Some Biomathematical Models Applying the Adomian Method Pedro Pablo Cárdenas Alzate* 1 , José Gerardo Cardona Toro 2 , and Luz María Rojas Duque 3 1 Research in Nonlinear Differential Equations (GEDNOL), Department of Mathematics, Universidad Tecnológica de Pereira, Pereira, Colombia 2 Research in Statistics and Epidemiology (GIEE), Department of Mathematics, Universidad Tecnológica de Pereira, Pereira, Colombia 3 GIEE, Fundación Universitaria del Área Andina, Pereira, Colombia Abstract : The approximate interpretation of some natural phenomena has led to introduce in certain types of differential equations changes in the temporal variable called delays, which makes these equations and their solutions have a more consistent behavior with reality. These equations, called differential equations with delay require complex methods for their solution and in most cases, only a numerical approximation is achieved. In this article we initially show a theoretical development on the decomposition method applied to ordinary differential equations with delay in which the most important properties were studied. Subsequently, the most relevant Adomian polynomials were tested; some biological models that involve differential equations with delay and integro-differential equations were solved. Finally, the numerical comparison was made with other approximation methods and the convergence of the method in some solutions was analysed. Keywords: Biomathematical Models, Adomian Method. Introduction The Adomian Decomposition Method is of great importance in the resolution of non-linear differential equations with initial value and at the border, with the need to know methods that are generally of the semi-analytical numerical type using solutions 1,2,3 of the form ()  ∑     . In general, this method consists of converting a differential equation of real domain into a simpler one (iterative equation) of natural domain. We use the definition and a series of theorems that are applied depending on the characteristic of each of the terms of the differential equation to transform. In essence, this method has its reason for being in the so- called Adomian polynomials and their serial solution, since it is sought to reach an infinite series that represents the approximation of the solution of the equation 4,5 . Pedro Pablo Cárdenas Alzate et al /International Journal of ChemTech Research, 2018,11(07):239-246 DOI= http://dx.doi.org/10.20902/IJCTR.2018.110729 International Journal of ChemTech Research CODEN (USA): IJCRGG, ISSN: 0974-4290, ISSN(Online):2455-9555 Vol.11 No.07, pp 239-246, 2018