Real life application of Caputo fractional derivative for measles epidemiological autonomous dynamical system

Sheikh, 2011, Measles susceptibility in children in Karachi, Pakistan, Vaccine, 29, 3419, 10.1016/j.vaccine.2011.02.087 Yanagi, 2006, Measles virus: cellular receptors, tropism and pathogenesis, J Gen Virol, 87, 2767, 10.1099/vir.0.82221-0 Coughlin, 2017, Perspective on global measles epidemiology and control and the role of novel vaccination strategies, Viruses, 9, 11, 10.3390/v9010011 Griffin, 2016, The immune response in measles: virus control, clearance and protective immunity, Viruses, 8, 282, 10.3390/v8100282 Gay, 1995, Interpretation of serological surveillance data for measles using mathematical models: implications for vaccine strategy, Epidemiol Infect, 115, 139, 10.1017/S0950268800058209 Agur, 1993, Pulse mass measles vaccination across age cohorts, Proc Natl Acad Sci, 90, 11698, 10.1073/pnas.90.24.11698 Schenzle, 1984, An age-structured model of pre-and post-vaccination measles transmission, Math Med Biol, 1, 169, 10.1093/imammb/1.2.169 Roberts, 2000, Predicting and preventing measles epidemics in New Zealand: application of a mathematical model, Epidemiol Infect, 124, 279, 10.1017/S0950268899003556 Edward, 2015, A mathematical model for control and elimination of the transmission dynamics of measles, Appl Comput Math, 4, 396, 10.11648/j.acm.20150406.12 Aldila, 2019, A deterministic model of measles with imperfect vaccination and quarantine intervention, J Phys, 1218, 12044 Okyere-Siabouh, 2013, Mathematical system for the study of measles in cape coast metropolis, Int J Modern Biol Med, 4, 110 Adewale, 2014, Mathematical analysis of effect of area on the dynamical spread of measles, IOSR J Eng, 4, 43, 10.9790/3021-04324357 Fred, 2014, Mathematical modeling on the control of measles by vaccination: case study of KISII county, kenya, SIJ Trans Comput Sci Eng Appl, 2, 61 Peter, 2018, Mathematical system for the control of measles, J Appl Sci Environ Manage, 22, 571 Ashraf, 2019, Nonstandard finite difference scheme for control of measles epidemiology, Int J Adv ApplSci, 6, 79, 10.21833/ijaas.2019.03.012 Atangana, 2016, Modelling the spread of river blindness disease via the Caputo fractional derivative and the beta-derivative, Entropy, 18, 40, 10.3390/e18020040 Qureshi, 2019, Mathematical modeling for the impacts of deforestation on wildlife species using Caputo differential operator, Chaos Soliton Fract, 126, 32, 10.1016/j.chaos.2019.05.037 Atangana, 2016, Modeling the spread of rubella disease using the concept of with local derivative with fractional parameter: beta derivative, Complexity, 21, 442, 10.1002/cplx.21704 Qureshi, 2019, Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data, Physica A, 122496, 10.1016/j.physa.2019.122496 Atangana, 2015, Application of fractional calculus to epidemiology, 174 Arqub, 2013, Solution of the fractional epidemic system by homotopy analysis method, J King Saud Univ, 25, 73, 10.1016/j.jksus.2012.01.003 Qureshi, 2019, Mathematical analysis of dengue fever outbreak by novel fractional operators with field data, Physica A, 526, 121127, 10.1016/j.physa.2019.121127 Ullah, 2019, A fractional order HBV model with hospitalization, Discret Cont Dyn Syst, 957 Qureshi, 2019, Modeling chickenpox disease with fractional derivatives: from Caputo to Atangana-Baleanu, Chaos Soliton Fract, 122, 111, 10.1016/j.chaos.2019.03.020 Ullah, 2018, A fractional system for the dynamics of TB virus, Chaos Soliton Fract, 116, 63, 10.1016/j.chaos.2018.09.001 Qureshi, 2019, Fractional derivatives applied to MSEIR problems: comparative study with real world data, Eur Phys J Plus, 134, 171, 10.1140/epjp/i2019-12661-7 Khan, 2019, The dynamics of zika virus with Caputo fractional derivative, AIMS Math, 4, 134, 10.3934/Math.2019.1.134 Qureshi, 2019, Transmission dynamics of varicella zoster virus modeled by classical and novel fractional operators using real statistical data, Physica A, 534, 122149, 10.1016/j.physa.2019.122149 