Solving fractional Hantavirus model: A new approach

TL;DR

This paper introduces a novel algorithm combining Daftardar-Jafari Method and implicit θ-method to solve the Caputo time-fractional Biodiversity Hantavirus model with optimal control, providing insights into parameter effects.

Contribution

A new numerical algorithm is developed for solving fractional differential equations, specifically applied to the optimal controlled Caputo fractional Hantavirus biodiversity model.

Findings

The algorithm effectively solves the fractional model.

Parameter variations significantly affect model outcomes.

The solutions provide detailed insights into disease spread dynamics.

Abstract

A three equation differential biodiversity model depicting spread and propagation of Hantavirus epidemic amongst rodent species under the influence of alien competing mouse species was introduced by Peixoto and Abramson in 2006. We analyze the Caputo time-fractional version of the Biodiversity model along with added optimal control parameters as done by Yusof, Abdullah et al. A new algorithm is proposed to solve fractional differential equations which is derived from the implementation of Daftardar-Jafari Method(DJM) and implicit $\theta$-method with $\theta=1$. This newly proposed algorithm is then used to integrate the Optimal controlled Caputo time-fractional version of Biodiversity Hantavirus model (OC-CTFBH model). The obtained solutions are plotted and analyzed further for the effects of parameter variations.