A basic general model of vector-borne diseases

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

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.

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Published: 2018-02-12

How to Cite this Article:

S. Y. Tchoumi, J. C. Kamgang, D. Tieudjo, G. Sallet, A basic general model of vector-borne diseases, Communications in Mathematical Biology and Neuroscience, Vol 2018 (2018), Article ID 3

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.

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