Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection
Tài liệu tham khảo
Christen, 2017, Modeling a SI epidemic with stochastic transmission: Hyperbolic incidence rate, J. Math. Biol., 6, 1
Fuhrman, 2004, Asymptotic behavior of an SI epidemic model with pulse removal, Math. Comput. Modelling, 40, 371, 10.1016/j.mcm.2003.10.047
Aguiar, 2008, Epidemiology of dengue fever: A model with temporary cross-immunity and possible secondary infection shows bifurcations and chaotic behaviour in wide parameter regions, Math. Model. Natural Phenon., 3, 48, 10.1051/mmnp:2008070
Jiao, 2016, Impulsive vaccination and dispersal on dynamics of an SIR epidemic model with restricting infected individuals boarding transports, Physica A, 449, 145, 10.1016/j.physa.2015.10.055
Witbooi, 2017, Stability of a stochastic model of an SIR epidemic with vaccination, Acta Biotheoret., 65, 151, 10.1007/s10441-017-9308-5
Chen, 2016, Global stability of an SEI model for plant diseases, Math. Slovaca, 66, 305, 10.1515/ms-2015-0137
Liu, 2016, Asymptotic behavior of a stochastic delayed SEIR epidemic model with nonlinear incidence, Physica A, 462, 870, 10.1016/j.physa.2016.06.095
Lin, 2015, Nontrivial periodic solution of a stochastic epidemic model with seasonal variation, Appl. Math. Lett., 45, 103, 10.1016/j.aml.2015.01.021
Augeraud-Véron, 2014, Seasonal dynamics in an SIR epidemic system, J. Math. Biol., 68, 701, 10.1007/s00285-013-0645-y
Zhang, 2013, Chaos analysis and control for a class of SIR epidemic model with seasonal fluctuation, Inter. J. Biomath., 6, 1250063, 10.1142/S1793524512500635
Sun, 2009, Effect of noise on the pattern formation in an epidemic model, Num. Meth. Part. Diff. Equations, 26, 1168, 10.1002/num.20483
Chen, 2016, Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise, Commun. Nonlinear Sci. Numer. Simul., 42, 379, 10.1016/j.cnsns.2016.06.012
Bashkirtseva, 2016, Noise-induced extinction in Bazykin-Berezovskaya population model, Eur. Phys. J. B, 89, 165, 10.1140/epjb/e2016-70345-6
Tsimring, 2001, Noise-induced dynamics in bistable systems with delay, Phys. Rev. Lett., 87, 250602, 10.1103/PhysRevLett.87.250602
Duncan, 2016, Noise-induced transitions in rugged energy landscapes, Phys. Rev. E, 94, 032107, 10.1103/PhysRevE.94.032107
I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, 1999.
Rida, 2012, Approximate analytical solution of the fractional epidemic model, Inter. J. Appl. Math. Res., 1, 17, 10.14419/ijamr.v1i1.20
Ameen, 2016, The solution of fractional order epidemic model by implicit Adams methods, Appl. Math. Model., 43, 78, 10.1016/j.apm.2016.10.054
Yi, 2012, Bifurcations analysis and tracking control of an epidemic model with nonlinear incidence rate, Appl. Math. Model., 36, 1678, 10.1016/j.apm.2011.09.020
Xiao, 2003, The dynamics of an eco-epidemic model with biological control, Ecol. Model., 168, 203, 10.1016/S0304-3800(03)00197-2
Chávez, 2017, An SIR-Dengue transmission model with seasonal effects and impulsive control, Math. Biosci., 289, 29, 10.1016/j.mbs.2017.04.005
Chen, 2014, Optimal vaccination and treatment of an epidemic network model, Phys. Lett. A, 378, 10.1016/j.physleta.2014.09.002
Zhang, 2016, The effect of state-dependent control for an SIRS epidemic model with varying total population, J. Appl. Math. Phys., 4, 1889, 10.4236/jamp.2016.410191
Giamberardino, 2017, Optimal control of SIR epidemic model with state dependent switching cost index, Biomed. Sig. Proc. Control, 31, 377, 10.1016/j.bspc.2016.09.011
Gueron, 1998, Controlling one-dimensional unimodal population maps by harvesting at a constant rate, Phys. Rev. E, 57, 3645, 10.1103/PhysRevE.57.3645
Liz, 2010, How to control chaotic behaviour and population size with proportional feedback, Phys. Lett. A, 374, 725, 10.1016/j.physleta.2009.11.063
Odibat, 2008, Generalized differential transform method: Application to differential equations of fractional order, Appl. Math. Comput., 197, 467, 10.1016/j.amc.2007.07.068
Chen, 2009, Measuring complexity using FuzzyEn, ApEn, and SampEn, Med. Eng. Phys., 31, 61, 10.1016/j.medengphy.2008.04.005
Costa, 2002, Multiscale entropy analysis of complex physiologic time series, Phys. Rev. Lett., 89, 705, 10.1103/PhysRevLett.89.068102
Wolf, 1985, Determining lyapunov exponents from a time series, Physica D, 16, 285, 10.1016/0167-2789(85)90011-9