@article{fdi:010055796,
  title = {{S}tability and {H}opf bifurcation of a mathematical model describing bacteria-fish interaction in marine environment},
  author = {{K}acha, {A}. and {H}bid, {M}. {L}. and {A}uger, {P}ierre},
  editor = {},
  language = {{ENG}},
  abstract = {{I}n this work, we present and study a model of a host-parasite system in marine environment, which describes the population dynamics of fish ({T}ilapia) which can be infected by botulinum. {T}he mathematical model is structured by levels of infection. {U}sing the characteristic curves method, we transform the model into a system of distributed delay differential equations. {W}e study the existence of {H}opf bifurcation. {F}ollowing the method presented by {H}assard et al. (1981) [5], we prove analytically the stability of limit cycle periodic solutions. {W}e present numerical and computer simulations of the model.},
  keywords = {{S}tructured population model ; {D}istributed delay ; {L}ocal stability ; {H}opf bifurcation ; {B}otulinum ; {T}ilapia},
  booktitle = {},
  journal = {{A}pplied {M}athematics and {C}omputation},
  volume = {218},
  numero = {17},
  pages = {8226--8241},
  ISSN = {0096-3003},
  year = {2012},
  DOI = {10.1016/j.amc.2010.12.084},
  URL = {https://www.documentation.ird.fr/hor/fdi:010055796},
}