A numerical study on the dynamics of SIR epidemic model through Genocchi wavelet collocation method.

Epidemic models can play a major role in understanding the spread of diseases and their control. These mathematical models have plenty of significance in various scientific domains, including public health, to investigate disease propagation and ecology. This article explains the dynamics of SIR epidemic model of arbitrary order with aid of a precise numerical approach called Genocchi wavelet collocation method. The main purpose of this investigation is to explore and discover the results for system of nonlinear ordinary differential equations arising in the considered mathematical model and to investigate the dynamical aspects of SIR model via Caputo fractional derivative which is non-local in behaviour. The projected method depicts rapid algorithms and is extremely precise, reliable, and uses fewer computational resources. Also, this method is simpler than the other traditional numerical methods as it merges the operational matrix with the collocation method in order to transform fractional-order problem into algebraic equations which enables to obtain satisfactory results. The approximate solution obtained using proposed algorithm exposes the nature of their interactions. Furthermore, the numerical outcomes are represented through graphs for different fractional order and compared the results with Runge-Kutta method and residual power series method. The projected technique is very effective, accurate, free from controlling parameters and consume less time to investigate nonlinear complications arising in diverse fields of epidemical and biological models. Ultimately, the current study help to inspect the wild class of models and their performance which are occurring in real world.