A basic general model of vector-borne diseases

Tchoumi, S. Y.; Kamgang, J. C.; Tieudjo, D.; Sallet, G.

doi:10.28919/cmbn/3485

Commun. Math. Biol. Neurosci. 2018 (2018), Article ID 3

A basic general model of vector-borne diseases

S. Y. Tchoumi, J. C. Kamgang, D. Tieudjo, G. Sallet

PDF (453.7 KB) https://doi.org/10.28919/cmbn/3485

Abstract

We propose a model that can translate the dynamics of vector-borne diseases, for this model we compute the basic reproduction number and show that if $\mathcal{R}_0<\zeta<1$ the DFE is globally asymptotically stable. For $\mathcal {R}_0>1$ we prove the existence of a unique endemic equilibrium and if $\mathcal {R}_0 \leq 1$ the system can have one or two endemic equilibrium, we also show the existence of a backward bifurcation. By numerical simulations we illustrate with data on malaria all the results including existence, stability and bifurcation.

Published: 12 February 2018
Volume: 2018 (2018)
License: CC BY 3.0

Copyright © 2018 S. Y. Tchoumi, J. C. Kamgang, D. Tieudjo, G. Sallet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

S. Y. Tchoumi, J. C. Kamgang, D. Tieudjo, G. Sallet, A basic general model of vector-borne diseases, Commun. Math. Biol. Neurosci. 2018 (2018), 3. https://doi.org/10.28919/cmbn/3485

BibTeX

@article{Tchoumi2018,
  author  = {Tchoumi, S. Y. and Kamgang, J. C. and Tieudjo, D. and Sallet, G.},
  title   = {A basic general model of vector-borne diseases},
  journal = {Commun. Math. Biol. Neurosci.},
  volume  = {2018},
  year    = {2018},
  pages   = {3},
  doi     = {10.28919/cmbn/3485}
}