Stochastic Models in Biology

Code: MA665 | L-T-P-C: 3-0-0-6

Prerequisites: MA 225 or equivalent and MA 590 or equivalent

Course Content/ Syllabus: Review of probability theory and stochastic processes; Discrete-time Markov chains, classification of states, first passage time, stationary probability distribution, finite Markov chains, Monte Carlo simulation, biological applications of discrete-time Markov chains; Discrete-time branching processes; Continuous-time Markov chains, generator matrix, embedded Markov chains, classification of states, Kolmogorov differential equations, stationary probability distribution, finite Markov chains, generating function techniques, biological applications of continuous-time birth, death and Markov chains; Diffusion process, stochastic differential equations, biological applications of stochastic differential equations.

Texts:

1. Linda J.S. Allen, An Introduction to Stochastic Processes with Applications to Biology, Second Edition, CRC Press, 2011.

References:

1. James D. Murray, Mathematical Biology I: An Introduction, Interdisciplinary Applied Mathematics, Third Edition, Springer, 2007.