A first dynamic population invasion study from reactive-telegraph equation and boundary element formulation

A second dynamic population invasion study from reactive telegraph equation and boundary element formulation – a numerical assay about tumour growth in vitro

“…One disadvantage of all the usual models is that they go to the carrying support faster than what is expected (Varalta, 2014). This is one of the advantages of the telegraphic model proposed by (Pettres, 2021), and it is here that this paper seeks to contribute with the theme, continuing the research based on a probabilistic model of an avascular-tumour growth in vitro simulating a tissue healthy (Ward and King, 1997), as well as a phenomenon of population invasion, under a more complete approach in relation to the model proposed by (Forys and Marciniak-Czochra, 2003), in which the authors used a simple logistic equation with time delay and simulated a diffusion problem.…”

“…In biological sciences, the telegraph equation can be used in studies of dispersal of species and/or populations in homogeneous environments in a probabilistic way, as in the work presented by Godoi (2021), by Malinzi (2021) about a model for oncolytic virus spread using the telegraph equation and also by Pettres (2021), in that the author present a variation of the telegraph equation, called the reaction-telegraph equation to simulate a problem of population invasion in a two-dimensional domain, making an analogy with the process of tumour growth in healthy tissue.…”

“…For this purpose, an expanded version of the two-dimensional formulation of the boundary element called D-BEM presented by this author in (Pettres, 2021) is used, which is now presented as a continuation of the study already carried out on the telegraphic-diffusive phenomenon, here applied to tumour growth in vitro from different reactive terms defined by four growth models in the formulation.…”

“…D-BEM formulation used in this paper, widely deduced and explored in (Pettres, 2021), uses a time-independent fundamental solution to the potential problem in 2D combined with a timeadvance scheme based on the finite difference for the diffusion term (first derivative) and the wave term (second derivative) to solve the telegraph equation. This formulation reached a correlation level higher than 0.9 measured at the R 2 coefficient and with an average percentage error of approximately 8 per cent as described in (Pettres, 2021) from two problems with known analytical solutions. D-BEM formulation appears as a good option for the development of a hybrid numerical method, with the possibility of inserting different reactive terms in a simple way.…”

Linear barycentric rational collocation method for solving telegraph equation

“…A modified Galerkin method 21 is used to solve the two‐dimensional telegraph equation. The boundary element method (BEM) 22 is proposed to solve the 2‐D telegraph equation with application in population dynamic invasion. The sinc‐Chebyshev collocation method 23 is used to solve time fractional order telegraph equation.…”