Abstract:
Crop host-pathogen interaction have
been a main issue for decades, in particular for food
security. In this paper, we focus on the modeling
and long term behavior of soil-borne pathogens. We
first develop a new compartmental temporal model,
which exhibits bi-stable asymptotical dynamics. To
investigate the long term behavior, we use LaSalle
Invariance Principle to derive sufficient conditions
for global asymptotic stability of the pathogen
free equilibrium and monotone dynamical systems
theory to provide sufficient conditions for permanence
of the system. Finally, we develop a partially
degenerate reaction diffusion system, providing a
numerical exploration based on the results obtained
for the temporal system. We show that a traveling
wave solution may exist where the speed of the wave
follows a power law.
