ABSTRACT
In this study, an algorithm based on collocation approach for the investigation of the acute inflammatory response dynamic model is proposed. The analytical results for linear stability of the system around the equilibria are also presented. A previously described model that is analysed here explains the dynamics of acute inflammatory response of the body under circumstances of infection. Then, the problem is considered including initial conditions, and its numerical solutions are obtained by a numerical method. The method transforms the problem into the matrix equations and the collocation points are applied to find solutions point wise at the given interval. On the other hand, stability analysis of the dynamical system around the positive equilibrium is performed. Besides, an error analysis, some simulations related to the numerical solutions and the results for bifurcation analysis of the system are given in order to show the efficiency and applicability of the method and the behaviour of the model.
