# Numerical investigation of Differential Biological Models via RBF collocation Method with Genetic Strategy

## TL;DR

This paper combines the Kansa method with a genetic algorithm to optimize the shape parameter in RBF collocation for solving biological differential models, demonstrating improved accuracy and convergence.

## Contribution

It introduces a genetic algorithm-based approach to select the optimal shape parameter in RBF collocation, enhancing solution accuracy for biological differential equations.

## Key findings

- Genetic strategy effectively finds near-optimal shape parameters.
- Pseudo-Combination crossover accelerates convergence.
- Method improves solution accuracy for HIV and Influenza models.

## Abstract

In this paper, we use Kansa method for solving the system of differential equations in the area of biology. One of the challenges in Kansa method is picking out an optimum value for Shape parameter in Radial Basis Function to achieve the best result of the method because there are not any available analytical approaches for obtaining optimum Shape parameter. For this reason, we design a genetic algorithm to detect a close optimum Shape parameter. The experimental results show that this strategy is efficient in the systems of differential models in biology such as HIV and Influenza. Furthermore, we prove that using Pseudo-Combination formula for crossover in genetic strategy leads to convergence in the nearly best selection of Shape parameter.