Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission

Zafar Iqbal, Nauman Ahmed, Dumitru Baleanu, Waleed Adel, Muhammad Rafiq, Muhammad Aziz-ur Rehman and Ali Saleh Alshomrani

Chaos, Solitons & Fractals, 2020, vol. 134, issue C

Abstract: In this article, an integer order nonlinear HIV/AIDS infection model is extended to the non-integer nonlinear model. The Grunwald Letnikov nonstandard finite difference scheme is designed to obtain the numerical solutions. Structure preservence is one of the main advantages of this scheme. Reproductive number R0 is worked out and its key role in disease dynamics and stability of the system is investigated with the following facts, if R0 < 1 the disease will be diminished and it will persist in the community for R0 > 1. On the other hand, it is sought out that system is stable when R0 < 1 and R0 > 1 implicates that system is locally asymptotically stable. Positivity and boundedness of the scheme is also proved for the generalized system. Two steady states of the system are computed and verified by computer simulations with the help of some suitable test problem.

Keywords: HIV/AIDS disease transmission; Structure preserving algorithm; Fractional order epidemic model; Simulations (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:134:y:2020:i:c:s0960077920301089

DOI: 10.1016/j.chaos.2020.109706

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