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

Authors

1 University of Gunma, Hoshikuki-cho 798-8, Chuou-Ward, Chiba 260-0808, Japan

2 Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Pusan 608-737, Republic of Korea

3 Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577-8502, Japan

4 Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

https://doi.org/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.

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