Sensitivity and Bifurcation Analysis of Fuzzy SEIR-SEI Dengue Disease Model

Abstract

Dengue is one of the most serious mosquito-borne infectious diseases in the world. The number of dengue cases is increasing every year worldwide. In this work, we discuss the fuzzy epidemic SEIR-SEI compartmental model with the intervention of bed nets and fumigation to describe the transmission dynamics of dengue disease. We consider the biting rate, transmission rate, and recovery rate of the disease as fuzzy numbers. With different amounts of virus loads, we discuss the dynamical behavior of the system. The sensitivity analysis of the model is performed to compare the relative importance of the model parameters and to discuss the importance of fumigation, use of bed nets, and the effectiveness of bed nets. We demonstrate the bifurcation of the equilibrium point of the system with and without fumigation, with and without bed net user, and with different levels of effectiveness of bed nets. Numerical simulations are made to illustrate the mathematical results graphically. The infectivity of the disease depends on the amount of virus loads. The mathematical and simulated result shows that the intervention strategies, use of fumigation and bed nets, reduces the value of the basic reproduction number. Thus, this study suggests that the endemic situation of the disease can be brought under control by the effective use of the combination of fumigation and bed nets.