Meshless method for solving a equation arisen form the spatial spread of an epidemic

The model of the spread of an infection within a spatially distributed population under some epi-demiological assumptions can be simulated by a nonlinear integral equation of mixed Volterra-Fredholm type. In this paper, we intend to propose a computational method for solving these types of biological problems. The presented scheme utilizes the shape functions of the local radial basis functions constructed on distributed data as a basis in the discrete collocation method. The algorithm of the new approach is computationally attractive and easy to implement on computers. Since the scheme does not require any mesh generations on the domain, it can be identi ed as a meshless method. The validity and efficiency of the new technique are demonstrated through one numerical example.

Keywords:

Infectious contagion equation , Computational biology , Volterra-Fredholm integral equation , Meshless method