Dynamical behavior and sensitivity analysis of a dengue reinfection model for vertical transmission incorporating multiple control strategies

Abstract

The dynamics of dengue disease with reinfection and three control techniques are proposed in this research. The epidemic model includes a saturated incident function in virus transmission among humans. The vertical transmission of the virus in vectors and a reinfection scenario in the human population are added to the proposed dengue epidemic model. In relation to the basic reproduction number R₀, the existence and stability of the equilibrium points of the proposed epidemic model are studied. The equilibrium states of the epidemic model are examined for both local and global stability. For the basic reproduction number R₀, a sensitivity analysis is carried out in relation to various parameters. Bifurcation analysis is performed for the proposed model, and the bifurcation parameter is identified. In the proposed dengue epidemic model, we introduce three time-dependent controls: protection control, treatment control, and insecticide spray control. In the proposed model, a control problem is identified and analytically solved. The conditions for the optimal control strategies for the control problem are derived using Pontryagin’s maximal principle. In order to demonstrate the effectiveness of the control measures, numerical simulations are used. Finally, suggestions for preventing the spread of the dengue virus are presented.