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

• Published in: Nonlinear analysis: real world applications Vol. 50; pp. 144 - 170
• Main Authors: Khan, M.A., Shah, Syed Wasim, Ullah, Saif, Gómez-Aguilar, J.F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.12.2019; Elsevier BV
• Subjects: Asymptotic properties; Backward bifurcation; Bednets; Bifurcations; Communities; Control stability; Disease control; Infections; Insecticides; Mathematical models; Mosquitoes; Numerical results; Optimal control; Optimal control strategies; Optimal controls; Public health; Runge-Kutta method; Spraying; Stability results; Viruses; Zika asymptomatic carrier model; Zika virus; Optimal control strategies; Stability results; Optimal controls; Zika asymptomatic carrier model; Numerical results; Backward bifurcation
• ISSN: 1468-1218; 1878-5719
• DOI: 10.1016/j.nonrwa.2019.04.006

A 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 controls are solved numerically by using backward Runge–Kutta method and obtain the graphical results. The graphical results are obtained by setting appropriate set of controls and the associated results are shown. We show that each strategy has its own importance for the elimination of zika virus infection, but we suggest based on the numerical results that the uses of bednets as a prevention from the zika mosquitoes, the treatment of individuals infected through zika mosquitoes and the insecticides spraying on mosquitoes could be more useful for the elimination of zika virus infection from the community. With this new idea of asymptotic carrier class the results provided in the present paper would be more useful for public health department and other health agencies to reduce the burden of zika virus infection from the community.