Numerical Assessment of Some Semi-Analytical Techniques for Solving a Fractional-Order Leptospirosis Model.

Abstract

This research aims to apply and compare two semi-analytical techniques, the Variational Iterative Method (VIM) and the New Iterative Method (NIM), for solving a pre-formulated mathematical model of Fractional-order Leptospirosis. Leptospirosis is a significant bacterial infection affecting humans and animals. By implementing the VIM and NIM algorithms, numerical experiments are conducted to solve the leptospirosis model. Comparing the obtained findings demonstrates that VIM and NIM are effective semi-analytical methods for solving systems of fractional differential equations. Notably, our study unveils a crucial dynamic in the disease's spread. The application of VIM and NIM offers a refined depiction of the biological dynamics, highlighting that the susceptible human population gradually decreases, the infectious human population declines, the recovered human population increases, and a significant rise in the infected vector population is observed over time. This nuanced portrayal of the disease's dynamics is crucial for understanding the intricate interplay of Leptospirosis among human and vector populations. The study's outcomes contribute valuable insights into the applicability and performance of the methods in solving the Fractional Leptospirosis model. Results indicate rapid convergence and comparable outcomes for both methods.