In   this presentation, I will first talk about the discrepancies between   theoretical predictions and lab observations on the wave speeds of traveling   waves formed by amoebas' dispersal. Then I will present analytical solutions   to the telegraph equations with/without bias, which correspond to correlated   random walks with/without bias.

Our   simulations show that the solutions can be approximated very well by   correlated random walks. Furthermore, the mean first passage time is also   highly consistent with that obtained from the corresponding random walks.This   suggests an easy method for biologists to estimate parameter values of the   telegraph equations. Finally, I will present some related open questions.