Fuzzy Approach Analyzing SEIR-SEI Dengue Dynamics.

Dengue fever is a mosquito-borne infectious disease threatening more than a hundred tropical countries of the world. The heterogeneity of mosquito bites of human during the spread of dengue virus is an important factor that should be considered while modeling the dynamics of the disease. However, traditional models assumed homogeneous transmission between host and vectors which is inconsistent with reality. Mathematically, we can describe the heterogeneity and uncertainty of the transmission of the disease by introducing fuzzy theory. In the present work, we study transmission dynamics of dengue with the fuzzy SEIR-SEI compartmental model. The transmission rate and recovery rate of the disease are considered as fuzzy numbers. The dynamical behavior of the system is discussed with different amounts of dengue viruses. Also, the fuzzy basic reproduction number for a group of infected individuals with different virus loads is calculated using Sugeno integral. Simulations are made to illustrate the mathematical results graphically.