Modeling the Dynamics of Arboviral Diseases with Vaccination Perspective

Authors

  • Hamadjam Abboubakar Department of computer sciences, University of NgaoundГ©rГ©
  • Jean Claude Kamgang ENSAI-University of NgaoundГ©rГ©
  • Nkague Leontine Nkamba ENS--University of YaoundГ© I
  • Daniel Tieudjo ENSAI-University of NgaoundГ©rГ©
  • Lucas Emini Polytechnic–St. Jerome Catholic University, Douala

DOI:

https://doi.org/10.11145/j.biomath.2015.07.241

Keywords:

Mathematical model, Arboviral disease, Vaccination, Stability, Backward bifurcation, Sensitivity analysis, Numerical scheme.

Abstract

In this paper, we propose a model of transmission of arboviruses, which take into account a future vaccination strategy in human population. A qualitative analysis based on stability and bifurcation theory reveals that the phenomenon of backward bifurcation may occur; the stable disease-free equilibrium of the model coexists with a stable endemic equilibrium when the associated reproduction number is less than unity. We show that the backward bifurcation phenomenon is caused by the arbovirus induced mortality in humans. Using theВ direct Lyapunov method, we show the global stability of the trivial equilibrium. Through global sensitivity analysis, wedetermine the relative importance of model parameters for disease transmission. Simulation results using a qualitatively stable numerical scheme, are provide to illustrate the impact of vaccination strategy in human community.

Author Biographies

Hamadjam Abboubakar, Department of computer sciences, University of NgaoundГ©rГ©

Department of Computer Science, Assistant-Lecturer

Jean Claude Kamgang, ENSAI-University of NgaoundГ©rГ©

Department of Mathematics and Computer Science

Nkague Leontine Nkamba, ENS--University of YaoundГ© I

Department of mathematics

Daniel Tieudjo, ENSAI-University of NgaoundГ©rГ©

Department of mathematics and computer science

Lucas Emini, Polytechnic–St. Jerome Catholic University, Douala

Department of Mathematics,

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Published

2015-08-27

Issue

Section

Original Articles