Nonstandard theta Milstein method for solving stochastic multi-strain tuberculosis model

• Main Authors: Nasser H. Sweilam, Seham M. AL-Mekhlafi
• Format: Article
• Language: English
• Published: SpringerOpen 2020-03-01
• Series: Journal of the Egyptian Mathematical Society
• Subjects: A non-standard theta Milstein method; Multi-strain Tuberculosis; Mean square stability analysis
• Online Access: http://link.springer.com/article/10.1186/s42787-020-00073-9

Abstract In this article, a novel stochastic multi-strain tuberculosis model is presented. Numerical simulations for this model are the main aim of this work. A non-standard theta Milstein method is constructed to study the proposed model, where the proposed method is based on choosing the weight factor theta. The main advantage of this method is it can be explicit or implicit with large stability regions using the idea of the weighed step introduced by R.E. Mickens. Mean-square stability of nonstandard theta Milstein method is studied. The new scheme shows a greater behavior compared to the theta Milstein method. It is concluded that the proposed scheme preserves the positivity of the solution and numerical stability in larger region than the standard method.