Numerical investigation of differential biological models via Gaussian RBF collocation method with genetic strategy

Document Type : Regular paper


1 Department of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 ‎Department of Computer Engineering, Chosun University, Gwangju 61452, Republic of Korea

3 Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University


In this paper, we use radial basis function collocation method for solving the system of differential equations in the area of biology. One of the challenges in RBF method is picking out an optimal 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 optimal shape parameter. For this reason, we design a genetic algorithm to detect a close optimal shape parameter. The population convergence figures, the residuals of the equations and the examination of the ASN2R and ARE measures all show the accurate selection of the shape parameter by the proposed genetic algorithm. Then, the experimental results show that this strategy is efficient in the systems of differential models in biology such as HIV and Influenza. Furthermore, we show that using our pseudo-combination formula for crossover in genetic strategy leads to convergence in the nearly best selection of shape parameter.


Volume 1, Issue 2 - Serial Number 2
December 2022
Pages 46-64
  • Receive Date: 13 November 2022
  • Revise Date: 01 January 2023
  • Accept Date: 04 January 2023
  • First Publish Date: 04 January 2023