Design, analysis and simulation of a robust numerical method to solve Zika virus models

Abstract

This thesis deals with the analysis and robust simulation of mathematical models describing Zika virus disease. Some background information about the occurrences of this disease and most recent literature indicating some research gaps is presented. Governing models are very complex and their analytical solutions are hard to obtain. This necessitates the use of robust numerical methods. Several models from literature are presented in this work. One particular model is further studied in details for the purpose of understanding key qualitative features of the solutions of these types of models. These features are essential when we wish to develop a robust numerical method. After studying these properties on the dynamics of the solution for a particular model, we developed a novel numerical method, known as the non-standard nite difference method (NSFDM). A detailed theoretical analysis of this method, which is in line with necessary qualitative features of the solution of the governing model, is also presented. Finally, extensive numerical results showing competitiveness of this new method, as compared to other classical methods, are provided. In particular, we have shown how classical methods fail when the discretization step-size is large whereas NSFDM still gives excellent in such cases.