Applied Mathematics & Information Sciences

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In this paper, we introduce the multi−strain TB model of fractional-order derivatives, which incorporates three strains: drug−sensitive, emerging multi−drug resistant(MDR) and extensively drug−resistant(XDR ). Numerical simulations for this extended fractional order model is the main aim of this work, where the adopted model is described by a system of non-linear ordinary differential equations and the fractional derivative is defined in the sense of the Grünwald−Letnikov definition. Two numerical methods are presented for this model, the standard finite difference method (SFDM) and the nonstandard finite difference method (NSFDM). Numerical comparisons between SFDM and NSFDM are presented. It is concluded that the proposed NSFDM preserves the positivity of the solutions, and it is numerically stable in large regions than SFDM.

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