Qureshi, 2020, Effects of vaccination on measles dynamics under fractional conformable derivative with Liouville Caputo operator, Eur Phys J Plus, 135, 63, 10.1140/epjp/s13360-020-00133-0 Diethelm, 2013, A fractional calculus based model for the simulation of an outbreak of dengue fever, Nonlinear Dyn, 71, 613, 10.1007/s11071-012-0475-2 Almeida, 2019, A fractional measles model having monotonic real statistical data for constant transmission rate of the disease, Fract Fract, 3, 53, 10.3390/fractalfract3040053 Berhe, 2019, Deterministic modeling of dysentery diarrhea epidemic under fractional Caputo differential operator via real statistical analysis, Chaos Soliton Fract, 109536 Abro, 2019, A comparison of heat and mass transfer on a waltersb fluid via Caputo-Fabrizio versus Atangana-Baleanu fractional derivatives using the fox-h function, Eur Phys J Plus, 134, 101, 10.1140/epjp/i2019-12507-4 Gmez-Aguilar, 2019, Chaos in a calcium oscillation system via Atangana-Baleanu operator with strong memory, Eur Phys J Plus, 134, 140, 10.1140/epjp/i2019-12550-1 Bas, 2019, Fractional systems with singular and non-singular kernels for energy efficient buildings, Chaos, 29, 23110, 10.1063/1.5082390 Arqub, 2019, Application of reproducing kernel algorithm for solving Dirichlet time-fractional diffusion-Gordon types equations in porous media, J Porous Media, 22, 10.1615/JPorMedia.2019028970 Abu Arqub, 2018, Solutions of time fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space, Numer Methods Partial Differ Equ, 34, 1759, 10.1002/num.22236 Qureshi, 2019, Using Shehu integral transform to solve fractional order Caputo type initial value problems, J Appl Math Comput Mech, 18, 75, 10.17512/jamcm.2019.2.07 Qureshi, 2019, On the use of aboodh transform for solving non-integer order dynamical systems, Sindh Univ Res J, 51, 53, 10.26692/sujo/2019.01.10 Abu Arqub, 2019, Application of residual power series method for the solution of time-fractional Schrödinger equations in one-dimensional space, Fundam Inform, 166, 87, 10.3233/FI-2019-1795 Podlubny, 1998 Wang, 2017, Edge-based SEIR dynamics with or without infectious force in latent period on random networks, Commun Nonlinear Sci Numer Simul, 45, 35, 10.1016/j.cnsns.2016.09.014 Wang, 2012, Global analysis of an SIS model with an infective vector on complex networks, Nonlinear Anal Real World Appl, 13, 543, 10.1016/j.nonrwa.2011.07.033 Wang, 2019, Global behavior of a two-stage contact process on complex networks, J Franklin Inst, 356, 3571, 10.1016/j.jfranklin.2019.02.020 IndexMundi. https://www.indexmundi.com/pakistan/demographics_profile.html Accessed: 2019-09-01. Huang, 2018, Seasonal transmission dynamics of measles in China, Theory Biosci, 137, 185, 10.1007/s12064-018-0271-8 Kim, 2004, Fixed points of condensing multivalued maps in topological vector spaces, Fixed Point Theory Appl, 385170, 10.1155/S1687182004310041 De la Sen, 2010, On a generalized time-varying SEIR epidemic model with mixed point and distributed time-varying delays and combined regular and impulsive vaccination controls, Adv Differ Eqn, 281612, 10.1186/1687-1847-2010-281612 De La Sen, 2011, On the existence of equilibrium points, boundedness, oscillating behavior and positivity of a SVEIRS epidemic model under constant and impulsive vaccination, Adv Differ Eqn, 2011, 748608 Sadovskii, 1967, A fixed-point principle, Funct Anal Appl, 1, 151, 10.1007/BF01076087 Diethelm, 2002, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn, 29, 3, 10.1023/A:1016592219341 Qureshi, 2018, L-stable explicit nonlinear method with constant and variable step-size formulation for solving initial value problems, Int J Nonlinear SciNumer Simul, 19, 741, 10.1515/ijnsns-2017-0267 Qureshi, 2018, Convergence of a numerical technique via interpolating function to approximate physical dynamical systems, J Adv Phys, 7, 446, 10.1166/jap.2018.1448 Aliya, 2018, Development of a nonlinear hybrid numerical method, Adv Differ Eqn Control Process, 19, 275, 10.17654/DE019030275 Li, 2015