A dynamical study of a fuzzy epidemic model of Mosquito-Borne Disease

Abstract

Numerical models help us to understand the transmission dynamics of infectious diseases. Since vectors transmit many diseases, vector host models are very important. The transmission dynamics of Dengue fever with an incubation period of the virus with fuzzy parameters have been analyzed in this article. Sometimes it is very difficult and almost impossible to collect numerical data as a fixed value. Due to the lack of precise numerical data for the parameters, the fuzzy model is considered here. Fuzzy theory is a very powerful mathematical tool for dealing with imprecision and uncertainties. In this article, the chance of the occurrence of dengue infection β_h(a), the recovery rate r(a) and the mortality rate of the human population μ_h(a) due to dengue fever are considered fuzzy numbers. The stability of equilibrium points of the model has been determined and a reproduction number has been derived respectively in a fuzzy sense. A numerical model is designed for the studied model having fuzzy parameters and some numerical experiments are performed which indicate that the proposed method shows positivity, stability, and convergence at each time step size. Hence the method preserves the essential features of the dynamic epidemic models.

Keywords: Convergence analysis; Dengue fever; Fuzzy basic reproduction (FBR) number; Fuzzy nonstandard finite difference (FNSFD) technique; Fuzzy parameters; Stability analysis.