Mathematical analysis of a new nonlinear dengue epidemic model via deterministic and fractional approach
Yu Gu, Mohabat Khan, Rahat Zarin, Amir Khan, Abdullahi Yusuf, Usa Wannasingha Humphries
Abstract
We developed a dengue epidemic model by considering hospitalized class and harmonic mean incidence rate. A qualitative study of the proposed model was conducted. The Basic reproduction number, and local and global stability are established. The highly dominant parameters on basic reproduction number R0 have been found by sensitivity analysis. NSFD and RK-4 schemes are used for numerical solutions. Furthermore, this manuscript considers the novel fractional-order operator developed by Atangana-Baleanu for transmission dynamics of the Dengue epidemic. 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, we shall formulate the model by using the classical operator of ordinary derivatives. We utilize the fractional order derivative and the model will be extended to a model containing fractional order derivatives. The operator being used is the fractional differential operator and has fractional order Φ1. The approach of newton’s polynomial is considered and a new numerical scheme is developed which helped in presenting an iterative process for the proposed ABC system. Based on this scheme, sample curves are obtained for various values of Φ1 and a pattern is derived between the dynamics of the infection and the order of the derivative.