  We develop non-linear integro-differential kinetic equations for
proliferating L\'{e}vy walkers with birth and death processes. A hyperbolic
scaling is applied directly to the general equations to get the Hamilton-Jacobi
equations that will allow to determine the rate of front propagation. We found
the conditions for switching, birth and death rates under which the propagation
velocity reaches the maximum value, i.e. the walker's speed. In the strong
anomalous case the death rate was found to influence the velocity of
propagation to fall below the walker's maximum speed.
