models Akhil Alapaty Mentor

Comparison of Virus Spread Models Akhil Alapaty Mentor: Philip Paré N 2 State Model N-intertwined Markov Chain Model if xm = 1, i = j + 2 m-1 Initial Condition if xm = 0, i = j – 2 m-1 2 N State Model Chain Model * if i = j N-intertwined Markov ** otherwise Error Between Models ||E(y(t)) – p(t)|| Line Graph Error 1/10 1 10 n ------ 6 0 8 Star Graph Error ------ 1/10 ------ 1. 02 0. 64* 0 1. 12 0. 39** 0 1. 24 0. 31 0 1. 36 10 0 1. 43 0. 33 0 1. 67 0. 37 0 1/10 1 10 n ------ 6 0 1. 02 0. 45 8 0 1. 24 10 0 13 n 6 8 10 13 Tree Graph 1/10 ------ 0 1. 05 0. 48 0. 06 0 1. 36 0. 25 1. 55 0. 04 0 1. 52 0. 28 1. 80 0. 03 0 1. 80 0. 03 10 1/10 ------ ------ 0 1. 12 0. 35 0 1. 05 0. 41 0. 04 0 1. 36 0. 02 0 1. 36 0. 01 1. 43 0. 02 0 1. 55 0 0 1. 52 0. 01 0 1. 67 0. 02 0 1. 80 0 1/10 1 10 -----0 0 -----1. 12 1. 36 1. 55 1. 80 -----0 0 -----1. 02 1. 24 1. 43 1. 67 -----0. 45 0. 04 0. 02 1/10 -----0 0 1 1 -----1. 12 1. 36 1. 55 1. 80 10 -----0. 35 0. 02 0 0 1 Conclusion Analyzing the errors between the two models for the different sets of parameters (healing rate, infected rate, number of agents, initial agents being sick), it seems clear that the Markov Chain Model, in some cases, is a fairly good approximation, and always upper bounds the 2 N State Model. 10 -----0. 35 0. 02 0 0