Mathematical Analysis of Fractional Order Co-Infection TB and HIV Model

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Muhammad Farman
Muhammad Usman
Aqeel Ahmad
M.O. Ahmad


A mathematical model of HIV/AIDS and TB including its co-infections is formulated. We find the Equilibrium points and with the help of numerical simulation, we have analyze that the sub-models of TB, HIV/AIDS and its co-infections. The Caputo and Caputo Febrizo fractional derivative operator of order α ∈ (0, 1] is employed to obtain the system of fractional differential equations. Laplace Adomian Decomposition Method was successfully used for solving the different differential equations.Laplace transform is a perfect technique in various field of biological science,engineering,pure and applied mathematics. The latest technique Laplace Adomian Decomposition Method is employed on the developed fractional order model for the numerical solutions. Finally numerical simulations are also established to investigate the influence of the system parameter on the spread of disease and which show effect of fractional parameter α on our obtained solutions.

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  1. N. T. J. Bailey, The mathematical approach to biology and medicine, John Wiley, New York, 1967.
  2. E. J. Williams, The development of biomathematical models. 36th session, International Statistical Institute, Sydney, 1967.
  3. H. F. von Helmholtz, On the sensations of tone as a physiological basis for the theory of music. (2nd ed.) Dover Publics, New York, 1954.
  4. S. Freud, Project on a Scientific Psychology, in The Standard Edition of the Complete Psychological Works of Sigmund Freud, Vol I, pp 283-346. Hogarth Press, London, 1966.
  5. N. Wiener, Cybernetics, (2nd ed.) MIT Press, Cambridge, 1961.
  6. R. Thom, Structural Stability and Morphogenesis, Westview Press; New Ed edition, 2001.
  7. G. Edelmann, Neural Darwinism: The Theory of Neuronal Group Selection, Basic Books, New York, 1987.
  8. R. Penrose, The Emperors New Mind: Concerning Computers, Minds, and the Laws of Physics, Amer. J. Phys. 58(1990), 1214.
  10. S. Suchindran, Is HIV infection a Risk Factor for Multi-Drug Resistant Tuberculosis? A Systematic Review, PLoS One, 4 (5) (2009), e5561.
  11. UNAIDS, Global Report: UNAIDS Report on the Global AIDS Epidemic 2013, World Health Organization, Geneva, Switzerland, 2013
  12. Implementing the WHO Stop TB Strategy: a handbook for national tuberculosis control programmes, Geneva, World Health Organization, 2008, p67.
  13. Global Tuberculosis Control 2017, WHO, Geneva, 2017.
  14. International Classification of Diseases (ICD), WHO, Geneva, 2010.
  15. A. Ahmad, M. Farman, F. Yasin, M. O. Ahmad, Dynamical transmission and effect of smoking in society, Int. J. Adv. Appl. Sci. 5 (2) (2018), 71-75.
  16. A. Ahmad, M. Farman, M.O. Ahmad, N. Raza, M. Abdullah, Dynamical behavior of SIR epidemic model with non-integer time fractional derivatives: A mathematical analysis, Int. J. Adv. Appl. Sci. 5 (1) (2018), 123-129.
  17. Farah Ashraf, Aqeel Ahmad, Muhammad Umer Saleem, Muhammad Farman, M. O. Ahmad, Dynamical behavior of HIV immunology model with non-integer time fractional derivatives, Int. J. Adv. Appl. Sci. 5(3) (2018), 39-45.