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

Iqbal, Zafar; Ahmed, Nauman; Băleanu, Dumitru; Adel, Waleed; Rafiq, Muhammad; Rehman, M. A.; Alshomrani, Ali Saleh

doi:10.1016/j.chaos.2020.109706

Cited by 54 publications

(22 citation statements)

References 16 publications

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“…Researchers have focused their attention on studying models of infectious disease like HIV, AIDS, etc under fractional order derivatives and integrals. For more detail we refer [40] , [41] , [42] , [43] , [44] . Some authors have also extended the area to classical and arbitrary order mathematical models of real world problems in physical sciences, see, for instance, [45] , [46] .…”

Section: Discussionmentioning

confidence: 99%

Mathematical analysis of COVID-19 via new mathematical model

Abdullah

Ahmad

Owyed

et al. 2021

Chaos, Solitons & Fractals

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We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, the healthy (resistive) class, the infected class, and the quarantine class, . We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.

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Section: Discussionmentioning

confidence: 99%

Mathematical analysis of COVID-19 via new mathematical model

Abdullah

Ahmad

Owyed

et al. 2021

Chaos, Solitons & Fractals

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“…In this section, we construct a novel numerical method called GL-NWAFDM as an extension to the method given in [ 24 , 28 ]. This method can be an explicit method (easy for coding) or an implicit method (more stable and efficient), depending on the weight factor .…”

Section: Numerical Methods For Solving Focpsmentioning

confidence: 99%

On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

et al. 2020

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In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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“…Having being inspired from plethora of research works carried out in fractional mathematical epidemiology (see, for example [28,29,30,31,32,33,34,35] and most of the references cited therein),…”

Section: Formulation Of Caputo Sir Modelmentioning

confidence: 99%

Caputo SIR Model for COVID-19 under Optimized Fractional Order

Ullah

Băleanu

2020

Preprint

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Everyone is talking about coronavirus from last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed and as many as 180 countries are so far affected with 928,287 (14 September, 2020) deaths within couple of months. Ironically, 29,185,779 are still active cases. Having seen such drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. Major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 01 April to 15 March, 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam-Hyers and its generalized version. Best parameters have been obtained via nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than classical version of the SIR model [4]. Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case (ν = 1). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

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

Cited by 54 publications

References 16 publications

Mathematical analysis of COVID-19 via new mathematical model

Mathematical analysis of COVID-19 via new mathematical model

On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

Caputo SIR Model for COVID-19 under Optimized Fractional Order

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