@article{fdi:010044348,
  title = {{M}athematical study of a bacteria-fish model with level of infection structure},
  author = {{K}acha, {A}. and {H}bid, {M}. {H}. and {B}ravo de la {P}arra, {R}afael},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this paper, we propose a mathematical model to study a bacteria-fish system, based upon the interactions between {C}lostridium botulinum and tilapia, {O}erochromis mossambicus. {T}he fish population is divided into susceptible and infected, and the infected fish population is considered structured by the level of infection. {T}he model is thus a system with the infected fish equation being an evolution equation, while those corresponding to the susceptible fish and bacteria in water are ordinary differential equations. {T}he model is firstly transformed into a system with distributed delay for susceptible fish and bacteria and, further, under some assumptions, into a system with discrete delay. {T}he study of this system gives us some results concerning the existence, uniqueness, positivity and boundedness of solutions; we also discuss the existence and stability of its equilibrium points, including conditions for the appearance of {H}opf bifurcation. {T}he theoretical results are illustrated by some numerical simulations.},
  keywords = {{C}ontinuous host-parasitoid model ; {S}tructured population ; {T}ime delay ; {L}ocal stability ; {H}opf bifurcation},
  booktitle = {},
  journal = {{N}onlinear {A}nalysis - {R}eal {W}orld {A}pplications},
  volume = {10},
  numero = {3},
  pages = {1662--1678},
  ISSN = {1468-1218},
  year = {2009},
  DOI = {10.1016/j.nonrwa.2008.02.021},
  URL = {https://www.documentation.ird.fr/hor/fdi:010044348},
}