Backward Bifurcation and Control in Transmission Dynamics of Arboviral\n Diseases

Abstract

In this paper, we derive and analyze a compartmental model for the control of\narboviral diseases which takes into account an imperfect vaccine combined with\nindividual protection and some vector control strategies already studied in the\nliterature. After the formulation of the model, a qualitative study based on\nstability analysis and bifurcation theory reveals that the phenomenon of\nbackward bifurcation may occur. The stable disease-free equilibrium of the\nmodel coexists with a stable endemic equilibrium when the reproduction number,\nR 0 , is less than unity. Using Lyapunov function theory, we prove that the\ntrivial equilibrium is globally asymptotically stable; When the disease--\ninduced death is not considered, or/and, when the standard incidence is\nreplaced by the mass action incidence, the backward bifurcation does not occur.\nUnder a certain condition , we establish the global asymptotic stability of the\ndisease--free equilibrium of the full model. Through sensitivity analysis, we\ndetermine the relative importance of model parameters for disease transmission.\nNumerical simulations show that the combination of several control mechanisms\nwould significantly reduce the spread of the disease, if we maintain the level\nof each control high, and this, over a long period.\n