Optimal control for a time delay multi-strain tuberculosis fractional model: a numerical approach
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[1] H. A. A. El-Saka,et al. The Fractional-order SIR and SIRS Epidemic Models with Variable Population Size , 2013 .
[2] Nasser Hassan Sweilam,et al. An efficient method for solving fractional Hodgkin–Huxley model , 2014 .
[3] Praveen Agarwal,et al. On the fractional differential equations with not instantaneous impulses , 2016 .
[4] A. M. Nagy,et al. Numerical solution of two-sided space-fractional wave equation using finite difference method , 2011, J. Comput. Appl. Math..
[5] P. Small,et al. Management of tuberculosis in the United States. , 2001, The New England journal of medicine.
[6] Nasser H. Sweilam,et al. Numerical study for multi-strain tuberculosis (TB) model of variable-order fractional derivatives , 2015, Journal of advanced research.
[7] Delfim F. M. Torres,et al. Multiobjective approach to optimal control for a tuberculosis model , 2014, Optim. Methods Softw..
[8] Liu Yang,et al. Solvability for fractional p-Laplacian differential equations with multipoint boundary conditions at resonance on infinite interval , 2017 .
[9] Richard Bellman,et al. Differential-Difference Equations , 1967 .
[10] Junesang Choi,et al. FRACTIONAL CALCULUS OPERATORS AND THEIR IMAGE FORMULAS , 2016 .
[11] Khalid Hattaf,et al. Optimal Control of a Delayed HIV Infection Model with ImmuneResponse Using an Efficient Numerical Method , 2012 .
[12] Edy Soewono,et al. An optimal control problem arising from a dengue disease transmission model. , 2013, Mathematical biosciences.
[13] Nasser Hassan Sweilam,et al. Nonstandard finite difference method for solving the multi-strain TB model , 2017 .
[14] Nasser Hassan Sweilam,et al. Comparative Study for Multi-Strain Tuberculosis (TB) Model of Fractional Order , 2016 .
[15] V. G. Pimenov,et al. Numerical methods for solving a hereditary equation of hyperbolic type , 2013 .
[16] Om P. Agrawal,et al. A Formulation and Numerical Scheme for Fractional Optimal Control Problems , 2008 .
[17] N Toft,et al. Comparing the epidemiological and economic effects of control strategies against classical swine fever in Denmark. , 2009, Preventive veterinary medicine.
[18] Michael C. Mackey,et al. Relaxation Oscillations in a Class of Delay Differential Equations , 2002, SIAM J. Appl. Math..
[19] R. D. Driver,et al. Ordinary and Delay Differential Equations , 1977 .
[20] Mohamed Adel,et al. ON THE STABILITY ANALYSIS OF WEIGHTED AVERAGE FINITE DIFFERENCE METHODS FOR FRACTIONAL WAVE EQUATION , 2012 .
[21] Fathalla A. Rihan,et al. Dynamics of Tumor-Immune System with Fractional-Order , 2016 .
[22] Praveen Agarwal,et al. New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations , 2015 .
[23] C. Sreeramareddy,et al. Time delays in diagnosis of pulmonary tuberculosis: a systematic review of literature , 2009, BMC infectious diseases.
[24] Ted Cohen,et al. Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness , 2004, Nature Medicine.
[25] K. Diethelm. AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER , 1997 .
[26] Nasser Hassan Sweilam,et al. Numerical Studies for Fractional-Order Logistic Differential Equation with Two Different Delays , 2012, J. Appl. Math..
[27] Khalid Hattaf,et al. Optimal Control of a Delayed SIRS Epidemic Model with Vaccination and Treatment , 2015, Acta biotheoretica.
[28] Fathalla A. Rihan,et al. Numerical modelling in biosciences using delay differential equations , 2000 .
[29] A. Bellen,et al. Numerical methods for delay differential equations , 2003 .
[30] Xia Huang,et al. A Numerical Method for Delayed Fractional-Order Differential Equations: Based on G-L Definition , 2013 .
[31] Abdelhadi Abta,et al. The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model , 2014 .
[32] C. Castillo-Chavez,et al. To treat or not to treat: the case of tuberculosis , 1997, Journal of mathematical biology.
[33] Linda J. S. Allen,et al. An introduction to mathematical biology , 2006 .
[34] R. Rakkiyappan,et al. Fractional-order delayed predator–prey systems with Holling type-II functional response , 2015 .
[35] Nasser H Sweilam,et al. Legendre spectral-collocation method for solving fractional optimal control of HIV infection of CD4+T cells mathematical model , 2017 .
[36] I. Podlubny. Fractional differential equations , 1998 .
[37] J. Watmough,et al. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.
[38] Dumitru Baleanu,et al. On Analytical Solutions of the Fractional Differential Equation with Uncertainty: Application to the Basset Problem , 2015, Entropy.
[39] J. Hale. Theory of Functional Differential Equations , 1977 .
[40] Benito M. Chen-Charpentier,et al. Construction of nonstandard finite difference schemes for the SI and SIR epidemic models of fractional order , 2016, Math. Comput. Simul..
[41] Delfim F. M. Torres,et al. Optimal control of a tuberculosis model with state and control delays. , 2016, Mathematical biosciences and engineering : MBE.
[42] Nasser Hassan Sweilam,et al. On the optimal control for fractional multi‐strain TB model , 2016 .
[43] Y. Kuang. Delay Differential Equations: With Applications in Population Dynamics , 2012 .
[44] K. Toman,et al. Tuberculosis case-finding and chemotherapy: Questions and answers , 1979 .
[45] Robin M. Warren,et al. A Threshold Value for the Time Delay to TB Diagnosis , 2007, PloS one.
[46] Patrick W Nelson,et al. Mathematical analysis of delay differential equation models of HIV-1 infection. , 2002, Mathematical biosciences.
[47] Julien Arino,et al. A model for the spread of tuberculosis with drug-sensitive and emerging multidrug-resistant and extensively drug resistant strains , 2015 .
[48] Hal L. Smith,et al. An introduction to delay differential equations with applications to the life sciences / Hal Smith , 2010 .