A dynamical model of asymptomatic carrier zika virus with optimal control strategies

Publication date: December 2019Source: Nonlinear Analysis: Real World Applications, Volume 50Author(s): M.A. Khan, Syed Wasim Shah, Saif Ullah, J.F. Gómez-AguilarAbstractA dynamical model of asymptomatic carrier zika virus model with optimal control strategies is presented. The basic model zika without control and basic mathematical results are obtained. The stability results for the zika model without controls are obtained when the basic reproduction number is less than unity at the disease free case. We show that the zika model without controls is locally and globally asymptotically stable when the basic reproduction number is less than 1. Further, we show the model stability at the endemic equilibrium and present that the model at the endemic equilibrium is locally and globally asymptotically stable when R0>1. Further, for the case when R0=1, we analyze the model and presents its backward bifurcation, and it may have the phenomena of backward bifurcation if the conditions provided is satisfied. After that we chose the appropriate controls for the zika virus eliminations and formulated the zika control model. These controls are the preventions through bednets, the treatment of the infected individuals due to zika virus infection, and the insecticides spraying on mosquitoes. With these controls, the model and the optimal controls characterizations are obtained. Furthermore, we provided the existence of optimal control problem. The model with controls and the model without c...
Source: Nonlinear Analysis: Real World Applications - Category: Research Source Type: research