Deterministic and fractional analysis of a newly developed dengue epidemic model

Abstract

This paper presents a new non-linear dengue epidemiological model with a new type of incidence rate called convex incidence rate. A qualitative study of the proposed model was conducted. Local and global stability and the threshold value are established. By using sensitivity analysis, the highly dominant parameters on the threshold value have been found. For numerical solutions, RK-4 and NSFD schemes are used. Moreover, the novel fractional-order operator created by Atangana-Baleanu for transmission dynamics of the Dengue epidemic model is considered in this paper. Assuming the importance of the non-local Atangana-Baleanu fractional-order approach, the transmission mechanism of Dengue has been investigated while taking into account different phases of infection and various transmission routes of the disease. To conduct the proposed study, first of all, By using the classical operator of ordinary derivatives, we will formulate the model. The fractional order derivative is used and We will expand the model to include fractional order derivatives. The operator being used is the fractional differential operator and has fractional order considered the process of Newton's polynomial for the proposed ABC model a new numerical scheme is developed which helped in presenting an iterative process. Using this scheme, for different values of sample curves are obtained and a pattern is established between the order of the derivative and the dynamics of the infection.